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ECONOMICS – A TO Z GOUTAM BUCHHA

PGPSE PARTICIPANT2009

AFTERSCHO☺OL (www.afterschoool.tk) – DEVELOPING CHANGE MAKERS

CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME –

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http://www.afterschoool.tk/


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INTRODUCTION

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Ten Principles of Economics


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Economy. . .

. . . The word economy comes from a Greek word for “one who manages a household.”


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TEN PRINCIPLES OF ECONOMICS

• A household and an economy face many decisions: – Who will work?– What goods and how many of them should be

produced?– What resources should be used in

production?– At what price should the goods be sold?


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Society and Scarce Resources: – The management of society’s resources is

important because resources are scarce.– Scarcity. . . means that society has limited

resources and therefore cannot produce all the goods and services people wish to have.


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Economics is the study of how society manages its scarce resources.


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• How people make decisions.– People face tradeoffs.– The cost of something is what you give up to

get it.– Rational people think at the margin.– People respond to incentives.


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• How people interact with each other.– Trade can make everyone better off.– Markets are usually a good way to organize

economic activity.– Governments can sometimes improve

economic outcomes.


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• The forces and trends that affect how the economy as a whole works. – The standard of living depends on a country’s

production.– Prices rise when the government prints too

much money.– Society faces a short-run tradeoff between

inflation and unemployment.


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Principle #1: People Face Tradeoffs.

“There is no such thing as a free lunch!”


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Making decisions requires trading off one goal against another.

Principle #1: People Face Tradeoffs.

To get one thing, we usually have to give up another thing.

– Guns v. butter– Food v. clothing– Leisure time v. work– Efficiency v. equity


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Principle #1: People Face Tradeoffs

• Efficiency v. Equity– Efficiency means society gets the most that it

can from its scarce resources.– Equity means the benefits of those resources

are distributed fairly among the members of society.


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Principle #2: The Cost of Something Is What You Give Up to Get It.

• Decisions require comparing costs and benefits of alternatives.– Whether to go to college or to work?– Whether to study or go out on a date?– Whether to go to class or sleep in?

• The opportunity cost of an item is what you give up to obtain that item.


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Principle #2: The Cost of Something Is What You Give Up to Get It.

LA Laker basketball star Kobe Bryant chose to skip college and go straight from high school to the pros where he has earned millions of dollars.


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People make decisions by comparing costs and benefits at the margin.

Principle #3: Rational People Think at the Margin.

• Marginal changes are small, incremental adjustments to an existing plan of action.


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Principle #4: People Respond to Incentives.

• Marginal changes in costs or benefits motivate people to respond.

• The decision to choose one alternative over another occurs when that alternative’s marginal benefits exceed its marginal costs!


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Principle #5: Trade Can Make Everyone Better Off.

• People gain from their ability to trade with one another.

• Competition results in gains from trading.

• Trade allows people to specialize in what they do best.


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Principle #6: Markets Are Usually a Good Way to Organize Economic Activity.• A market economy is an economy that

allocates resources through the decentralized decisions of many firms and households as they interact in markets for goods and services.– Households decide what to buy and who to

work for.– Firms decide who to hire and what to produce.


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Principle #6: Markets Are Usually a Good Way to Organize Economic Activity.• Adam Smith made the observation that

households and firms interacting in markets act as if guided by an “invisible hand.”– Because households and firms look at prices

when deciding what to buy and sell, they unknowingly take into account the social costs of their actions.

– As a result, prices guide decision makers to reach outcomes that tend to maximize the welfare of society as a whole.


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Principle #7: Governments Can Sometimes Improve Market Outcomes.• Market failure occurs when the market fails

to allocate resources efficiently.

• When the market fails (breaks down) government can intervene to promote efficiency and equity.


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Principle #7: Governments Can Sometimes Improve Market Outcomes.

• Market failure may be caused by – an externality, which is the impact of one

person or firm’s actions on the well-being of a bystander.

– market power, which is the ability of a single person or firm to unduly influence market prices.


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Principle #8: The Standard of Living Depends on a Country’s Production.

• Standard of living may be measured in different ways:– By comparing personal incomes.– By comparing the total market value of a

nation’s production.


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• Almost all variations in living standards are explained by differences in countries’ productivities.

• Productivity is the amount of goods and services produced from each hour of a worker’s time.


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• Standard of living may be measured in different ways:– By comparing personal incomes.– By comparing the total market value of a

nation’s production.


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Principle #9: Prices Rise When the Government Prints Too Much Money.

• Inflation is an increase in the overall level of prices in the economy.

• One cause of inflation is the growth in the quantity of money.

• When the government creates large quantities of money, the value of the money falls.


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Principle #10: Society Faces a Short-run Tradeoff Between Inflation and Unemployment.• The Phillips Curve illustrates the tradeoff

between inflation and unemployment:

Inflation Unemployment

It’s a short-run tradeoff!


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Summary

• When individuals make decisions, they face tradeoffs among alternative goals.

• The cost of any action is measured in terms of foregone opportunities.

• Rational people make decisions by comparing marginal costs and marginal benefits.

• People change their behavior in response to the incentives they face.


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Summary

• Trade can be mutually beneficial.

• Markets are usually a good way of coordinating trade among people.

• Government can potentially improve market outcomes if there is some market failure or if the market outcome is inequitable.


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Summary

• Productivity is the ultimate source of living standards.

• Money growth is the ultimate source of inflation.

• Society faces a short-run tradeoff between inflation and unemployment.


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On July 29, 2006 I was reading the Omaha World Herald. On this Saturday morning my eye caught the car ads section. On the front page of that section is a question and answer section by “Click & Clack.” I do not remember their real names. They also host (used to, anyway, and maybe they still do) a PBS radio show about cars. I rarely read this section, but I did this day.

The first question had to do with going on a long trip in a car. The question was about washing and waxing the car before the trip and then washing the car along the way. The person asking the question felt the washing would help save on gas and so the questioner wanted information from the experts.

The experts said that yes there is some benefit to the washing, but so little benefit that the cost of the washing and waxing would be larger than the benefits obtained. So, from a dollars and cents point of view the washing did not pay off.


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I was all excited about reading the story because I thought it made sense and maybe I could use the story in my classes – so here we are. I would like to repackage the story to make a more general point. I will make a little diagram to aid in my story.

Policy or action or proposal

Benefits

Costs


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The policy in the example is

Wash car before, and while on, long car trips.

The benefit(s):

Better gas mileage and thus a cost saving.

The cost(s):

The cost of the car wash.

Economics is a science that when looking at policies the focal point is on the benefits and costs of the policy.

In our personal lives, when a policy has benefits that clearly outweigh the costs, many people engage in what the policy recommends.

Examples: Brushing your teeth everyday, washing your hands after using the restroom, and the list goes on and on.


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We have government in our world. Policies are recommended in this arena. Every policy that gets mentioned has benefits. But every policy also has costs. Please remember this.

Is the following good social policy from an economic point of view? Every person in northeast Nebraska should give Chuck Parker $1 each time they drive by Dairy Queen .

Hey, businesses have policies too. Most organizations have policies. The economic approach to viewing the world is looking at the benefits and costs of the policy.

It seems that a lot of restaurants have a policy that if you buy a pop you can get free refills. Is this a good business policy? The benefits are…………………….

The costs are…………………..


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Well, here is my little story triggered by my reading the “Click & Clack” article.

Should I make it a policy as a professor at WSC to bring in current events and other items I find in the paper?


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Overview

In consumer theory we started with the x and y axes both referring to a good or service, with each axis representing a different specific good. Sometimes, though, we only want to focus on one good against everything else we could buy.

If we think of the Y good as a composite commodity then we can say the price of the good is $1 per unit and the commodity is really then how much we spend on all goods except good x.

The budget line and indifference curves we saw before are essentially the same as we saw before.


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Budget line

Y

X

Before we said the budget line was PxX + PyY = I, with vertical intercept = I/Py, horizontal intercept = I/Px and slope –Px/Py.

In the context of the composite commodity we have PxX + Y = I, with vertical intercept = I (our income amount), horizontal intercept = I/Px still and slope = -Px

I

I/Px


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Utility max

X

Y

X1

I – PxX1

With the composite good our utility max story is the same as before except when we see point X1 the Y point is the amount of income we have left after buying X1 units of X.

The point of the composite commodity idea is we can focus on the x good and everything else in a lumped up amount.

Consumer SurplusWhen consumers buy products in the market they may pay less than the full amount they are willing to

pay – they receive consumer surplus.


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Do you want to buy some eggs?

Who here would buy a dozen eggs for $1.59?

Who would pay $1.29?

Say the actual price of the dozen is $0.89. Do you think the buyers would pay the $1.29 to the grocer when the grocer has a sign out that says $0.89?

So if consumers are willing to pay, in this example, more than $0.89, then they receive an extra benefit in the market called consumer surplus.


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consumer surplusConsumer surplus is an idea people I know have a hard time accepting. Consumer surplus equals the maximum amount you are willing to pay for an item minus what you have to pay. It seems the hard part is distinguishing between what you have to pay and what you would be willing to pay.

The amount you would be willing to pay is on the demand curve for each unit of the product. In fact the law of demand is an expression that you are not willing to pay as much for additional units as you did for previous units. The amount you have to pay is market determined.


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Willing to payP

21

18

1512

1 2 3 4

24a

b c

d e f

g h i j

k l m n

When the price is 24, 0 units are demanded. At P=21, 1 unit is demanded. 21 is the maximum price this person would pay for the first unit. Let’s say the market price is 10. Then the surplus on the first unit is 11. The surplus on the2nd....................…,3rd....................... units is?

Q


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willing to payYou will notice on the previous screen at price 21, the quantity demanded is 1. The area b + d + g + k equals the $21 the consumer would pay for the 1st unit. The area a is under the demand curve but not part of what the consumer would be willing to pay for the first unit. We will add in area a to calculate the consumer surplus. It makes the calculation easier. The second unit would be demanded if the price is 18. The area e + h + i = $18. The area c is under the demand curve but not part of what the consumer would be willing to pay for the second unit.


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willing to pay

The point I am getting to on the previous screen is if we add in areas like a and c, that are really not a part of what consumers are willing to pay, we have an easier calculation to find out what consumers are willing to pay for a certain number of units. It is simply the area under the demand curve out to a quantity.

P

QQ1

What consumers are willing to pay for the Q1 units


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Consumer surplus againP

25

10

300 Q

A

B

Area A = .5(300)(25-10) =2250

Area B = 10(300) = 3000

Note consumers would be willing to pay 3000 + 2250for 300 units.But the consumers only have to pay 3000 for the

300 units.So the consumer surplus is area A and equals 2250.

Say with S & D we get the P = 10 and Q = 300.


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Refresher on areas

The area of a triangle is ½ of the base times the height.

The area of a rectangle, of which the square is a special case, is the base times the height.

We use these ideas from time to time because they assist in the development of economic ideas.


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consumer surplus again

What do consumers do with the surplus received?

They may spend it on more units of the item in question, they may spend it on other items, or they may save it for a rainy day.

The point here is that the surplus is useful to the consumer!

Market Demand from Individual Demand


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In this section we want to think about market demand as the result of adding up demands from many individuals. Remember individual demand is the result of each consumer going about utility maximization.

Let’s do an example with 3 people. qi is the demand from the ith consumer. Say,

q1 = 10 - p, q2 = 15 - 2p, and q3 = 18-3p. Often the demand is written in inverse form (where we isolate the p term). We have

p = 10 - q1, p = 15/2 - (1/2)q2, and p = 18/3 - (1/3)q3

We usually express demand in inverse form when we want to graph the demands in the P, Q graph. I have a graph on the next screen with each demand in it.


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P

Q

10

7.5

6

10 15 18

Note at a price above 10 no one demands any units. At a price above 7.5 only person 1 demands units. At a price above 6 only person 1 and person 2 demand units. If price is below 6 all three people demand units.

The dashed line here is the market demand. It is found by looking at each price and adding the quantities each person would demand.


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To get the market demand we horizontally add the demand from each person. This amounts to saying q1 + q2 + q3 = Q.

We saw before the demand from each person was

q1 = 10 - p, q2 = 15 - 2p, and q3 = 18-3p. To get the market demand we add

q1 + q2 + q3 to get (10 - p) + (15 - 2p) + (18 -3p) = (10 + 15 + 18) - (p + 2p + 3P), or

Q = 43 - 6P, but this is only true when price is less than or equal to 6. In other words all three people demand units when the price is less than 6.

Note if P = 1 q1 = 9, q2 = 13, q3 = 15 and Q = 37, or

if P = 2 q1 = 8, q2 = 11, q3 = 12 and Q = 31.


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PRemember if the price is above 6 but less than or equal to 7.5 the demand comes from only the first two people and the demand curve isq1 + q2 = Q = 25 - 39, andif the price is above 7.5 the demand is only from the first person and the demand curve isq1 = Q = 10 - p.

So the market demand curve we have come to know and work with is really the addition of the demand from many people as they have gone about maximizing their utility.

Q

Price elasticity of demandOften in economics we look at how the value of one variable

changes when another variable changes. The concept called

elasticity is a summary statement about those changes.


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Elasticity The law of demand or the law of supply is a statement about the direction of change of the quantity demanded, or supplied, respectively, when there is a price change.

The concept of elasticity adds to these concepts by indicating the magnitude of the change in quantity, given the price change. The magnitude of the change is reported in percentage terms.


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own price elasticity of demand

Ed = (% change in Q)/(% change in P)

As an example, if Ed = -2 we say for every 1 % change in the price of the good the quantity demand changed in the opposite direction by 2 %.


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absolute value

You may recall a function in math called the absolute value. Basically this function makes negative values positive and leaves positive values positive.

In the notes I will write abs( ) to mean take the absolute value.

The own price elasticity of demand is a negative number, so we will take the absolute value to describe some concepts about it.


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Elasticity can have three basic values

If abs(Ed) > 1 we say demand is elastic. This means the % change in the Qd is greater than the % change in price.

If abs(Ed) = 1 we say demand is unit elastic. This means the % change in the Qd is equal to the % change in price.

If abs(Ed) < 1 we say demand is inelastic. This means the % change in the Qd is less than the % change in price.


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Elasticity again

P

Q

P1P2

Q1 Q2

In the upper left of the demand curve the % change in the Qd is greater than the % change in the P and thus the Ed > 1 .

Without a real formal proof of the above statement, we can see the % change in Qd is about 100 % and the % change in P is less than 100 %. Demand is elastic here.


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Elasticity has several ranges of values

P

Q

P1P2 Q1

Q2

In the lower right of the demand curve the % change in the Qd is less than the % change in the P and thus the Ed < 1.

Without a real formal proof of the above statement, we can see the % change in Qd is less than 100 % and the % change in P is about 100 %. Demand is inelastic here.


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Elasticity has several ranges of values

P

Q

P1P2

Q1 Q2

In the middle of the demand curve the % change in the Qd is equal to the % change in the P and thus the Ed = 1.

Without a real formal proof of the above statement, we can see the % change in Qd is about equal to the % change in P. Demand is unit elastic here.


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Calculation point slope method

P

11

10 Q

If we know the slope of the demand curve the elasticity at a point is found by using the Q and P value of the point and the slope in the following way:

(P/Q)(1/slope).

Example say the slope here is -1. The elasticity is (11/10)(1/-1) = -1.1

When we take absolute value we get 1.1. Elastic in this case.

Own price elasticity and total revenue changes

Total revenue (TR) is price times quantity. Along the demand curve P and Q move in opposite directions. Knowledge of Ed assists in knowing

how TR will change.


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Elasticity and total revenue relationship

When we look at the collection of consumers in the market, at this time in our study we assume each consumer pays the same price per unit for the product.

Also at this time in our study the total expenditure of the consumers in the market would equal the total revenue (TR) to the sellers.

So, here we look at the whole demand side of the market in general.


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P

Q

P1

Q1

TR in the market is equal to the price in the market multiplied by the quantity traded in the market. In this diagram TR equals the area of the rectangle made by P1, Q1 and

the horizontal and vertical axes. We know from math that the area of a rectangle is base times height and thus here that means P times Q.


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We will want to look at the change in values of a variable and in order to do so we want to have a consistent measure of change. In this regard let’s say the change in a variable is

the later value minus the earlier value.

Thus if the price should change from P1 to P2, then the change in price is

P2 - P1, or similarly if the TR should change the change in TR is

TR2 - TR1.


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P

Q

P1P2

Q1 Q2

Now in this graph when the price is P1 the TR = a + b(adding areas) and if the price is P2 the TR = b + c.

The change in TR if the price should fallfrom P1 to P2 is (b + c) - (a + b) = c - a.

Similarly, if the price should rise from P2 to P1 the change in TR is a - c. I will focus on price declines next.

a

b c


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P

Q

P1P2

Q1 Q2

Since the change in TR is c - a, the value of the change will depend on whether c is bigger or smaller, or even equal to, a. In this diagram we see c > a and thus the change in TR > 0.

This means that as the price falls, TR rises. I think you will recall that in the upper left of the demand the demand is price elastic. Thus if the price falls in the elastic range of demand TR rises.

a

b c


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Elasticity and TR

You will note on the previous screen that I had c - a. In the graph c is indicating the change in TR because we are selling more units. The area a is indicating the change in TR when there is a price change. We have to bring the two together to get the change in TR.

Thus a lower price has a good and a bad.Good - sell more units.Bad - sell at lower price.


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P

Q

P1P2 Q1

Q2

Now in this graph when the price is P1 the TR = a + b(adding areas) and if the price is P2 the TR = b + c.In this diagram we see c < a and thus the change in TR < 0.

I think you will recall that in the lower right of the demand the demand is price inelastic. Thus if the price falls in the inelastic range of demand TR falls.

ab

c


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P

Q

P1P2

Q1 Q2

Now in this graph when the price is P1 the TR = a + b(adding areas) and if the price is P2 the TR = b + c.In this diagram we see c = a and thus the change in TR = 0.

I think you will recall that in the middle of the demand the demand is unit elastic. Thus if the price falls in the unit elastic range of demand TR does not change.

a

b c


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Elasticity and TRP

Q

TR

Q

D

When the price falls the quantity demanded always rises. As the quantity demanded rises (because of the price change) the TR is first rising in the elastic range, levels off when demand is unit elastic and TR falls in the inelastic range.


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Marginal revenueMarginal revenue is defined as the change in total revenue as the number of units cold changes. In the demand graph we have seen that in order to sell more the price has to be lowered. So, there is a relationship between elasticity and marginal revenue.

If price falls and demand is elastic we know TR rises so MR is positive.

If Price falls and demand is inelastic we know TR falls and so MR is negative.

If price fall and demand is unit elastic we know TR does not change.

Other demand elasticities

There are other elasticities besides the own price elasticity of

demand. Let’s see a few here.


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demand shifters

We saw that things like taste and preference, price of other goods, income and the number of buyers shift the demand curve if they change. How much do they shift the demand curve?

We use other elasticity concepts as an indication of how much the curve will shift given a change in one of these factors.


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cross price elasticity of demand

Edxy = % change in Qdx / % change in Py.

The bigger the value the more the demand shifts.

If the value is negative we have complements and if positive we have substitutes.

If the absolute value is between 0 and 1 the cross elasticity is inelastic, if = 1 unit elastic and if greater than 1 elastic.


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income elasticity of demand

Edxm = % change in Qdx / % change in M.


If the value is negative we have an inferior good and if positive we have a normal good.

If the absolute value is between 0 and 1 the income elasticity is inelastic, if = 1, unit elastic, and if greater than 1, elastic.


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Elasticity of supply

The elasticity of supply is used to indicate the percentage change in the quantity supplied given a percentage change in price.

The elasticity of supply is calculated in a manner similar to the other elasticities we have seen and has a similar interpretation in terms of the range of values the elasticity might take, i.e. elastic, inelastic and unit elastic.


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Decisions under uncertainty

A Different look at Utility Theory


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Overview

The author says that economic decisions made under uncertainty are essentially gambles. Let’s first look at some gambles, and then come back to decisions under uncertainty.

Initially, our gamble will be to flip a fair coin (one where the probability of a head is .5 and the probability of a tail is .5). The payout will depend on which side of the coin is showing when the coin lands at rest.


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Facts about several gambles with a fair coin:

Gamble 1 – heads means you win $100 and tails means you lose $0.50

Gamble 2 – heads means you win $200 and tails means you lose $100

Gamble 3 – heads means you win $20000 and tails means you lose $10000

Note what a person would lose on each gamble. Many people would say the loses in gambles 2 and 3 make them uneasy and they wouldn’t take those gambles. But, some folks out there might take gambles 2 and 3.

Examples


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Digress – the mean

What is the mean or the average of the numbers 4 and 6? You probably said 5 and you are right. This could be written

(4+6)/2 = (4/2) + (6/2) = (1/2)4 + (1/2)6, where

in this last form you see each number multiplied by ½. In this context the mean is said to be a simple weighted average, with each value weighted by ½. What would the weights be if we wanted the average of 4, 5, and 6? 1/3! In general with n numbers the weight is 1/n.

In other situations we may look at a weighted average (not simple), though the weights are found in a different way.


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Back to example

The expected value of a gamble is a weighted average of the possible payout values and the weights are the probabilities of occurrence of each payout. We talk about EVi as the expected value of gamble i.

EV1 = .5(100) + .5(-0.50) = 50 – 0.25 = 49.75. (Notice when you lose the loss is subtracted out.)

EV2 = .5(200) + .5(-100) = 100 – 50 = 50

EV3 = .5(20000) + .5(-10000) = 10000 – 5000 = 5000


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Example

In our example the EV for each gamble is positive. The EV is the highest for gamble 3. But, remember we said not many folks would probably like it because of the uneasiness they would feel by losing the 10000.

A couple of guys named Von Neumann (both names are just the person’s last name) and Morgenstern created a model we now call the expected utility model to deal with situations like this. They indicated folks make decisions based not on monetary values, but based on utility values. Of course the utility values are based on the monetary values, but the utility values also depend on how people view the world.


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Expected Utility

Say we observe a person always buying chocolate ice cream over vanilla ice cream when both are available and both cost basically the same, or even when chocolate is more expensive and always when chocolate is the same price or cheaper. So by observing what people do we can get a feel for what is preferred over other options. When we assign utility numbers to options the only real rule we follow is that higher numbers mean more preference or utility.Even when we have financial options we can study or observe the past to get a feel for our preferences.


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Expected Utility Theory is a methodology that incorporates our attitude toward risk (risk is a situation of uncertain outcomes, but probabilities are known) into the decision making process.Utility value

Monetary value

It is useful to employ a graph like this in our analysis. In the graph we will consider a rule or function that translates monetary values into utility values. The utility values are our subjective views of preference for monetary values. Typically we assume higher money values have higher utility.


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In general we say people have one of three attitudes toward risk. People can be risk avoiders, risk seekers , or indifferent toward risk (risk neutral).

Monetary value

Utility value

Risk avoider

Risk indifferent

Risk seeker

Utility values are assigned to monetary values and the general shape for each type of person is shown at the left. Note that for equal increments in dollar value the utility either rises at a decreasing rate(avoider), constant rate or increasing rate.


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Utility

$X1 X2

U(X2)

U(X1)

Here we show a generic example with a risk avoider. Two monetary values of interest are, say, X1 and X2 and those values have utility U(X1) and U(X2), respectively


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Expected Utility

In expected utility theory we want to focus on wealth values and utility values. Gambles will lead to adjustments in wealth.

Let’s call W the initial wealth which can always be retained if no gamble is taken, and call the wealth at a loss X1 = W – loss, and the wealth at a win X2 = W + win.

The expected value of wealth from a gamble is then (p1 is the probability of a loss and p2 is the probability of a win)

EV = p1X1 + p2X2

Note we called the expected value of a gamble EV and I now have the expected value of wealth with a gamble being EV. EV will mostly stand for expected value of wealth, unless otherwise stated.


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Expected Utility

The following is what needs to be considered to get the expected utility of a gamble:

1) Start with a person’s initial wealth W,

2) If the gamble is taken identify X1 and X2,

3) Assign to each wealth value in 2) the respective utility value U1, and U2 and in a graph connect the U1 and U2 values with a chord.

4) Calculate the expected value of wealth with the gamble EV.

5) Calculate the expected utility of the gamble as EU where EU = p1U1 + p2U2, and find the value on the chord above the EV.


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Utility

$X1 EV X2

U2

U1EU


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Example continued

Say utility is assigned by the function U = sqrt(wealth) and a person has initial wealth 10000. Then for the three gambles we had before the EU’s would be

EU1 = .5sqrt(9999.5) + sqrt(10100) = 100.248

EU2 = .5sqrt(9900) + sqrt(10200) = 100.247

EU3 = .5sqrt(0) + sqrt(30000) = 86.603

So in terms of EU’s the preferred order of gambles for this person is gamble 1, then 2, and the 3. When we looked at EV’s the order was 3, 2, and 1. So expected utilities of gambles may have a different rank ordering than when looking at the EV’s.


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Fair gambles

A fair gamble is one where the expected value of the gamble is zero, i.e., p1(-loss) + p2(win) = -p1(loss) + p2(win) = 0.

This implies that the expected value of wealth with the gamble is equal to the value of wealth when not gambling at all, which you might call your certain wealth.

For fair gambles

EV = p1(W – loss) + p2(W + win)

= p1W +p2W – p1(loss) + p2(win) = (p1+p2)W + 0 = W, since p1+p2=1.


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Risk averse fair gamble

wealth

Utility

X1 X2EV

= W

UwEU

In this graph I have the generic view of a risk lover. With the fair gamble we have the EV and the EU is on the chord above the EV.

If the person does not gamble wealth will be W and the utility there is just read off the utility function here as Uw (note a risk averter has diminishing marginal

utility of wealth.)


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Risk Averse fair gamble

For the fair gamble we again know EV = W, but for a risk averse person Uw > EU. Thus we can conclude risk averse folks will not accept fair gambles.

On the next slide you can see I thickened part of the horizontal axis and the chord connecting the two points on the utility function associated with the wealth values under the gamble. The probabilities of the gamble could be changed (and the gamble would no longer be fair) and the only way the person would accept the gamble over having the certain wealth W is if the EV was greater than W*.

So, a risk averse person may gamble, but it has to be at favorable odds.


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wealth

Utility

X1 X2EV

= W

UwEU

If the EV of a gamble is above W* (and is no longer a fair gamble, but a favorable one), then the person will end up on the chord segment that has not been thickened and thus only then have EU>Uw.

Risk averse fair gamble

W*


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Risk Seeker fair gamble

U

WX1 X2EV =W

EU

Uw

In this graph I have the generic view of a risk seeker. With the fair gamble we have the EV and the EU is on the chord above the EV.If the person does not gamble wealth will be W and the utility there is just read off the utility function here as Uw (note a risk seeker has

increasing marginal utility of

wealth.


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For the fair gamble we again know EV = W, but for a risk seeker person Uw < EU. Thus we can conclude risk seeker folks will always accept fair gambles.

On the next slide you can see I thickened part of the horizontal axis and the chord connecting the two points on the utility function associated with the wealth values under the gamble. The probabilities of the gamble could be changed (and the gamble would no longer be fair) and the only way the person would NOT accept the gamble over having the certain wealth W is if the EV was less than W*. So, risk seeker may NOT gamble, but it has to be at unfavorable odds.


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U

WX1 X2EV =W

EU

Uw

If the EV of a gamble is below W* (and is no longer a fair gamble, but an unfavorable one), then the person will end up on the chord segment that has not been thickened and thus only then have EU<Uw.

.

W*


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Risk Neutral fair gamble

U

W

Uw = EU

X1 EV =W

X2

The risk neutral person is indifferent between a fair gamble and not gambling at all. If odds are switched to favorable gambles will be favored and if switched to unfavorable gambles will not be taken.


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Certainty Equivalents

In a more general sense we could talk about gambles that are fair or unfair. The certainty equivalent of a gamble will be the sum of money or wealth for which the individual would be indifferent between the certain sum and the gamble. We will examine these certainty equivalents for folks with risk aversion, neutrality and risk seeking prefrences.


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Utility

$X1 X2

U2

U1

The decision maker may have an option that is certain. If so, the EU is simply the utility along the utility curve (I called it Uw before). So in this diagram we see that any sure bet greater than Y has an expected utility greater than the expected utility of the risky option.

EV

EU

Y

Risk averse – certainty equivalent


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Another Example

Say Utility U = square root of X, where X is a dollar amount the person ends up with,

Then U(4) = 2 and U(16) = 4, for example.

Say a risky option will result in 4 50% of the time and 16 50% of the time. The expected value is 10 because

.5(4) + .5(16) = 10 and the expected utility is 3 because

.5U(4) + .5U(16) = .5(2) + .5(4) = 3.

Now, if there is an option that will pay more than 9 with certainty, than the certain option is better. So, 9 is the certainty equivalent of this uncertain gamble. Let’s see this on the next slide.


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4 9 10 16 x

U(x)

U(16)=4

EU = 3

U(4)=2

U(x)

Any certain option above 9 gives a utility value greater than the expected utility of the uncertain option.


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Risk seeker – certainty equivalent

U

WX1 X2EV

EU

Uw

In this graph I have the generic view of a risk seeker. With the fair gamble we have the EV and the EU is on the chord above the EV.Y is the certainty equivalent of the gamble. Any certain option above Y would be preferred to the gamble shown by the risk seeker.

Y


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Reducing Risk


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In a previous section we mentioned that sometimes we face an uncertain situation with regards to monetary values. We saw

1) The expected monetary value, EV, of the uncertain situation (what I will now call a gamble) is the sum of some numbers, where each number is a monetary value multiplied by its probability of occurring,

2) The expected utility of a gamble (what I will now write as EU) is the sum of some numbers, where each number is the utility of a monetary value multiplied by its probability of occurring,

3) The expected utility of a gamble does not occur on the utility function (unless the person is risk neutral), but on the chord or line segment that connects utility values of each part of the gamble and directly above the EV of the gamble.


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U

YY1 EMV Y2

U(Y1)

U(Y2)

EU

Say we have a risk lover and the gamble G leaves Y1 p1 % of the time and Y2 p2% of the time.

EV =p1Y1 + p2Y2

EU = p1U(y1) + p2U(Y2)


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U

YY1 EMV Y2

U(Y1)

U(Y2)

EU

Say we have a risk avoider and the gamble G leavesY1 p1 % of the time and Y2 p2% of the time.

EMV =p1Y1 + p2Y2

EU = p1U(y1) + p2U(Y2)


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On the last few slides I show you generic cases of a risk lover and a risk avoider. You see a gamble with monetary values Y1 and Y2, with associated probabilities p1 and p2 (where p2 = 1- p1).

I now want to show something we saw in the previous section, but I want to be more precise in my language.

Sometimes we may have an opportunity that is known with certainty. The utility of the opportunity will be on the utility function for the individual and will be noted U(C).

The decision rule for choosing between a gamble and a certain payoff is

-choose the certain option when U(C) > E[U(G)], and

-choose the gamble when U(C) < E[U(G)].

Of course, when the two are equal the individual would be indifferent between the two.


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Back on the slides I have some vertical dashed lines. I put them there on purpose. I want you to think of the location as values of a certain payoff, I now call C, and then we can see that

U(C) = EU. The payoff C is called the certainty equivalent of the gamble.


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U

YY1 EV Y2

U(Y1)

U(Y2)

EU

Say we have a risk avoider and the gamble G leaves Y1 p1 % of the time and Y2 p2% of the time.

The risk premium, rp, of a gamble is the EV of the gamble minus the certainty equivalent of the gamble.

rp = EV - C and will always be positive for a risk avoider.

The risk premium for a risk lover will be negative and it will be zero for a risk neutral person.

C


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U

YY1 EV Y2

U(Y1)

U(Y2)

EU

C

A Gamble of no fire insurance Say Y2 is value of property if no fire and Y1 is the value of the property with a fire.

The EV = p1Y1 + p2Y2.

EU = p1u(Y1) + p2U(Y2)

C is the certainty equivalent of the gamble.


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If a person buys insurance it changes the risky situation into a certain situation.

If Y2 - C = fee paid for insurance the individual will have C with certainty. To see this we note

If no fire the individual has Y2 - fee = C, and

If fire the individual gets restored to Y2 and has still paid the fee so the certain property value is C.

SOOOOOO

Y2 - C is really the maximum fee the person would pay for insurance and they would like to pay less. Y2 – C is called the reservation price for insurance.


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Let’s take the point of view of the insurance company - and we do not have to look at the graph here.

They pay claim of Y2 - Y1 p1% of the time and they pay 0 p2% of the time for an expected claim of

p1(Y2 - Y1) + p2(0) = p1(Y2 - Y1)

This is called the actuarially fair insurance premium - meaning this is the minimum they have to charge to be able to pay out all the claims.

Now look in the graph - here is an amazing result:

Y2 - EV = Y2 - (p1Y1 + p2Y2) = Y2(1 - p2) -p1Y1

= p1(Y2 - Y1), so Y2 - EV is the actuarially fair premium


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Review

Y2 - EMV = least insurance company will charge,

Y2 - C = Most person will pay,

(Y2 - C) - (Y2 - EMV) = EMV - C is the room the person and the insurance company have to negotiate for the insurance. Before we said EMV - C was the risk premium and now we see it is the most the person would pay over the actuarially fair premium to insure against the gamble.

Now insurance companies pay out claims and pay employees and electricity and other admin. expenses. The company has to get some of EMV - C to pay these expenses.


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People won’t buy the insurance if the insurance company needs more than EMV - C to cover its other expenses because the person would have more utility without it in that case.

Next let’s look at how information can be beneficial in reducing risk.


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Y

U

Y

U

Y1 C EMV Y2

Y1’ c’ EMV’ Y2

situation without information

situation with information


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On the previous slide I show two graphs. Both have the same utility function for an individual. The top graph is a situation where the individual has no information and the bottom graph shows what happens when more information is obtained.

Note more information may not eliminate risk, but it can reduce it. Let’s study an example to show context.

Say an individual can buy a painting and if it is a real master painting the wealth of the individual will be Y2. If the painting is a fake the individual will lose some of his expenditure because the painting is no big deal - wealth is Y1. We see the certainty equivalent of the gamble is C. Presumably the individual will buy the painting if the certainty equivalent of the gamble is better than his wealth by not buying the painting at all.


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Now say the person can hire a painting expert to see if the painting is a fake or not. If the expert says the painting is a fake then you will not buy it and will not lose on the low end. But if it is a real painting you will have the same high end wealth because you will buy the painting.

So information from an expert in this case gives you the same high end value but makes your low end value better than without information.

But, the expert is going to want to charge you for the information. How much should you pay?

Since C’ is the certainty equivalent with information and C is the certainty equivalent without the information, the person would pay up to C’ - C for the information and the utility of the person would be improved.

Game Theory

Here we study a method for thinking about oligopoly situations.

As we consider some terminology, we will see the

simultaneous move, one shot game.


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Simultaneous Move, One Shot Games

We will again assume there are only two decision makers. For now we assume both have to make their decisions at the same time. This is a simultaneous move game. The main point about a simultaneous move game is that although I may know all the information about what the other guy might do, I do not actually see what is done before I do my thing.

Games could be sequential, where one player follows the other.

Some games have only one decision by each player involved. Other games involve repeated rounds of play. Here we focus on the one shot games.


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Normal Form

In the normal form of a game, information about the options of each player is presented in a matrix. The “row” player’s options are described in each row and the payoff is the first number in each cell.

The “column” player’s options are described in each column and the payoff is the second number in each cell.

Since we have a simultaneous move game each player will choose its options without knowing what the other player will choose. But the choice of the other player may be anticipated.

Let’s check out an example on the next few screens.


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Column player left right

Row up a, A c, CPlayer down b, B d, D

Let’s make sure we understand this table. Here we have two players: the Row Player and the Column Player (Miller and Bud, if you want).This is a generic game for now and all the Row Player can do is choose up or down (in rock, scissors, paper you can choose one of the three, but for the Row Player here the choice is up or down.)The Column Player can only choose left of right.

Now, let’s say the row player picks up and the column player picks left.


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Now, let’s say the row player picks up and the column player picks left just as an example to see what each would get.

If the game ended at up, left, the row player would get “a” and the column player would get “A.”

Note all these letters usually are dollar amounts for us and can be negative amounts. But, sometimes the letters represent other concepts besides dollars. As an example the numbers could represent jail time.


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If the game ended at down, right, the row player would get “d” and the column player would get “D.”

Caution: If as ROW Player you pick down thinking you get “b” remember that what you get is also influenced by Column Player. So, you could actually get “d” if the Column Player picks right.

Next we want to think about how each player should decide what strategy to pick.


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Row player should think this way: (As the row player) I do not know what the column player will do. But, I can look at each option of the column player, one strategy at a time.

If the column player picks left my choices are

up a

down b

As the row player I would pick the option that has the highest value: pick up if a > b, or pick down if a < b.

If the column player picks right my choices areup cdown d

As the row player I would pick the option that has the highest value: pick up if c > d, or pick down if c < d.


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For the row player the choice of strategy is up or down.

A strategy is called a dominant strategy for a player if it has a higher payoff no matter what the other player chooses.

So, up would be a dominant strategy for the row player if both

a > b and c > d.

Down would be a dominant strategy for the row player if both a < b and c < d.


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Example

column player left right

Row up 10, 20 15, 8Player down -10, 7 10, 10

The row player will think in the following way(look at each column). If column man picks left I can have 10 if I go up and –10 if I go down. So I will go up. If column man goes right I can have 15 if I go up and 10 if go down. So I will go up.In this example the row player sees it is best to go up no matter what the column player is doing. In this sense we say “up” is a dominant strategy for the row player.


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Example



This is the same slide as before, but I show in each column what the ROW player will look at. If the highest value in each column is in the same row – the person has a dominant strategy.Again, up is a dominant strategy here for the row player.


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Column player should think this way: (As the column player) I do not know what the row player will do. But, I can look at each option of the row player, one strategy at a time.

If the row player picks up my choices areleft right A C

As the column player I would pick the option that has the highest value: pick left if A > C, or pick right if A < C.

If the row player picks down my choices areleft right B D

As the column player I would pick the option that has the highest value: pick left if B > D, or pick right if B < D.


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For the column player the choice of strategy is left or right.

A strategy is called a dominant strategy for a player if it has a higher payoff no matter what the other player chooses.

So, left would be a dominant strategy for the column player if both A > C and B > D.

Right would be a dominant strategy for the column player if both

A < C and B < D.


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Example



The column player will think in the following way(look at each row). If row man picks up I can have 20 if I go left and 8 if I go right. So I will go left. If row man goes down I can have 7 if I go left and 10 if go right. So I will go right.In this example the column player does not have a dominant strategy. What to do? If the other player has a dominant strategy, assume he will play it and then do the best you can.Column player should go left.


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Example



This is the same slide as before, but the column player looks at his possibilities in each row.


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Nash Equilibrium

A set of choices by the players would be considered a Nash equilibrium if each player would NOT want to change their choice given the choice of the other player. The choices up and left represents a Nash equilibrium because neither would choose to change given the choice of the other.

The row player says – if the column player will be at left, then it is best for me to stay at up.

The column player says - if the row player will be at up, then it is best for me to stay at left.


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Let’s pick a different cell than up, left to see why another cell might not be a Nash equilibrium.

Let’s look at up, right.

The row player says - if the column player is at right then I want to stay at up (Nash Equilibrium may still be in the running).

The column player says – if the row player is up, then I want to change from right to left.

Because the column player wants to change, the cell considered is not a Nash Equilibrium.

Note: You look for dominant strategies before the game is played and you see if you have a Nash equilibrium after the game is played.


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Applications

Here we look at several applications. We will see a classic

example of a dilemma that can arise in such games.


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Pricing Example

column player low price high price

Row low price 0, 0 50, -10Player high price -10, 50 10, 10

The numbers in the matrix represent profit. The row player has a dominant strategy of a low price (0 is better than -10 and 50 is better than 10) and the column player has a dominant strategy of a low price as well (similar numbers). And, low low is a Nash equilibrium.

A dilemma that arises here is that both could be better off if they both went with a high price.


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Prisoner Dilemma Games

The game we just saw has the characteristic that has come to be known as the prisoners’ dilemma. When the players act separately (competitively) the outcome is worse than if they cooperated.


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Don’t be taken advantage ofIn the pricing example each might be tempted to get together and both charge the high price and both do better than the low price strategy. The problem of the high, high solution is that it is not a Nash equilibrium and thus each would have the incentive to change to the low price strategy. Your stockholders would not want you to be taken advantage of by a double crosser. Don’t collude here, for it is not likely to pay off. Let’s see why.Say you are the row player and you agree (illegally) to set prices high with the column player. After you finish the meeting you will note 1) if you as the row player see the column stay at a high price the it is better for you to have a low price (this is part of why high, high is not a Nash equilibrium), and 2) perhaps more importantly you will note the column player also has the incentive to switch to low (this is the other part of high, high not being a Nash equilibrium). So, if you stay at high you will look bad!


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Advertising Example

column player ad no ad

Row ad 4, 4 20, 1Player no ad 1, 20 10, 10

Profits are in the matrix. Each player has a dominant strategy of advertise. This outcome is a Nash equilibrium.

A similar dilemma arises here as before. No ads would be better but each does not want to get taken advantage of in this situation. If you don’t have ads when the other does you won’t be on the minds of the consumers and thus you will not make enough.


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Coordination example

column player 120 volt 90 volt

Row 120 volt 100, 100 0, 0Player 90 volt 0, 0 100, 100

In this example say you have consumer appliance manufacturers who have the choice between making the appliances run on 120 or 90 volt plugs. If they both do not use the same plug they will earn less profit because consumers will have to spend on different plugs and thus not be willing to spend as much on the appliances. The game has two Nash equilibria – both doing the same plug. The next question is how do they get the same plug?


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Coordination Example

In this example, the firms need to figure out a way to get on the same page. Agreements to coordinate may be looked at negatively legally, so maybe companies lobby the government to set the standard for a product.


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Hawks and Doves


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TastesIn economics we largely take the tastes and preferences of the consumer to be a given piece of information. Within that context, the consumer attempts to maximize utility also given prices and income. We have spent some time thinking about how the consumer changes their actions when income or prices change. But we leave preferences stable.

Biologists assume (I am told) an organism’s tastes are forged by the pressure of natural selection to help the organism solve important problems in their environment.

Please read the book example about out tastes for sweets.


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Strategic PreferenceA strategic preference helps the individual solve important problems of social interaction and the usefulness of having the preference depends on the fraction of the population who share them.What we will look at next is a model of preference formation. The example is taken from biology, but put into the language of economics. Note how there are basic assumptions and then conclusions are reached.

On to the example of hawks and doves – a model of the taste for aggressive behavior.


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The ModelSay people are all the same except for some are hawks (have a strong preference for aggressive behavior) and some are doves (prefer to avoid aggressive behavior).

Whenever two individuals come into conflict over an important resource (food, a mate, and so on) the hawk’s strategy will be to always fight for it while the dove’s strategy will be to never fight.

Remember economics is about using scare resources. Hawks may kill doves and get the resources, but hawks might kill each other for the resource. Doves do not fight each other, but share resources.


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The ModelSay a food unit has 12 calories.

When two doves meet close to a food unit they share it and each gets 6 calories.

When a hawk and a dove meet close to a food unit the dove defers and the hawk gets all 12 calories.

When two hawks meet close to a food unit there is a battle. The winner gets the 12 calories and the loser gets none. Also, each spends 10 calories in the fight. So, the winner has a net gain of 2 calories and the loser has a net gain of -10 (sometimes called a lose). If over time a hawk wins half of the encounters with other hawks and loses the other half the average payoff is -4.


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The ModelThe average payoffs can be put in tabular form as:

Individual Yhawk dove

Individual X hawk -4 each 12 for X, 0 for Y

dove 0 for X, 12 for Y 6 each.

So you can see, for example, if 2 doves meet each will get 6 calories on average.

Say h is the proportion of the population that is hawk and thus 1-h is the proportion that is dove. Then a hawk would meet another hawk h of the time and the payout would be -4 and would meet a dove 1-h of the time and the payout would be 12 for an average payoff of Ph = h(-4) + (1-h)12.


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The ModelSimilarly, the dove would have an average payoff of Pd = h(0) + (1-h)6.

Whenever we consider a value for h, if hawk has a higher average payoff then hawks will flourish and doves will diminish and h will grow. For example, if h = .5,Ph = .5(-4) + .5(12) = 4 and Pd = .5(0) + .5(6) = 3 and thus hawks will get most of the calories and thus they will have larger families and that trait will grow. But, if at an h doves have a higher average payoff then their families will grow and h will fall. For example, if h = .75, Ph = .75(-4) + .25(12) = 0 and Pd = .75(0) + .25(6) = 1.53 and thus doves will get most of the calories and thus they will have larger families and that trait will grow.


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ConclusionNow, if the average payoff is the same at an h that h will remain and the family sizes will stabilize. We find this h by setting Ph = Pd and solving for h. We haveh(-4) + (1-h)(12) = h(0) + (1-h)(6) and solving for x we get-4h + 12 – 12h = 0 + 6 -6h, or12 – 6 = 4h + 12h – 6h, orh = 6/10, or .6The average payoff is 2.4 for each.

Income and substitution effects


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Here we want to explore some more of the detail of a price change on the demand for a good. Here is the basic idea. Say the price of x falls. When this happens we think two things are at work: an income effect and a substitution effect.

The income effect: If initially we buy the same amount of x as we purchased before, since x has a lower price we will have more of our own income left and so it will feel like we have more income. We saw when we have more income we want more normal and less inferior goods. So, the income effect of a price change means if the price is lowered we could want more or less of the good.


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The substitution effect: The sub effect is an indication that as the price of a good falls we want more of the good and we use it in substitution for other goods.

In economics we like to show the income and substitution effects in the diagram of consumer utility maximization.


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change in price - optimal point changey

xx1

y1

Say the consumer starts out at x1, y1. If the price of x should fall the budget line rotates out in a counterclockwise fashion. The dashed line above x1 is similar to the one in the income change diagram. Except here we do not think the consumer

will end up to the left of the dashed line when there is a price decline.


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change in price - optimal point change

The reason we feel the consumer will not end up to the left of the dashed line is twofold:when the price falls1) at the initial amount of x purchased the consumer feels richer and we saw this may make them buy more or less of x(income effect of a price change),2) x becomes relatively cheaper and we feel people move toward now relatively cheaper products and away from now relatively more expensive items(substitution effect of a price change).


156


So, the income effect means more or less x given a price decline, and the substitution effect means more x given a price decline.Now if the good is an inferior good1) the income effect says less x2) the substitution effect says more x.

The only way we could end up to the left of the dashed line on the previous screen is if the income effect operating with an inferior good is larger than the substitution effect. Economists have felt this rarely, if ever, happens – if so we call it a Giffen good.


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income and substitution effect

y

xr s t

Focusing only on good x here, say we start at point r. With a price decline in x this consumer would end up at point t. But I have also shown point s. Here is how to think about this point: after the price fall think about the consumer losing enough income so that the initial

utility level could be obtained.


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The movement from r to s highlights the substitution effect because the consumer had the income effect of the price change taken away. The movement from s to t is the income effect.


159

The demand curveP

x (usually we put Q)

P1

P2

Q1 Q2(r t)

From 2 screens ago we saw a pricedecline had us move from point r to t. When we put this info into a price, quantity graph we see the demand curve is downward sloping.


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The demand curve

You and I already knew the demand curve was downward sloping, but now we also know it is because we think substitution effects outweigh income effects. Plus we know at each point along the demand curve the consumer is maximizing their utility given the situation they find themselves in. We also know now that at lower prices the consumer reaches a higher level of satisfaction. This was not always obvious along just the demand curve.


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y

xt s r

Focusing only on good x here, say we start at point r. With a price increase in x this consumer would end up at point t. But I have also shown point s. Here is how to think about this point: after the price increase think about the consumer getting enough income so that the initial utility level could be obtained.

r to s sub effect

s to t income effect


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To highlight the income and substitution effects of a price change we put in an intermediate point. Essentially what we did was say after the price change let’s show a hypothetical change in income to get the consumer back to the original indifference curve that they started with.

(Lower price, take income away, higher price, give income back.)

The movement along the original indifference curve is then the substitution effect. Then take the income change back out to see the income effect.

Impact of Change in Income

Here we want to consider the change consumers will make if

they experience a change in income.


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change in income.

Note that the budget line is a summary of the baskets of goods that a consumer can buy. The consumer ultimately picks the basket that is able to be purchased and gives the individual the most satisfaction or happiness.

For the next few slides let’s just think about the budget line and not about consumer utility maximization.


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change in income - budget change

y

x

Remember on the budget line we are measuring the amount of x and y the consumer can buy given their income and given the fact that prices must be paid.x1

y1

I have illustrated one basket the consumer can buy. With the price of x = Px and the price of y = Py the consumer here could buy x1, y1.


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change in income - budget changey

x

There are many ways to think about how the budget line would change given an income change, but one way to think about it would be to pick a given amount of x, say x1. Before the income

x1

y1

change say that once x1 is bought that leaves only y1 of y. Now if there is an income increase, after x1 is bought that would leave more money to spend on y and thus y2 could be bought (I just say could – it may not be bought).

y2


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From the previous screen we can see more y can be bought if there is more income available, but how much more depends on the prices of x and y and it depends on the income change.

But, as income rises more y can be bought, given an amount of x is bought. Thus the budget line shifts out in a parallel fashion if income grows and by a similar logic shifts in parallel if there is an income decline.


168

change in income - optimal point change

Now that we know how the budget changes given an income change, let’s see how the consumer optimum changes(given that taste and preferences do not change).


169

change in income - optimal point change y

x

Say the consumer starts out at point a - x1, y1 gives maximum satisfaction. Note I have extended a line above point x1.Now with more income the budget line shifts out. The consumer will end up either

x1

y1

to the right or the left of the dashed line. If the consumer ends up to the right, more x is wanted with more income. If the consumer ends up to the left of the dashed line then less x is wanted when more income is obtained.

a


170


A normal good is one where that as the consumer gets more income more of the product is demanded (or less income means less of the good is demanded).

An inferior good is one where as the consumer gets more income less of the product is demanded (or less income means more of the good is demanded).


171


x

It just so happens here that when income went up the consumer moves to a point where there is more x than before. This is the case of a normal good.

x1

y1a


172


x

It just so happens here that when income went up the consumer moves to a point where there is less x than before. This is the case of an inferior good.

x1

y1a

Example: When you think of music CD’s are probably normal and cassettes are probably inferior.

In general we are not sure if goods are normal or inferior until we do a study. Here we show what happens in each case.


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Income consumption pathy

xx1 x2

y1

When we look at several consumer optimum points at various levels of income and then trace out the points with a line we get the income consumption path. Here both goods are normal goods. Would the income consumption path be downward sloping if only one of the goods were inferior?

a


174

Engel curve - normal goody

xx1 x2

y1

In the right hand picture we can see an income increase and from the left graph we take the new x, x2, and draw it in with the new income level. The Engel curve for a normal good is upward sloping. What about for an inferior good?

a

x

income

I2I1

x1 x2


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Budget Today or Tomorrow

Here we study the properties of the budget line in the context of consumption over time.


176176

Budget Line

In the context of consumption today or consumption tomorrow, the budget line is a bit different than in the typical consumer behavior model.

One difference is we have consumption today (C1) on the horizontal axis and consumption tomorrow (C2) on the vertical axis. Another difference is the presence of an “endowment” point. It is assumed the consumer has an initial set amount of possible consumption today and a set amount of consumption next period and these come from income each period, called M1 and M2. The budget line must go through the endowment point, but borrowing or lending (saving) can move the consumer away from the endowment.


177177

Budget Line

C today

C1

C tomorrow

C2

Endowment point (M1, M2)

Borrow today

Lend today

paid back + interest

Pay back + interest


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Budget Line

On the previous screen the endowment point shows what the person can have in each period.

If the person borrows - takes more today than the endowment - then next period 1 + r must be paid back for every 1 taken today.

If the person lends - gives some of today’s consumption up - then next period 1 + r is received for every 1 given up today.

The slope of the budget is –(1 + r), or 1+ r in absolute value.


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Change in the interest rate

C today

C tom.

original

New

The original line has a lower interest rate because when borrowing occurs less is given back next period, or if lending occurs less is paid back. So, the higher the interest rate the steeper the curve through the endowment point.


180180

Example

C today

C tomorrow

Endowment point (50000, 60000)

Borrow today

Lend today

paid back + interest

Pay back + interest

The endowment point here means the income is 50000 today and 60000 tomorrow (Next year). Say the interest rate is 20%

Horizontal intercept

Vertical intercept.


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Example continued

The vertical intercept means you consume nothing today and everything next period. The 50000 this period will earn interest and thus the total will be 50000(1.2) + 60000=120000.

The horizontal intercept means you spent all you current income and as much as you can borrow and use next years income to pay it off. This would be 50000 +(60000/1.2) = 100000. This horizontal intercept is the present value of lifetime income.


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Example continued

When the interest rate is 20% and the endowment point is (50000, 60000) the budget line can be thought of in math form in the following ways:

1) In terms of the future C2 + 1.2C1 = 120000,

2) In terms of the present C1 + (C2/1.2) = 100000, or

3) As we do in the graph C2 = 120000 – 1.2C1.

The slope is -1.2 and means if you spend $1 today you give up the ability to consume $1.20 next year.


183

Equation for budget line

183

When we have endowments M1 and M2 and interest rate r the equation for C2 and C1 isC2 = M2 + M1(1 + r) – (1 + r)C1.

Thus, 1) If C1 = 0, C2 = M2 + M1(1 + r). This is the vertical intercept.2) If C2 = 0, 0 = M2 + M1(1 + r) – (1 + r)C1, orC1 = M1 + M2[1/(1 + r)]. This is the horizontal intercept and is called the present value of lifetime income.


184184

Indifference Curves

Here we study indifference curves in the context of consumption over time.


185185

Indifference Curves

Indifference curves in this context are basically the same as we saw in the past. The curves slope downward, do not cross, fill the graph (although we do not always draw many in a graph), and are convex (meaning they get flatter as you move down the curve.)


186186

Present or Future Oriented

C today

C tom.


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Present or Future Oriented

On the previous screen we have a curve for two separate people. Each one gives up a unit of C today.

The flat curve person does not need much C tomorrow back in return for the C today given up. This type of person is tomorrow oriented or patient.

The steep curve person needs more C tomorrow (relative to flat curve) in return for the C today given up. This type of person is today oriented or impatient.


188188

Marginal rate of time preference (MRTP)

The absolute value of the slope of an indifference curve at a point is called the MRTP. The slope is change in C2 divided by the change in C1.

If the MRTP > 1 the consumer has a positive time preference meaning when giving up 1 unit of C1 more than 1 unit of C2 must be given back to have the same utility.

If the MRTP < 1 the consumer has a negative time preference meaning when giving up 1 unit of C1 less than 1 unit of C2 must be given back to have the same utility.

If the MRTP =1 1 the consumer has a neutral time preference meaning when giving up 1 unit of C1 1 unit of C2 must be given back to have the same utility.


189189

Equilibrium

Given an interest rate, we see here the point consumers end up at in order to maximize their utility.


190190

A borrower

Endowment pointC tom.

C today

Notice at the endowment the consumer’s indifference curve goes through the budget steeper then the budget- they are willing to pay back more than they have to, so they borrow today and become happier than at the endowment.


191191

A lender

C tom.

C today

Endowment point

Notice at the endowment the consumer’s indifference curve goes through the budget flatter than the budget - They get more in the future than they require to have the same utility so they lend today and are happier doing so.


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Note

Both the lender and the borrower at the point of equilibrium have the MRTP = 1+the interest rate and this is greater than 1. This means that both borrowers and lenders have positive time preferences in equilibrium. Again, this means when giving up 1 unit of C1 more than 1 unit of C2 must be given back to have the same utility.

Also note that with a given interest rate some people are lenders and some borrowers based on their preferences. Later on we show how folks might change from being a lender to a borrower, and vice versa, depending on changes in the interest rate.


193193

Changes in Equilibrium

Here we study how the consumer position changes given changes in the interest rate.


194194


Endowment point

C today

C tom.

l

m

n


195195


We have seen in the past that as the interest rate falls the budget line becomes flatter. At the highest interest rate in the example on the previous screen, we see the individual go to point l (and is actually a lender.) This point has a certain amount of C today involved (as well as a certain of C tom.) As the interest rate falls the consumer moves to point m and then point n. So the amount of current consumption rises as the interest rate falls.

The point here is that the demand for current consumption is a function of the interest rate. In fact, we say as the interest rate falls the quantity demanded for current consumption rises.


196196


r

C today

l

m

n

This is the demand for current consumption curve and is derived from the graph two slides before this one.


197197

Permanent income hypothesis

Let’s consider an example where your income will 1000 in each of two years and the interest rate will be 25%.C2 = M2 + M1(1+r) – (1+r)C1.a. Suppose that you save all of your money to spend next year. How much will you be able to spend next year? This is the same as asking on the budget what is C2 when C1 = 0? C2 would be 1000 + 1000(1.25) = 2250.

How much will you be able to spend today is like what is C1 if C2 = 0. C1 would be 1000 + (1000/1.25) = 1800.


198198

b. Suppose you borrow $800 and spend $1800 today. How much will you be able to spend next year? If C1 = 1800, C2 = 1000 + 1000(1.25) – 1800(1.25) = 0.

c. The graph is on the next slide with C1 on the horizontal and C2 on the vertical axis. Note the vertical intercept is (0, 2250), the horizontal intercept is (1800, 0) and the endowment point is (1000, 1000)

The slope = (2250-0)/(0-1800) = -1.25, so the slope shows that the price of spending $1 today means you can not spend $1.25 next year.

Note if C1= M1, then C2 = M2, and vice versa. This means the person can have their endowment point and neither borrow or lend.


199199

c1

c2

(0, 2250)

(1800, 0)

(1000, 1000)


200200

c1

c2

(0, 2250)

(1800, 0)

(1000, 1000)

Say you find $400 in your desk drawer. Your endowment today becomes 1400. How does the budget shift?

Note the new intercepts and endowment point.

(2200, 0)

(1400, 1000)

(0, 2750)


201201

c1

c2

(0, 2250)

(1800, 0)

(1000, 1000)

Say you will get $500 more in pay next year but this year you only have 1000. Your endowment next year becomes 1500. How does the budget shift?

Note the new intercepts and endowment point.

The budget shifts just like in the previous example.

(2200, 0)

(1400, 1000)

(0, 2750)

(1000, 1500)


202202

c1

c2

(0, 2250)

(1800, 0)

(1000, 1000)

Now say the person has endowment 1000 and 1000 initially. They consume at point A.

If C1 and C2 are normal goods, then if the endowment in period 1 rises to 400, or the endowment in period 2 rises to 500, the individual will end up here.

(2200, 0)

(1400, 1000)

(0, 2750)

A


203203

In this example we see if income in period 1 goes up 40% consumption in period 1 is not likely to go up 40%. Some of the increase is spread out into the next year.

Similarly, if income next period goes up 50% (Say you expect to graduate and make more money) your consumption in period 2 is not likely to go up 50%.

Permanent income is the present value of our lifetime income and we saw this has the horizontal intercept.

Given our preferences, permanent income is what determines our consumption pattern. Another way to say this is that our consumption pattern over time is influenced not only by the income in he period in which we consume, but by the income in every period.


204204

The Behavior of Consumers

Here we study an elementary view of the economic approach to how consumers go

about spending their money – you could say this is a model of how consumers confront the

basic economic problem.


205205

Consumers of goods and services face the incredible task of having to decide how much to buy, if any, of literally thousands of items in the marketplace. In economics we say the goal of the consumer is to maximize the utility they can get from the goods and services that are available.

Utility here means the happiness or satisfaction that goods and services provide for the consumer.

Let’s work with an example where there is only two goods consumers can buy – let’s pick steak and potatoes (I pick two goods to make the example relatively easy to work with, but others have studied this stuff and have shown the things I point out apply when there are tons of goods and services to choose from).

Now, let’s look at something called the budget line or constraint of the consumer. Say a consumer has $10 to spend and say a pound of steak costs $1 and a pound of potatoes costs $1 (I made up the numbers to just get us started – but we usually only have a certain amount to spend and we have to pay prices for the goods and services we buy).

Can the consumer buy 20 pounds of steak? Not right now. The $10 of income and the price of $1 per pound constrains the individual to only a maximum of 10 pounds of steak – and in this case no potatoes could be purchased if all is spent on steak.


206206

Pounds of Steak Pounds of Potatoes

10 09 18 27 36 45 54 63 72 81 90 10

Each line in this table represents a combination of steak and potatoes the consumer can buy. How did I get these numbers?

Well, the amount spent on steak plus the amount spent on potatoes should add up to $10. So we really have the equation

$10 = amount spent on steak + amount spent on potatoes.

On the next screen let’s put the information into a graph. The graph will have the quantity of steak on the horizontal axis and the amount of potatoes on the vertical axis. Each line in the table is represented by a point in the graph.

Note the amount spent on good X is the price of X times the quantity of X taken.


207207

Consumption Possibilities

10, 09, 1

8, 27, 3

6, 45, 5

4, 63, 7

2, 81, 9

0, 10

0

2

4

6

8

10

12

0 2 4 6 8 10 12

Pounds of Steak

Poun

ds of

Potat

oes

Note: From the table on the previous screen, the first row of the table is the point on the bottom right of the table.

Then as we go down the table we move up the line in the graph.


208208

The economic approach to consumer behavior is based on the idea that a consumer can evaluate how much they like each combination of goods.

Here is a way to see which basket the consumer will choose to maximize utility given that they have $10 and each good costs $1 per unit. Start at the bottom right basket – 10 steaks and 0 potatoes (to save on typing we assume each steak and each potato is a pound.)

Now, the individual is getting utility from steak only at the first point. Think about moving to point (9, 1). If the consumer moves from (10, 0) to (9,1) the consumer will lose 1 steak, but gain 1 potato.

With this move there is

1) A loss in utility from the 1 steak that is given up,

2) A gain in utility from the 1 potato gained.

If the gain is greater than the loss, then the consumer will make the move from (10, 0) to (9, 1). The same type of movement will be investigated between (9, 1) and (8, 2). Move to the point (8, 2) if the second potato adds more utility than the loss in utility from giving up the 9th steak.


209209

Digress: true story – my daughter JoAnn and her buddy Meg were playing one day and I heard Meg say she liked horses more than JoAnn liked horses. Have you every heard kids say this type of stuff? Well, anyway, in economics we think it is hard to compare how much two different people like certain items. BUT, we think it is very natural for a single person to compare how much they like, or how much utility they get, from different types of items like steak and potatoes.

Another component to our story about consumer behavior:

Notice when the consumer starts in the bottom right of the table there is a set of 10 steaks and no potatoes. We have to have a time frame in mind, so let’s say it is a week of time. If you are like me, you like steak, but does each pound give the same utility in a certain amount of time?

In economics we think that the more units of an item you have in a certain amount of time the happier you probably are, but the additional units add less and less happiness for you. The marginal utility (the utility added by another unit) of each unit is said to diminish.


210210

Let’s add the concept of marginal utility to the steak and potatoes example:

Say you think about buying 10 steaks and 0 potatoes. Now compare this to 9 steaks and 1 potato. The 10th steak would have relatively low utility as far as steak goes, because diminishing returns would have set in, and the first potato would have relatively high utility as far as potatoes go. So, for many of us we would take the first potato and give up the 10th steak. But maybe not every one would. Some might just take 10 steaks and no potatoes.

Now, if a person didn’t take the first potato they are done (stick a fork in them). They have maximized utility at (10, 0). So, when the price of steak is $1 (and when the consumer has $10 and the price of potatoes is $1) the quantity demanded from some people will be 10 units.

Other people will move up the line in the graph because some units of potatoes add more utility than the utility lost by having less steak. I can not predict where any one person will end up, unless I know more about that person. But we think each person knows where they will end up. (where does the vegetabletarian - a person who eats only vegetables like potatoes - end up?)


211211

In steak and potatoes example I had before, the price of each good was $1 and the person had $10 to spend. Different people will have a different amount to spend, but will always follow the same basic method as presented here (remember this is the economic view.) The interesting thing is that although people have different incomes (money to spend), they can face the same prices when they shop in the same stores. When the price of each good is $1, taking 1 potato requires the person to give up 1 steak. Comparisons of the utilities involved can take place for each person and each person can maximize their own utility.

So, let’s say we have three people and when the price of steak is $1 we see the demand from each of the three as

Sally – 4 pounds, Sammy – 6 pounds and Billy – 7 pounds.

The next thing we want to explore is what happens to the amount folks want when the price of a good changes. Let’s explore a price decline to 50 cents per pound of steak. Let’s go back to our graph, which was created with the consumer having income of $10. Plus we will say half pounds of potatoes can be purchased.


212212

Consumption Possibilities

0

2

4

6

8

10

12

0 5 10 15 20 25

Pounds of Steak

Poun

ds of

Pot

atoe

sNote here when the price of steak fell we get a new budget line. The same maximum amount of potatoes can be bought, but now 20 steaks can be purchased if all the money is spent on steaks.

When the individual gives up a steak only half a potato can be purchased. But here the same type of comparison would happen as before. In other words, the 20th steak would be given up if the utility of the first half of potato is bigger than the utility of the 20th steak.


213213

At this point in our study I hope you can accept on faith that in economics we get the feeling that as the price of something falls people want a greater quantity of it. Before, when the price of steak is $1 we saw the demand from each of the three people asSally – 4, Sammy – 6 and Billy – 7. So when the price is 50 cents, the demand might be

Sally – 5, Sammy – 7 and Billy – 8.

Know, I have asked you to accept on faith that as the price of something falls a greater quantity is demanded. Some ideas called the income effect of a price change and the substitution effect of a price change provide some of the reasoning for what I asked you to accept on faith.

Let’s think about a price decline. The logic behind the income effect of a price decline is that if you buy the same amount of the good after the price decline as you did before the price decline then you will have more money left in your pocket. The price decline would make it seem like you got a raise in income – hence why I wrote an income effect. Now, in the real world we might buy more of a good if our income rises, but maybe we will buy less. It depends on the good.


214214

An inferior good is one that as we get more income we want less of the good. Do you have a good like this for you? What about cassette tapes for music? Have you desired less when you have gotten more income? Or what about white bread? Have you desired more of the other kinds and less white bread the more income you have obtained? If so, these goods are inferior for you.

A normal good is one where as you get more income you want more of the good. Maybe CD’s for music and rye bread are normal for you.

Review something: Before I mentioned that as the price of good falls I want you to accept on faith that the amount people want will increase. Now the income effect of a price decline says the amount will increase if the good is normal but will decline if the good is inferior. What is the deal on the inferior good? Well I need to mention the substitution effect.

It is thought that as the price of a good falls we will want more of it and use it as a substitute for other things. As an example of this, as the price of gas falls we will buy more gas to drive around instead of walking of riding our bike. (To walk or ride your bike you need energy that comes from food, so the gas can substitute for the food, the cheaper the gas.) So the substitution effect always says take more when the price falls.


215215

Finalize our thoughts here:

Inferior good price falls would mean the income effect says take less of the good but the substitution effect says take more of the good. From experience, economists have said the substitution effect is larger than the income effect and thus when the price of a good falls people want more of it.

Normal good price falls would mean both the income and substitution effects say take more of the good.

On the next screen I show a typical demand curve for one person (like Sally from before) in a graph. The curve is really the result of the individual maximizing utility and when the price of something falls a greater amount is desired due to the relationships known as the income and substitution effects.


216216

$ - here measuring Price per unit of steak

Quantity of steak

1

0.50

4 5


217217

All Else EqualYou may have noticed we tell stories in economics. Like I just told a story about when the price of a good falls from $1 per unit to $0.50 (fity cent) most folks demand a greater quantity of the item. As I told the story I implicitly assumed only the price changed form $1 to $0.50. All else was assumed the same. This means the person likes the good the same at either price and the consumer has the same income at either price.

If a person should change how much they like a good or if their income changes then we tell another story (just not now – maybe later).

Think back to the example developed here. When the person only had $10 to spend and each good costs $1 per unit we can conclude, given all else is equal,

1) The consumer was limited to buying one combination of steak and potatoes in the table, and

2) If the consumer wanted more of one good while moving along the line, then less of the other good could be obtained.

These two conclusions are the result of scarcity that the consumer faces. We sketch out a method the consumer might use to make a choice.

Monopoly

Here we see what a monopoly is and its revenue potential.


219

Overview

Monopoly means one seller.

In perfect competition many sellers were price takers. Any one seller could not influence the price of the product in the market. The competitive firm could only choose what amount to sell.

A monopoly firm will have to determine both how much to sell and at what price. Let’s look at these ideas a little more on the following few slides.


220

Review p

Market Q

In a market, consumers as a group are thought to want to buy a greater quantity the lower the price. We see this as a downward sloping demand curve.

D


221

Review p $

Market Q Firm Q

P=MR=D

In a competitive market, the market demand from consumers interacts with market supply from many sellers and we get an equilibrium price, like p* in the graph. At this point, since any one firm is a small part of the market, when we look at a firm it is a price taker. Thus, when the firm thinks about selling another unit it can sell that unit at the same price as the previous unit and thus MR = P for a competitive firm.

D

S

p*


222

Analogy: To think about the marginal revenue for a competitive firm I like to think about a pop machine. Say the price of a pop is $1.25.

Say the machine has been refilled and the pops are not chilled to perfection and you are the first one to make a purchase. What is the total revenue in the machine after you make your purchase? $1.25! Since the total revenue was zero before you bought, the change in total revenue from the sale of another unit (in this case the first one), was $1.25. This is exactly what we mean by marginal revenue. Marginal revenue is the change in total revenue from changing output by 1 unit.

Now say I buy a pop right after you. The total revenue in the machine is 1.25(2) = 2.50 and the marginal revenue is 1.25.

SO, MR = P for a competitive firm.


223

MonopolyFor a monopoly firm the demand is the same as the market demand we see in competition. The demand is downward sloping to the right, what is called less than perfectly elastic.

Since the monopolist is the only seller, it is natural they face the market demand curve.

The situation of monopoly is often called imperfect competition.


224

Sources of monopoly

1) Exclusive control of an input – deBeers is an example

2) Economies of scale – the case of a natural monopoly. The idea here is that AC can be pushed really low by one firm and it then makes sense for only one firm to serve the market.

3) Patents – protecting inventions for a time may give monopoly power.

4) Network economies – Microsoft Windows is an example of the idea – once enough people use a product sometimes using another type of product becomes less functional.

5) Granted by government


225

Maximize profitSince the monopolist is the only seller in the market, the monopolist must decide 1) what price to charge and2) how much to sell.

When the monopolist sells, she is worried about profit. The goal is to maximize profit. But, in order to maximize profit, the pattern of revenues and costs at various output levels must be understood. The pattern of cost was the topic of an earlier section. Now we look at the pattern of revenue.


226

Monopoly p

Market Q

Here the monopoly is the only firm in the market. When the price is 6, in this example the consumers want 2 units. Total revenue would be 12. But, this firm, if it wants to sell 3 units has to lower the price on all units to 5. The competitive firm didn’t have to worry about another price like the monopoly firm.

D

6

5

2 3


227

Monopoly – marginal revenue

So, because the way consumers are in this example on the previous screen, when P = 6, 2 units will be sold and when the P = 5, 3 units will be sold. Total revenue would move from 12 to 15 when the quantity moves from 2 to 3.

So, the additional revenue from the 3rd unit is $3. This is the marginal revenue of the 3rd unit.Note, the price to get the third unit sold is $5, but the marginal revenue is only $3.SO, P>MR at a quantity.


228

InterpretationWhen the price is lowered from 6 to 5 the amount sold rises. In fact, the 3rd unit sold brings in 5 in revenue. But this isn’t all we need to look at to have MR. Since the monopolist must sell to all consumers at the same price, the first 2 units now get sold at 5 as well. That means revenue on those 2 units will not include $6 per unit when the price is lowered.

Continuing with the example,

MR(of the 3rd unit) = 5 - (6-5) 2 = 3


229

interpretationP

Q

6

5

2 3

a

bc

Area a + b = 6 times 2= 12 = TR when P = 6Area b + c = 5 times 3 = 15 = TR when P = 5

MR = c - a = 5 - 2 = 3

area c is the gain in revenue from sellingmorearea a is the loss inrevenue from selling at a lower price.


230

Let’s do another exampleP Q 5 04 13 22 31 40 5

Say this is the demand from consumers in the market. If the price is 5 consumers want nothing, for instance. Let’s put TR on the next slide.


231

Let’s do another exampleP Q TR 5 0 04 1 43 2 62 3 61 4 40 5 0

Total revenue is just P times Q, so you should check what I have here.

Next let’s add MR to the table.


232

Let’s do another exampleP Q TR MR 5 0 0 ----4 1 4 43 2 6 22 3 6 01 4 4 -20 5 0 -4

MR, marginal revenue, is the change in TR when we add a unit of output. Note at Q = 0 I have the line --- because we have not had a change yet.

The MR = 4 for a Q = 1 because TR went from 0 to 4 when Q went from 0 to 4. The MR = 2 for Q = 2 because TR went from 4 to 6 when Q went from 1 to 2.

Note: MR can become negative, in theory. Also note that P > MR at each Q (except Q = 1, but we usually ignore this.)


233

MR from areas to heightP

Q

a

b c

P

Q

In the above diagram we think ofMR as area c - a and we get a number.

height = MR

In the bottom graph we can think of the numberas a height. Note still theMR is lower than the priceon the demand curve.

On the next screen we will see the whole MRcurve.

D

D


234

Monopoly MR in a graph$

Q

D

3

5

3

I do not have a prooffor you, but you can see in this diagramthat MR is also a straight line that startsat the same place asdemand in the upperleft, but is always below demand becauseP>MR. Like at Q = 3, MR = 3 and P = 5.

Note that a good way to draw in MR is to first draw demand and then put MR through the Q axis halfway out to the demand curve. I put an X at that point.

Monopoly Pricing and Output

We study the pricing and output decision of the monopoly firm.


236

Price and output decision for the monopolist in the short run

The amount of output the monopolist should sell in the short run is the amount where MR = MC(as long as P>AVC), just as in the case of the competitive firm.

The price charged would then be the price on the demand curve above the quantity where MR = MC. (recall P = MR for firms in comp, but P>MR for the monopolpy firm.)


237

Logic of MR = MC rule$

Q

D

MR

MC

a b c

The Q = b is the Q whereMR = MC. But look at Q = a. Atthat point, Q could be increased and more would be added torevenue than to cost and thus profit would rise. We know this because the MR > MC for these Q (Compare the heights of the curves).

Now let’s look at a Q greater than where MR = MC, like at point c. More has been added to cost than to revenue and thus profit would fall. We know this because MC > MR at this Q.


238

What price?$

Q

MC

D

MR

P*

Q*

At Q*, where MR = MC, P* is the price on the demand curveconsumers are willing to pay for Q* and thus this is the price charged by the monopolist.


239

Qualification$

MC

D

MR

P*= .10

20

ATC

AVC1

AVC2

AVC1=.11

AVC2= .08

Note that the ATCis above the demandcurve, so the firm will lose money. In the short run, the question is whetherthe firm should shutdown or continue to operate. Let’s go to the next screen and say moreabout this.

ATC = .12


240

continueNote that the Q where MR = MC = 20. So, if the firm operates at all it should make 20.

Note at Q = 20, the price on the demand curve is .10 but the ATC = .12Now, remember ATC = TC/Q so ATC times Q = TC.

TR = P Q = .1(20) = 2TC = ATC Q = .12(20) = 2.4Profit = TR – TC = 2 – 2.4 = - .4OrProfit = (P – ATC)Q = (1 - .12)20 = -.4 The firm is losing money.


241

continue 2

If the AVC curve is AVC2 for the firm then at Q = 20 the AVC = .08. This means the TVC = AVC Q = .08(20) = 1.6.

Thus the TR = 2 can cover the 1.6 of TVC and what is left of TR, .4 can go to paying some of the total fixed costs. If the firm shuts down it would have nothing going to fixed cost. So the firm should operate.

Thus, operate if at the Q where MR = MC the P > AVC.

Note if the AVC is AVC 1 = .11 the P < AVC. The firm should shut down. TR of 2 falls short of TVC of 2.2 and covers none of fixed while if the firm shuts down it only has to cover the fixed cost.


242

Quiz 1 – not a real quiz$

MC

D

MR

P*

Q*

ATC

Is this monopoly firmearning a profit? If so,draw in the graph therectangle that represents the profit.


243

Quiz 2 not a real quizMC

D

MR

P*

Q*

AVC

$

ATC Is it possible for a monopoly to lose money?

Indicate in the graphhow much thismonopoly is losing byindicating the lossrectangle.


244

Palm of hand

Thumb

Is a monopoly guaranteed a profit. I have a monopoly – I make a pizza fork (not really, but listen up). Look at the palm of your right hand, thumb up. When you wrap your hand around the fork your thumb is next to a button on the fork (sorry, only right handed version.). When you press the button

A razor blade edge comes out here and you move your hand so your thumb is now pointing left and you cut your pizza real easily.

The demand for my item is much lower than where my costs are.


245

Can Monopolies charge whatever price they want? The answer is yes, but with a qualification.

Remember consumers have a demand for the product and have prices they are willing to pay. As long as the monopoly is charging a price the consumers are willing to pay then they can charge whatever they like. But if the monopoly charges too high a price consumers will not buy at all.

OUR ECONOMIC RULE – sell Q where MR = MC, charge the price on the demand curve above this Q (So charge whatever you want but to profit max charge this one) and both of these ideas are dependent on the P>AVC at this Q.


246

The monopoly solution and elasticity

Without proof I tell you that with a given demand curve and MR curve for the monopoly, we have

MR = P (1 – F), where F = 1/absolute value of elasticity of demand.

Recall that elasticity of demand changes as we move down the demand curve (in absolute value the number gets smaller).

Monopoly mark-up

We see the monopoly has P > MC at its profit maximizing level of output. So the mark-up of P over MC as a percentage of the price is (P – MC)/P.


247

Mark-up and elasticity

The mark-up again is (P – MC)/P.

The profit maximization condition was MR = MC.

The MR, elasticity connection was MR = P(1 – F) = P - PF.

SO, the mark-up can be changed to

(P – MC)/P = (P – MR)/P = (P –(P – PF))/P = (P – P + PF)/P

= PF/P = 1/absolute value of elasticity of demand.

The monopoly mark-up is a function of the elasticity of demand. Note that since we have absolute value of elasticity, the mark-up is a positive number, and since P>MC, 1/abs <1, or abs>1. This means the elasticity of demand will be in the elastic range for a monopoly.

Compare Monopoly to Competition


249

Compare monopoly with competition

The main results here are the ideas that----1) a monopoly firm will charge a higher price than would occur in competition and----2) a monopoly will sell less output than would occur

in competition.

There seems to be a notion in the world that monopolieswill charge us outrageous prices. Economics does not settle this claim, but the science of Economics does tell us that we get higher prices than in competition. But, there are some willing to pay the higher price.


250

Q

P

D

S

Pc

Qc


251

On the previous slide we have the competitive market. Note the demand is coming from many consumers in the market. The demand from each person is essentially the marginal benefit curve of each person.

Note the supply is coming from many suppliers. The supply from each firm is basically the marginal cost curve (that part above AVC).

Because there are so many players in the market, none has an influence on price, so the “market” determines the price and each buyer and seller takes the price.

Now, if the industry is monopolized, one seller would meet all the consumers. Thus, the monopolist would see a MR curve and treat S as a MC curve.


252

Comparison continued$

Q

D

MR

S = MC

Pm

Pc

Qm Qc

If you focus your eyes on the point where S = D you see the competitive point with Pc and Qc. If you focus on the point where MR = MC you see themonopoly point with Qm and Pm (Note Pm is on demand curve above where MR and MC cross.). Assume that a monopolist comes in and buys up all the firms. It then operates

where MR=MC and charges the price on the demand curve at that Q.


253

Pm

Pc

Qm Qc

P

Q

a b

c d e

f g h

The graph

reproduced


254

Referring to the previous slide:

comp monop

con surp a b c d e a b

Prod surp f g h c d f g

So, consumers lose surplus of b, c, and e due to monopoly. Producers gain c and d from the consumers, but lose h.

Overall, there is a deadweight loss of e and h. This loss is a major reason why we have laws against monopoly. The Sherman Act of 1890 is the first law in US to be against monopoly. We have had revisions since, but basically this law is the driving force.


255

Problems of monopolyThe problems of monopoly are higher price and less output than in competition. Moreover, 1) The higher price means those who still buy have less money to spend on other things – c and d are surplus areas that consumer used to have for other things but now pays to monopoly.

2) Those who no longer buy must be worse off becausethey get less than what they were at their liberty to purchase under competition – area e represents the value of lost output to the consumers and is part of the deadweight loss of monopoly.

The Competitive Firm in the Long Run


257

Remember that the long run is that period of time in which all inputs to the production process can be changed. Before, in a section on production and cost we saw that the basic cost structure could be summarized in the following graph. (Note, since all costs are variable the AC curve is really an AVC curve, we just call it the AC curve.)

ACMC

$

Q

firm


258

The firm is still a price taker and P = D =MR = AR for the firm. The firm makes the output level where MR = MC, as long as the P>AC. The amount of the profit is calculated as (P – AC)times Q*, and the P and the AC are measured at the Q* level.

ACMC

$

Q

firmQ*

P

Profit rectangle


259

Here, where MR = MC, the P = AC so profit would be zero. Remember that zero profit means that accounting profit is greater than zero if there are some opportunity costs that are not explicit. Since at this price the firm breaks even we say the price here is the break-even price. So when MR = MC if P = AC, the price is called the break-even price.

ACMC

$

Q

firmQ*

P

Note when MC = AC, AC is at its lowest. Now at break-even point, P = MC and P = AC, so MC = AC.


260

Here, where MR = MC, the P < AC so profit would be negative. Firms would be better off exiting the industry.

ACMC

$

Q

firmQ*

P

The loss


261

The MC curve above the AC curve is the supply curve for the firm in the long run. If the price line comes through at any point in this area the firm will have positive profit and the quantity supplied will correspond with the amount on the MC curve. If the price is any lower the firm will exit and make nothing.

ACMC

$

Q

firmQ*


262

Let’s look at an example next.

Quantity TC MC AC P Q TR TC Profit

1 10 2 10

2 15 5 7.5

3 21 6 7

4 28 7 7

5 37 9 7.40

6 48 11 8Here is an example of Floyd’s Barbershop. Floyd operates in a competitive environment. If he didn’t have a barbershop he would make 8 bucks at a gas station. This cost has been factored into his TC. So, really at Q=0 TC=8 at the barbershop. MC = change in TC divided by change in Q, while AC = TC/Q.


263

Quantity TC MC AC P Q TR TC Profit 1 10 2 10 2 1 2 15 5 7.5 3 21 6 7 4 28 7 7 5 37 9 7.40 6 48 11 8

Here I have added a 2 under the P column and a 1 under the Q column. The P and Q column is the supply curve. The supply curve for a firm is the MC above the AC curve. But to draw the MC curve we will follow the rule that firms produce where P (=MR)=MC. Since the MC at Q = 1 is 2 the MC = 2 = P on the supply curve. What is the P if Q=2? Can you fill in the rest of these two columns? (sure you can!)


264

Quantity TC MC AC P Q TR TC Profit 1 10 2 10 2 1 2 2 15 5 7.5 5 2 3 21 6 7 6 3 4 28 7 7 7 4 5 37 9 7.40 9 5 6 48 11 8 11 6

Here I added the TR for the Q=1 by taking the P times Q. Can you fill in the rest of table? (SURE you can, because, dang it, you are good enough!)


265

Quantity TC MC AC P Q TR TC Profit 1 10 2 10 2 1 2 10 -8 2 15 5 7.5 5 2 10 15 -5 3 21 6 7 6 3 18 21 -3 4 28 7 7 7 4 28 28 0 5 37 9 7.40 9 5 45 37 8 6 48 11 8 11 6 66 48 18

Here I copied the TC and found profit as TR minus TC.

What have we done here? I HAVE NO IDEA!

No, really we looked at the graph on the next page.


266

So, in the graph, when P = 2, MR = MC at Q=1 and profit is less than zero. Firm really wouldn’t make this amount though, it would quit. So this part of the MC curve is not the supply curve. Only the part above AC is the supply curve Each row in the table can be put into this graph.

ACMC

$

Q

firm1

2

10

P

Profit=-8


267

Profits and losses

In a competitive industry it is felt the existence of profits at the firm level will attract more firms into the industry.

This will increase supply and lower price in the market.

With a lower price firm level profit falls.

The existence of losses at the firm level will make some firms leave the market.

This will decrease supply and raise market price.

The entry and exit of firms will stop when profit is zero. At that point P = MC = AC.

Competitive Industry in the Long Run

The case of a constant cost industry


269

In a constant cost industry it is assumed that

1) All firms are identical and thus all have the same identical cost curves, and

2) Those cost curves do not change as the industry expands or contracts (although the cost curves could change for other reasons).

The author points out that assumption 1 likely holds in industries that do not require special skills. Fast food joints might fit the bill here, while gourmet restaurants probably don’t.

Assumption 2 will hold in industries that are not large enough to affect the price of any input. This means that as the number of firms in the industry changes the price of inputs will stay the same because the industry is not a relatively large user of the input – other industries use the input as well.


270

In competition it is assumed that in the long run any firm that wants can enter or exit the industry. Furthermore,

If profit >0 for existing firms, more firms will enter,

If profit < 0 for existing firms, existing firms will exit, and

If profit = 0 there is no incentive for more firms to enter or existing firms to exit.


271

Useful diagramP

D1 S1 ATC1 MC1

P=MR1P1

Q1 q1Q q

Market Firm


272

Produce the q where MR = MC and see what type of profit exists by looking at (P - ATC) times Q or TR-TC at the q mentioned.

Profit = TR – TC.PQ = TRATC times Q = (TC/Q) times Q = TC

(P-ATC) times Q = PQ - (ATC times Q) = TR - TC

Hey, check this out.


273

Notes about diagram

MarketIn the market the price is determined by the interaction of supply and demand.When you think about the supply curve, there are a certain number of firms involved. You can think of this as being the short run where the amount of capital is fixed for each seller. In the short run, then, no new firms can enter either because they can’t get more capital either.


274

increase demandOn the next screen you will see demand increase in the market. Imagine consumers demand more. Then,1) The price in the market will increase to P2,2) The MR(price) for the firm will rise to MR2, 3) The output of the firm will expand to q2,4) The firm will have profit given by the shaded rectangle.


275

increase demandP

D1 S1 ATC1 MC1

P1=MR1P1

Q1 q1 q2

Q q

Market Firm

D2

P2P2 = MR2


276

demand increaseIn the short run when the demand increases, existing firms find it worthwhile to produce more, but they can not expand the production facility, by definition, and other firms can not enter the industry.The profit that exists in the short run are enjoyed by the firms in the industry. But in the long run other firms can enter the industry, as well as have existing firms expand their production facility. In the long run we want to note1) what impact profit has on firms and2) what happens to input prices.


277

profit impactIn the long run positive economic profit attracts firms to the industry. Firms will enter the industry until profit is driven to zero.The presence of economic losses(negative profits) forces some firms to leave the market. Firms will exit until the profit is zero.


278

input pricesBy definition in economics, resources are scarce. In the context of increasing demand for output we want to think about what might to the price of inputs. We consider three cases.1) Inputs are relatively abundant and thus there is no increase in input prices as the demand for inputs increases. This is called a constant cost industry.2) Inputs are in relative short supply and thus there is an increase in input prices as the demand for inputs increases. This is called an increasing cost industry.3) Inputs can be used in new ways and thus there is a decrease in input prices. This is called a decreasing cost industry.


279

ideas to comeNow, if a firm has positive economic profit we will see1) firms enter the market and thus market price falls, and2) the firms cost curves may shift if input prices change. This will have an impact on how much the supply curve shifts.


280

no change in input pricesP

D1 S1 ATC1 MC1

P1=MR1P1

Q1 q1 q2

Q q

Market Firm

D2

P2P2 = MR2

S2

Q2


281

no change in input pricesSince there is no change in input prices in this example profit will again be zero when the supply shifts out as far as the new demand to return the price to P1.

Supply S1 had a certain amount of firms involved and then some more firms entered(when profit was positive) to give us a certain amount of firms involved with S2. So there really is a separate supply curve for each specific number of firms in the industry. So in the long run we have variation in the number of firms in the industry, depending on the level of demand.


282

Long run supply curve

The long run supply curve in the market shows us the price and quantity combinations where1) the number of firms adjusts, and2) profit is zero.On the slide two screens ago we see the same price, P1, but two levels of output, Q1 and Q2. Since input prices didn’t change, P1 will always be the price that results in zero profit. On the following screen you will see the long run supply curve in the market in this constant cost case.


283

no change in input pricesP

D1 S1 ATC1 MC1

P1=MR1P1

Q1 q1 q2

Q q

Market long run supply Firm

D2

P2P2 = MR2

S2

Q2


284

Summary

In a constant cost industry in the long run

1) The supply curve in the industry is horizontal,

2) The supply curve is horizontal at the break-even price,

3) Each firm makes the amount where MR = MC, and P = AC.

Now,

Since MR = P for firms in comp., we also conclude

P = MC and since at break-even MC =AC, P = AC.

SO, P = MR = MC = AC at the profit maximizing level of output for each firm in the industry.

Profit

The word profit in economics really means economic profit.

Let’s see what this means.


286

Market types

Firms may operate in industries, or markets, that are called perfect competition, monopoly, oligopoly, and monopolistic competition.

No matter what type of market, we assume firms attempt to maximize profit.


287

Economic Costs

• Costs are accounting for the fact that when one thing is produced alternative goods and services are forgone.

• This is the idea of opportunity cost. When one thing is chosen, the opportunity to do the next best thing is forgone.


288

Example where revenue is 72,000

• Explicit costs• 12,000 hired labor• 5,000 rent• 20,000 materials• 37,000 total

• Implicit costs• 15,000 owner’s labor• 3,000 entrepre. cost• 4,000 inter. forgone• 22,000 total

•Accounting profit = 72,000-37,000 = 35,000•Economic profit = 72,000-37,000-22,000 = 13,000


289

Explicit cost

• In the example, the labor hired to make pottery would then not be used to make something else - an opportunity cost.

• These explicit costs represent payments to nonowners of the firm.


290

Implicit cost

• Costs of using owner supplied resources.

• The implicit costs represent money payments owner supplied resources could have earned in their next best use.


291

Profit

• Accounting profit = Revenue - explicit cost.

• Economic profit = Revenue - explicit cost - implicit cost.

• Profit will be used in general and this will mean economic profit. Implicit costs are incorporated into an economic analysis.


292

Profit

One last point. Since implicit costs are what owner supplied resources would have earned in their next best usage, we might call these costs normal profit.

SO, Economic profit = accounting profit – normal profit,

Or

Accounting profit = normal profit + economic profit.

Perfect Competition in the

Short Run


294

Perfect competition

Perfect competition is a type of market defined by:

1) All firms selling essentially the same product. The product of one firm would be a perfect substitute for the product of another firm.

2) All firms are price takers. No individual firm can have an influence on the market price based on how much the one firm produces. This usually occurs when there are a large number of firms in a market (or industry), but may happen with relatively few firms.

(two more conditions)


295

Perfect competition

3) Factors of production are perfectly mobile in the long run. This means in the long run a firm can get rid of all its inputs are add to what it currently has. Labor would be equally mobile. Note: remember the short run is when at least one input is fixed in amount for the firm.

4) Firms and consumers have perfect information. Essentially this means if there is knowledge out there these folks know about it.


296

Supply and demand

The model of supply and demand we have already seen is really the model of perfect competition. We will expand on that idea and focus our attention on a typical firm in that environment.


297

Firm in SR

The firm in the short run has some inputs that are fixed and some that are variable. The firm just accepts the market price.

With this in mind the firms has to decide how much output to sell to maximize profit.

Example: You can probably buy a 20 Mt. Dew at 10 places or so in Wayne and the price is basically 1.25, right? So the market for Mt. Dew is roughly perfectly competitive and each store has to decide how much to sell (which means they have to decide how much to stock on any given day).


298

Totals in a graphTR

TC$

QQ*

Profit

QQ*

If you plot the TR and TC curves the Q that gives the greatest distance between TR and TC is the profit max level of output, here Q*.

Next let’s turn to unit cost and price concepts.


299

Revenue potential

The market demand curve is downward sloping - in the whole market consumers will buy more at lower prices.

But, let’s say for any one firm the demand curve for the firm’s output is horizontal. Why? Any one seller is small relative to the market. 1) If the seller tries to charge a price higher than the market price no one will buy from them(because there are enough other places to buy), and2) The seller will not charge a lower price because they can sell all they want at the going price. The reason for this is because they are a small part of the market and already sell all they want at the going price.


300

Revenue potential

The ideas on the previous screen have the graphical interpretation shown here. The demand curve for the firm’s output is a horizontal line at the price that occurs in the market(assumed here to be P1).

P

Q

D

market

P

QFirm

d = PP1


301

Revenue potential

Since the firm in a competitive environment can not influence the market price on its own, the firm is said to be a price taker and this has implications for the revenue the firm can generate from sales of units of output.


302

Revenue potential

Total Revenue = TR = P times Q. For the firm here, P is a given value.As an example say P = 2.Units TR of output Notice the change in TR as 0 0 output changes is 2. This is 1 2 called the marginal revenue. 2 4 3 6 So the MR = P = firm demand 4 8 for a competitive firm.


303

Revenue potentialAs another example say P = 5.Units TR of output Notice the change in TR as 0 0 output changes is 5. Thus 1 5 marginal revenue = 5. 2 10 3 15 So the MR = P = firm demand 4 20 for a competitive firm.


304

review cost concepts

$/unit

Q or units

MCAC

AVC

30

b

a

The cost curves look this way in the short run due to diminishing returns.

I picked Q = 30 arbitrarily. At this Q the height of the

MC curve is the MC of this output and the height of the AVC and AC curves have similar interpretations. AC minus AVC equals AFC. Area a = TVC, a + b = TC


305

production rule$/unit

Q or units

MCThe profit maximizing firm will choose to produce the quantity of output where MR = MC(Q2 in graph).If the firm stops short of the rule, like at Q1, then the firmsacrifices units of output where MR > MC. In other

words, some units after Q1 add more to revenue than to cost. A profit max. firm wouldn’t pass up this opportunity.

Q1 Q2 Q3

P = MR


306

production rule

If the firm produces beyond Q2, MC > MR and the firm would thus add more to cost than to revenue on these units. A profit maximizing firm would not want to do this.

Now, since P = MR for the firm and since the firm goes to the Q where MR = MC, the firm in a competitive environment really produces where P = MC


307

operating rule

The operating rule is a qualification to the production rule. If operating is worth it at all, follow the production rule. Otherwise, shutdown. Now, in the short run there are fixed costs and variable costs. The fixed costs must be paid whether production is 0 or 1,000,000 or whatever. Variable costs must be paid only if variable inputs are employed. It is useful to think of hiring variable inputs only if they generate enough revenue to pay for themselves plus pay for some of the fixed costs.On the next few screens I want to present cases to see what the firm should do: operate or shutdown.


308

operating rule case 1$/unit

Q or units

MCAC

AVCb

c

The firm is a price taker - say it takes P

If firm operates if it shuts downTR = a + b + c TR = 0TC = b + c TC = TFC = bprofit = a profit = -b.

P MRa

Q1

This firm should operate where MR = MC and makea positive profit


309


Q or units

MCAC

AVC

d


If firm operates if it shuts downTR = e + f TR = 0TC = d + e + f TC = TFC = d + eprofit = -d profit = -d -e.

P MR

Q1

This firm should operate where MR = MC and have a loss, but not as big as if it shutdown.

e

f


310


Q or units

MCAC

AVC

g


If firm operates if it shuts downTR = i TR = 0TC = g + h +i TC = TFC = gprofit = -g -h profit = -g.

P MR

Q1

This firm should shutdown. Where MR = MC there is too big a loss, more than if the firm should shutdown.

h

i


311

operating ruleFrom these examples we can see that if the price is everywhere below the AVC curve the firm should shutdown. The firm will still have fixed costs to pay, but in this case revenue not only does not pay all fixed costs, it covers only some of variable costs. It is better to shutdown in this case.


312

firm short run supply curve

A supply curve is a curve that shows combinations of price and quantity the firm is willing to supply. In other words, we see the quantity the firm is willing to make available for sale at each price.

The short run supply curve is the segment of the MC curve that is above the AVC curve.


313

firm short run supply curve$/unit

Q or units

MCAC

AVC

If the price the firm accepts is above the AVC, then the MC curve acts as the line that shows the price, quantity relations we previously mentioned. The MC curve above the AVC is the supply curve of the firm.

P


314

Summary

A competitive firm will produce the Q where MR = MC, or, what is the same thing, P = MC, so long as at this Q the P > AVC.

The supply curve for the firm in this environment is the part of the MC curve above the AVC curve.

Competitive Industry in the Short Run


316

operating rule case 1

$/unit

Q or units

MCAC

AVCb

c


If firm operates if it shuts downTR = a + b + c TR = 0TC = b + c TC = TFC = bprofit = a profit = -b.

P MRa

Q1

This firm should operate where MR = MC and makea positive profit


317

Profit

I copied the slide form a previous set of notes. Recall we said the firm should produce the Q where MR = MC and have profit = (P – AC)Q.

Well PROFIT = TR – TC = P(Q) – TC(Q/Q) = (P – (TC/Q))Q = (P – AC)Q.

At the Q in the graph on the previous screen rectangle a has area (P – AC)Q. This is the profit amount.


318

We said the short run is the period of time in which at least one input is fixed. In the industry this means the number of firms is also fixed – firms outside the industry also can not get more of some input and since they are not in the industry they can not join it in the short run.

Since each firm’s supply curve is its MC curve above the AVC, the industry supply is the sum of each firm’s MC. We call the industry supply the horizontal sum of each firms supply because in the graph we sum the q’s of each firm at each price.

Let’s see this on the next screen.


319

Firm 1

Firm 2

P

Q

Add firm 1 onto firm 2

Here we just have two firms. If more, follow the same principle.

Many times we just show a smooth upward sloping curve just to show the basic idea.

Perfect Competition in Math Terms


321

Say you have a competitive market where the demand for consumers has been added up to be

Qd = 6000/9 – (50/9)P.

Also say there are 50 identical firms, where each has the total cost TC = 100 + 10Q + Q2.

The marginal cost for each firm would be MC = 10 + 2Q.

We know that firms that maximize profit produce the level of output where MR = MC (as long as P>=AVC). For a competitive firm P = MR, so MR = MC means

P = 10 + 2Q, or Q = (P – 10)/2 = .5P – 5 for each firm.


322

We know the supply curve in the competitive industry is basically the summation of the MC of each firm in the industry. For one firm we have in our example

P = 10 + 2Q. To add across all 50 firms we re-express MC as

Q = .5P – (10/2). Now we add all 50 firms together:Q = .5P – (10/2)Q = .5P – (10/2) (if firms are not identical, follow this … same basic process.)Q = .5P – (10/2)

Qs = 25P – 250

or P = 1/25Q + 10

The supply curve


323

Note the supply curve, Qs, adds up the supply curve of each firm. .5P50 times is 25P and (10/2) 50 times is 250.

So for the supply curve we have Qs = 25P – 250.

The market price and quantity traded are determined where Qs = Qd, so we have

25P – 250 = 6000/9 – (50/9)P, or

(225/9)P + (50/9)P = 6000/9 + 2250/9, or

(275/9)P = 8250/9, or

P = 8250/275 = 30. Plug P = 30 into either Qd or Qs to get the quantity traded in the market. In Qs we have 25(30) – 250 = 500.


324

Since the market price is 30, each firm will make

Q= (P – 10)/2 = (30-10)/2 = 10.

The profit for each firm TR – TC.

TR for a firm is P times Q, or PQ.

TR = 30(10) = 300.

TC = 100 + 10Q + Q2 for each firm in this example. So,

TC = 100 + 10(10) + 102 = 300.

Profit = 300 – 300 = 0.


325

P

D1 S1 ATC1 MC1

P=MR1P1=30

Q1=500 Q1=10Q q

MarketFirm


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D

S

P

Q

Industry or market firm

P=D =MR = AR

MC = S

Here we have the industry P and Q where S=D and the firm output level q where MR = MC, or we could say P = MC since P=MR. (presumably the firms MC are above AVC, so we have profit max positions.)


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Change in fixed cost

A change in the fixed cost for firms in the industry will not change the industry at all in the short run. In the short run a change in fixed cost will just affect the amount of profit for the firm. But it can not drive the firm out since the MC is above the AVC. Variable costs are covered and some amount of the fixed cost has to be covered.

In the long run we could have a very different story. But, let’s look at an analogy to get the short run story.

The fish tank analogy. Look at the next several slides quickly, to simulate a fish tank being filled with water.


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Hose and water going into tank

Water level


329


Water level


330


Water level


331


Water level


332


Water level

Wow, this is wild!


333

$/unit

Q or units

MCAC

AVC

d

P MR

Q1

e

f

Here is where we get the pay – off from the fish bowl analogy. Given the price, the firm looks at its revenue as e and f filling the tank as shown by d+e+f. Have the water fill in from the bottom up. Since the revenue covers the TVC – area f - and some of the TFC – area d + e – it is better to operate. A change in the fixed cost doesn’t change the fact that TVC would be covered and some of the fixed cost. If the firm shut down it would have no variable cost and all the fixed cost to pay with no revenue. By producing, the revenue covers all the variable and some of the fixed. So the firm loses less.

Remember, see the revenue fill area f and e from the bottom up.


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D

SP

Q

Industry or market firm

P=D =MR = AR

MC = S

Say variable costs rise in such a way that MC for firms rises. Here I show the MC curve shift left. The industry supply will shift left because the industry is simply the sum of all the firms. Market price will rise and output will fall. With a higher market price the firm demand line = price line will rise. Where I show the industry supply, the price means the firm would have the same level of output as before the change.

Can this be?


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The output for all firms in the industry can not be the same if the output in the industry is lower. On average, output has to fall at the firm level. If the firm shown had had slightly steeper curves the output for the firm would have fallen. So, we see a special case in my graph.

Demand in market rises

If demand in the market rises we would see a higher price and a greater quantity coming out of the market. Each firm would have more output at the higher price.

Next, we want to explore the cost of making the industry output. The conclusion is that firms as a group will make the industry output the cheapest that it can be made. Let’s turn to this next.


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Refresher – What information the marginal cost curve contains.

$

Q

MC

At a quantity, the height of the MC curve tells us how much is added to cost when that unit is added.

The height would also tell us how much cost would go down if that unit was not produced.


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Market – scale is larger than each firm

Firm 1 Firm 2Q Q Q

$ $ $

D

SMC1 MC2

Q1 Q2

P

The output made in the market is made with the lowest cost. Let’s see how. Normally each firm makes Q where MR = MC and since P = MR, P = MC. Say I have power to make firms change – say I make firm 1 make 1 more unit and to keep total output the same I make firm 2 make 1 less. Firm 1’s cost goes up by price + something. Firm 2’s cost goes down by the price.

So price + something minus price = something. Making firms change from what they want makes cost of market output rise.

Producer SurplusWhen producers sell products in

the market they may receive more than the amount they needed to receive to supply a unit – they

receive producer surplus.


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producer surplus

Recall that the supply curve shows various prices and associated quantities producers would make available for sale.The amount they need to receive to induce them to make available for sale units of a product are located on the supply curve. In fact the law of supply is an expression that they need to receive more in order to make available additional units.

The amount actually received is market determined.


340

need to receive

P S

Q

a b

c d e

P2

P1

1 2

Notice at P1 that only 1 unit is supplied. P1 is not enough of an amount to have the 2nd unit supplied. To get 2 units supplied, P2 is required.


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need to receiveOn the previous slide we see that to get 1 unit supplied P1 was need. P1 times 1 = P1 and is the area of the rectangle made up of C and D. This is the amount needed to supply the first unit. If we ignore area c we could say the area under the supply up to 1 unit is the amount needed to get that unit supplied. You see the area under the curve is an under-estimate of the amount needed but it makes life easy in terms of a visual look.

Similarly area b + e = P2, the amount needed to have the second unit supplied. If you ignore b we have just the area under the curve.

The area under the supply curve out to a quantity is the amount needed to supply those units.


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Producer surplus P

25

10

300 Q

A B

Area A = .5(300)(10 - 4) =900

Area A + B = 10(300) = 3000

Area B = A + B – A = 2100

Producers actually receive A + B = 3000, but only needed B = 2100, so the producer surplus is A = 900.

4

With S & D we get P = 10 and Q = 300


343

producer surplus

What do producers do with the surplus received?

They may use it to pay off some expenses or it could be a part of profit.

A PART OF THE INVISIBLE HAND

Do you see it?


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There is a story in economics that competitive market outcomes are efficient. Efficiency means two things really. What we make we have to make it as cheaply as possible. Plus we should make the things that people want the most.

What are some things we know?The market supply is the supply from all firms in the market added up.The market demand curve is the demand from each consumer added up. The price and quantity traded are determined in the market. Individual firms and individual buyers have no control over the price. The firms and individuals are price takers.


346

P

Q

A

B

C

P1

Q1

D

S


347

On the previous slide we see that consumer surplus plus producer surplus equals the area A + B, and this is the result of the market equilibrium P1 and Q1.

Inside your own head can you tell if you are willing to pay more for good x over good y? I would say you can because you can determine what you like!

As you compare two people can you tell who is willing to pay more for good x? This is harder, but we think the demand curve orders units in such a way that the first unit is demanded by the person who values it most in terms of their willingness to pay for it. The market price cuts off people who value the good less than those who value it more and thus the units of the good produced go to the people who value it most.


348

Think about sellers in the market. They want to make profit, where profit equals revenue minus cost. Can you tell between producers which can make units cheaper? It is hard but we think the supply curve orders units so that the first unit supplied comes from the lowest cost producer. The market cuts off suppliers who produce the good at too high a cost compared to those who produce at lower cost.

So, the market is efficient because goods go to those who value them most and are produced by the producers who can do it cheapest.


349

P

Q

A

B

C

P1

Q1

D

S

e

h

qless quamore

g


350

Another way to think about efficiency is the total amount of consumer and producer surplus together.

The total surplus is less when output is less than the market outcome at Q1, like at qless. Here we would see surplus fall by area e + h.

If output is higher than Q1, like at quamore, then we force on the market units of the good that costs more to make than people are willing to pay to get. This is not good.

Summary

A competitive market is most efficient because we get the most total surplus out of it.

Changes in Price

Here we explore the change in the price of good x and the impact this has

on the amount of x (and y chosen).


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Y

X

A BC

L M N

Z

U1

U2

U3


353

On slide 2 you see three budget lines and three indifference curves. The budget lines are different by the price of X.

Say the consumer has $10 of income and the price of Y is $1. Then point Z would be the situation where the consumer buys only good y and the amount of y would be 10 units (the consumer shown won’t go to point Z, but at least it is possible.)

Now if the price of x is $2 and the consumer spent all income on x then x would be 5. Let’s say this is the budget from Z to L. Then if the price of x is $1and the consumer spent all income on x then x would be 10. Let’s say this is the budget from Z to M. If the price of x is $0.50 (50 cent), and if all income is spent on x then x is 20. Let’s say this is the budget from Z to N.

Conclusion about budget line when price of x changes:

As price of x falls the budget line rotates counterclockwise around point Z, and as the price of x rises the budget line rotates clockwise around point Z.


354

Price consumption path

In our graph on slide two let’s focus on a price of x decline. Initially the consumer can have utility U1 by maximizing utility at point A. Then when the price of x falls the consumer gets more utility at point B (utility U2) and we see in this example more x is taken because point B is to the right of point A and this means more x.

If the price falls yet again the consumer moves to point C with more utility (U3) and even more x.

I have drawn a line in the graph that connects all the consumer utility maximum points at each price of x, given income and the price of y. This line is called the price consumption path. The line is an indicator of where the consumer will go at various levels of the price of good x.


355

Demand curve we know and love

Let’s review something.

Budget ZL had the highest price of x in our story – let’s say the price is P1.

Budget ZM had the 2nd highest price of x in our story – let’s say the price is P2.

Budget ZN had the 3rd highest price of x in our story – let’s say the price is P3.

When we take the price of x at each of these levels and keep track of the amount of x taken, we are getting the information we have always summarized in a graph of the demand curve. The demand curve is shown on the next slide.

So, the demand curve for an individual is a result of the individuals search for maximum utility at each price of x given their taste and preference for x (and y) as shown by the indifference curves, given the price of y and given income.


356

x (quantity of x)

Price of x

P1

P2

P3

D

1st degree price discrimination

A form of Monopoly Power


358

Our story of monopoly is incomplete. We have seen the case where the monopolist charges all customers the same amount. This is the single price monopoly case.

Do not get me wrong, monopolies can change their price. But once they do, the single price monopolies will charge all consumers the same price. But, some monopolies charge different consumers different prices. This type of monopoly is a price discriminating monopoly.

Some folks tell us that Microsoft discriminates when it sells Windows to the various computer makers. Some pay less than others.

You have probably heard of cases where senior citizens pay less, or maybe college students get to pay less. These are other examples of discrimination.


359

Why discriminate? The answer is that it may be more profitable than charging a single price.

Can every firm with monopoly power discriminate? Discrimination can only occur when both of the following hold.

1) The monopolist must have knowledge of how consumers differ in their demand for the good or service. Then the difference can be exploited.

2) Arbitrage must not be possible. Customers in the low price market segment must not be able to sell to the customers in the relatively high price segment.

We typically distinguish between three types of discrimination. I will finish this section by considering price discrimination of the 1st degree.


360

Example that I will explain on next slides

P Q TRs MRs TRd1 MRd1

11 0 0 Can’t do 0 Can’t do

10 1 10 10 10 10

9 2 18 8 19 9

8 3 24 6 27 8

7 4 28 4 34 7

6 5 30 2 40 6

5 6 30 0 45 5

4 7 28 -2 49 4

3 8 24 -4 52 3

2 9 18 -6 54 2

1 10 10 -8 55 1


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Say we have consumer demand of the form in the first two columns of the table on the last screen. You can see the quantity demanded rises as the price falls. TRs and MRs refer to the total revenue and marginal revenue when we have a single price monopoly. For example, when the price is 9, 2 units are demanded and the total revenue is 18. At a price of 10 the TRs was 10, so the additional revenue of the second unit – what we call the marginal revenue – is 8.

Remember that when we have a single price monopoly and the demand has the general form P = A – BQ, then the MRs = A – 2BQ.

TRd1 and MRd1 refer to the total revenue and marginal revenue when we have a price discriminating monopoly using the first degree method.


362

1st degree discrimination

In 1st degree price discrimination the monopoly knows what the individual is willing to pay for each unit and is able to extract that amount. In the example we know the individual will pay 10 for the first unit. Since two units are demanded at a price of 9, we know the individual is willing to pay 9 for the second unit. So on the two units the monopoly can charge 10 for the first one and 9 for the second one.

Think about a quantity discount idea. Pay 10 for one or get 2 for 19. The TRd1 for two units is thus 19 and the MRd1 for the second unit is 9. We follow the same idea the rest of the way down the columns


363

Note that the MRd1 and the P are the same. This is an example that shows that the price and marginal revenue are equal for a 1st degree price discriminator. Now if demand is

P = A – BQ, then MR = A – BQ.

The MRd1 curve is the demand curve for the 1st degree discriminator.

Now, all businesses make the output where MR = MC, as long as they are not losing more that the variable costs of production.

When you look at the table in the single price case if MC is 4 all the time the monopoly will make Q = 4 and charge $7 to each. If the MC is 4 always for a 1st degree discriminator, then the firm will sell 7 units, one for $10, one for $9 and so on down to one for $4.


364

$

Q

MC = 4 and special case of competitive supply

10

9

8

7

6

5

4

1 2 3 4 5 6 7

MRs

Demand of consumer and MRd1


365

On the previous screen we see the demand in the market. If the market was competitive we know the MR = MC output level is 7 because MR = P and P = MC cost at Q = 7. Consumer surplus would be the large triangle formed by the vertical axis, then horizontal line a $4 and the demand line.

If the market was single price monopoly we would use the MRs line and the Q where MR = MC would be at 4 and the price on the demand curve is 7. The consumer surplus falls to a smaller triangle than the one before, here we have the horizontal line at 7 as the base of the triangle. The monopoly takes the consumer surplus that would have existed had the market been competitive.


366

Now, if the monopoly can discriminate in the first degree in this example, then it will charge 10 for the first unit, 9 for the second unit, on down to 4 for the 7th unit. It would not want to sell 8 or more units because the MRd1 on those units is less that the MC and thus take away from profit.

NOTE 1st degree discriminator

1) sells same output as in competition,

2) charges a different price on each unit and the last unit has P = MC,

3) takes all the consumer surplus away from the consumer. Remember consumer surplus is what consumers are willing to pay minus what they have to pay and the 1st degree discriminator has the ability to get them to pay their willing amount on each unit.


367

Special way to look at 1st degree discriminator - two part tariff

A two part tariff is a special way to get the consumer to pay all they are willing to pay for units they buy. If you think back to the graph, the discriminator extracts all the surplus from consumers. It can do the same thing in two steps.

1) charge a single price for all units - the competitive price - or when P = MC,

2) charge a fee to be able to buy any units at all and make the fee the consumer surplus that would result in competition.

We see this type of pricing in buyer clubs, country clubs and other situations.

3rd Price Discrimination


369

Third degree discrimination

The third degree price discriminator see consumers as being in distinct groups with distinct elasticities. The key to this method working is that buyers in one group can not have the ability to sell to buyers in the other group.


370

3rd degree

MKT 1 MKT2 firm level analysis

MR1

D1 D2

MR2

MC

MR


371

3rd degreeIn this situation the firm is in two markets and would like to maximize profit. It has to decide what to charge in each market and how much to sell in each market. We assume here that the output is made in one location and so there is only one marginal cost to worry about. The way the monopolist proceeds is to 1) Figure marginal revenue at the firm level by horizontally summing the MR in each market2) Sell the total output where the firm MR = MC3) take this MC value back to each market and act like a monopolist in each market- sell where MR = MC and charge the price on the demand curve at those Q’s


372

3rd degree

The firm sells where MC = MR1 = MR2 or in words the firms sells the amount of output where the MC is equal to the marginal revenue in each market.

Mathematically this is similar to a multiplant monopoly, except here we sum across MR’s, not MC’s.


373

Let’s do a problem

P = 6 – Q in one group and P = 8 – Q in the other. Marginal revenues in both will be

MR = 6 – 2Q and MR = 8 – 2Q.

To add these two together we need to put them in Q form:

Q = (6/2) – (1/2)MR and Q = (8/2) – (1/2)MR.

So at the firm level we have

Q = 7 – 1MR, or MR = 7 – Q.

Say MC is constant at 4. Then at the firm level sell where MR = MC, or 7 – Q = 4, or sell a total of 3 units. How much to sell in each market?


374

Since MC = 4

In P = 6 – Q,

MR = 6 – 2Q = 4 = MC, so Q = 1 and price from the demand is 5.

In P = 8 – Q,

MR = 8 – 2Q = 4 = MC, so Q = 2 and price from the demand is 6.

Note that MC is a constant in this example. We would follow the same pattern if MC was not a constant.


375

The task we just completed could be bipassed if we had information about demand elasticities. Without proof I tell you

MR = P(1 – [1/E]) = P([E – 1]/E), where E is the absolute value of the elasticities.

Since MR = MC for firms, this would mean

MC = P([E – 1]/E) or

P = (E/[E-1])MC


376

3rd degree

Say MC is $6 for a firm (constant MC). Say in market 1 the elasticity –4 and in market 2 it is –2. Notice market 1 folks are more responsive to price.

The firm will sell where MR = MC in each market, so in market 1 we have

P = [-4/1 – 4]6 = 8 and in market 2 P = [-2/1-2]6 = 12. Take these prices back to each market, plug into the demand to get the amount to sell and figure profit in each market. Note the market with lower elasticity is charged more. Why? They do not respond as much to price changes


377

Let’s review the economic story about price discrimination.

1st degree – we can get the maximum each is willing to pay on each unit

2nd degree – (I didn’t cover) we have two groups and we can get what each is willing to pay on each unit (almost).

3rd degree – we have two groups and in each group we have to charge each the same amount in their group – kind of like a single price monopoly in each group.

Price Supports

Here are two examples of government intervention in a

market.


379

price floorP

S1

D1

QQ1

P1

A price floor is a minimum legal price. The government enacts one when it is felt the market price is too low. So an effective legal minimum must be above the equilibrium price so price can not get down to P1.

Qd Qs

Pf

a b c

d e

The downward arrow is here to suggest price can not get below Pf.


380

price floorWith the price floor we see:1) higher price Pf,

2) lower quantity demanded - from Q1 to Qd. This is really also the amount traded. The amount traded has fallen because sellers can only sell what buyers buy.

3) Higher quantity supplied - Q1 to Qs.

4) surplus = Qs - Qd.


381

One thing we notice with the floor is a surplus is created. What happens to the goods that are made and not purchased?

Maybe the government will buy them – the government would have to pay (Qs – Qd)times Pf to buy the surplus.

Maybe the government will ask producers not to make them.


382

price ceilingP

S1

D1

QQ1

P1

A price ceiling is a maximum legal price. The government enacts one when it is felt the market price is too high. So an effective legal maximum must be below the equilibrium price. Price can then not legally get to P1.

Pc

Qs QdThe upward arrow is here to suggest price can not get above Pc.


383

price ceilingWith the price ceiling we see:1) lower price Pc,

2) lower quantity supplied - from Q1 to Qs. This is really also the amount traded. The amount traded has fallen because buyers can only buy what sellers sell.

3) Higher quantity demanded - Q1 to Qd.

4) shortage = Qd - Qs.


384

price ceilingP

S1

D1

QQ1

P1

This screen is a repo of a previous screen. Imagine you are sitting at P1, do it! Where do you look for the ceiling? Down! Why not up?

A ceiling above P1 would cause a surplus and we know with a surplus the price will fall. It would fall to P1.

Pc


Price ceilings above equilibrium are not binding

Or are not effective!


385385

Production

In this section we want to explore ideas about production of output from using

inputs. We will do so in both a short run context and in a long run context.


386386

Production function

Here we will assume output is made with the inputs capital and labor. K = amount of capital used and L = amount of labor. The production function is written in general as Q = F(K, L),where Q = output,and F and the parentheses are general symbols that mean output is a function of capital and labor.The output, Q, from the production function is the maximum output that can be obtained form the inputs.


387387

Time Frame

In production, we have said that firms have the ability to use both capital and labor.

When you consider the fact that capital is basically the production facility – the building, equipment, machines and the like – you can get the feeling that it is probably less easy to change the capital than it is to change the amount of labor used.

When you look at how long it takes to change the amount of capital in production, during that time when capital can not be changed in amount the time period of production is said to be the SHORT RUN. When all inputs can be changed we are in the LONG RUN.


388388

Example

Say production of units of output follow the function

Q = 2KL. This means output is the multiplication of 2, the units of capital used, and the units of labor used. You can probably envision a table of numbers that puts units of labor across the top, units of capital down the side and inside the table is the output amount.

For example if we went down 1unit of capital and over to 2 units of labor and we would have output Q = 2(1)(2) = 4


389389

Long run

Labor

Capital On a curve we have different combinations of L and K that give the same amount of output. Curves farther out in the northeast direction have more output. Later we will say more about what the firm uses as a guide to choice of position in the graph. The position chosen will have implications for the amount of labor demanded.


390390

Short Run

Capital

Labor

K*

In the short run the firm would have a given amount of capital, say K* here. Production would occur along the dotted line.


391391

Short run/long run

The notion of a fixed or variable input is related to the time frame of production.The short run is that period of time when at least one input is fixed in amount. The long run is that period of time in which all inputs are variable.As an example of this consider fast food in Wayne. About any store in town could remodel and increase floor space in about 3 months. So after 3 months we have the long run, all inputs can vary - even floor space. But less than three months is the short run because there is only so much floor space to use.


392392

Labor

Capital

K=1

1 2 3 and so on

Q = 2

Q = 4

Q = 6

Say Q = 2KL. In short run say K=1.

Then if L = 1, Q = 2 and

if L = 2, Q = 4, and

if L = 3, Q = 6, and so on.

example


393393

Short run production function

Labor amount

Units of output Q

Typically in the short run we use the graph here instead of the previous one. We put the variable input on the horizontal axis and the output amount on the horizontal axis. Implicitly we have the capital amount fixed at a level when we draw the short run production function.


394394

Short run production functionexample Q = 2KL

Labor amount

Units of output Q

If K = 1 we have the production function Q = 2L. Some points would be if L = 1 Q = 2,

If L=2, Q=4 and so on. The graph is on the left here

1 2

4

2


395395

Short run Production example Q = sqrt(KL) when K = 4


396396

General short run example

Labor amount

Units of output Q

Here is a general short run production function. Notice 1) if labor input =0 output = 0, 2) initially output grows at an increasing rate when labor input rises, then 3) output grows at a decreasing rate (called diminishing returns), and 4) finally more labor may even make output start to decline.


397397

Malthus and diminishing returns

It has been suggested that enough production processes in the short run exhibit diminishing returns that we should take it seriously.

Malthus argued way back in late 1700’s that because of diminishing returns we would eventually starve to death. The fixed land (which places us in the short run) would eventually not be able to add food production at the rate at which the population increased.

In our model labor is the only variable input. In the real world there are many variable inputs. Technology has increased so much that Malthus has not been proven right, yet. Will he ever be proven right? Only time will tell (but I think NOT!)


398398

General example continued

In the general example, the relationship between the labor used and the total product (TP), or output Q, is called the short run production function. Behind the scenes we assume there is a given amount of capital.The marginal product of labor (MPL)is the additional output forthcoming from the additional unit of labor. Note that as the units of labor increases the marginal product first increases, but then begins to diminish after more labor is employed.


399399

example continued

The marginal product curve has the pattern it does because of the way the fixed input is used. Remember that the variable input is used in conjunction with only so much of the fixed input.In the beginning, as more labor is added, specialization of labor can occur and increasing returns to labor can result, but eventually as more labor is added there will be less of the fixed input to work with and thus additions to output have to diminish.The way output changes as the variable input is changed, with a given amount of a fixed input, is summarized with the phrase diminishing marginal product.


400400

The average product of labor (APL)is for each amount of labor the output produced divided by the labor amount.

The average product mimics, or follows, the marginal product. It is just a math thing.

Next let’s look at some graphs.

Definitions

APL = Q/L

MPL = change in Q / change in L

Example continued


401401

TP and MPL, APL

Marginal Product and Average Product

-100

0

100

200

300

400

0 5 10 15

Quantity of Labor

MP

and

AP

TP or Q

0

500

1000

1500

2000

2500

0 5 10 15

Quantity of Labor

Tota

l Pro

duct

of O

utpu

t

APL curve


402402

Notes about MPL and APL

Note 1)When the MPL is above the APL the APL rises.2)When the MPL is below the APL the APL falls.3)The APL continues to rise while the MPL is falling

only when the MPL is above the APL.


403403

APL from the graph of TP

Labor amount

Units of output Q

Q1

L1

I have reproduced the general short run production function, also called the total product, TP, curve. I have also put out a “ray” line through the origin. Note at L1 we get Q1. The APL = Q/L so at the point shown APL1 = Q1/L1.

Also note as you go along the ray line from the origin to the TP the slope of the ray is Q1/L1.

So the slope of the ray from the origin to the TP curve is the APL.


404404

APL from the graph of TP

Labor amount

Units of output Q

Q1

L1

Note 1) as labor is first increased the ray lines are moving from right to left and since the slopes are getting bigger the APL is rising, 2) at L* the ray is tangent to the TP curve and we can see the APL is at a maximum, and 3) beyond Y* the ray lines have less steep slopes and thus APL is falling.

L*


405405

MPL from the graph of TP

Labor amount

Units of output Q

Q1

L1

The MPL is the change in output divided by the change in labor. The MPL of an amount of labor is really the slope of the TP curve at the level of L used. A way to see the slope is to look at the slope of the tangent line at that point


406406

MPL from the graph of TP

Labor amount

Units of output Q

Q1

L1

Crazy graph, I know. Before L* the tangent lines have slopes that get bigger. But when the curve switches from increasing at an increasing rate to increasing rate at a decreasing rate it is before L*. So MP reaches it peak and begins to diminish before AP has reached its peak. At L* MP = AP.

Labor amount

Units of output Q

Q1

L1 L*


407407

Marginal analysis

It has been said economics is a science of marginal analysis. With this in mind, we see later MPL is the more interesting idea.

As an example of this, firms might ask, should another economist be hired?

By the way, when Q = 2KL and if K = 1, for example, we are in the short run. The APL = Q/L = 2L/L = 2, a constant, and MPL=2 as well.

You have to read pages 272-275 for a great example of why we focus more on margins than averages in economics.


408408

Long Run - isoquants

In the long run all inputs can be varied. On the next slide you see what we call an isoquant. Along the curve the amount of output is the same, but we have different combinations of K and L.

Again say Q = 2KL. To get one isoquant you pick a level of output. Say we pick Q = 100. Then we have

100 = 2KL. Since capital is on the vertical axis we might re-express this function as

K = 100/2L = 50/L. If L = 1 K =50 to get Q = 100. If L = 2 K = 25 to get Q = 100. Isoquants have properties similar to indifference curves for consumers.


409409

Marginal Rate of Technical Substitution - MRTS

Capital

Labor

Change in K Change in L

On the next slide I will refer to a change with the use of a triangle.

slope =

The MRTS = absolute value of the slope.


410410

MRTS

The slope of the curve at a point is

K/ L

Now, if the marginal product of an input is defined as the change in output divided by the change in the input, the slope can be manipulated to be:

K Q and since K = 1

L Q Q MPK

So the slope is MPL/MPK and is called the MRTS (in absolute value) and it is a measure of the rate at which inputs can be substituted and output remains the same.


411411

A few slides back I showed an isoquant. I also put a tangent line at a point on the curve. The slope of a curved line at a point is really the slope of a tangent line at the point.

You will notice that as you move along the curved line from left to right that the slope of a tangent line gets smaller (in absolute value).

Isoquants for perfect substitutes in production will be straight, downward sloping from right to left, lines.

Isoquants for perfect complements are L shaped. The production process is often called a fixed proportion process. An example would be you need a computer and a computer operator in many cases.


412412

LR – returns to scale

Remember in short run at least one input is fixed in amount. In LR all inputs can vary.

Returns to scale is idea that if all inputs are increased by a proportionate amount what happens to the amount of output. Since all inputs are changed it is a long run concept.

Example: We might be interested what would happen to output if all inputs were doubled.

It is not a done deal that if all inputs are increased in the same proportion that output will grow by that same proportion. But if it does the we say there are constant returns to scale.


413413

LR – returns to scale

If inputs are all increased by a proportionate amount and the resulting output grows by more than this proportion, then increasing returns to scale exists.

If inputs are all increased by a proportionate amount and the resulting output grows by less than this proportion, then decreasing returns to scale exists.

A given production function may exhibit each of these returns to scale at different ranges of output, with increasing returns happening first, then constant and finally decreasing returns happening.


414414

NOTE

Returns to scale is a long run concept when changing all inputs in the same proportion.

Diminishing returns is a short run concept when at least one input is fixed in amount and another input is changed in amount.

The two ideas are really not related in any general way.


415

Production and Costs in the Short Run


416

Overview

In this section we want to 1) Think about how production might occur and change as different amounts of inputs are used in the production process, and 2) Translate the production data into cost data. In other words, we will want to understand how the cost of producing various units of output might change as different amounts of inputs are used.


417

Fixed/variable inputs

Inputs can be classified as either fixed or variable.

A variable input is one that can be changed as the level of output is changed .A fixed input is one that can not be changed as the level of output is changed.

We often think of labor as a variable input and capital or land as a fixed input.


418

Short run/long run



419

example to illustrate some ideas

Quantity of L TP or Q MPL APL

0 0

1 5 5 5

2 12 7 6

3 21 9 7

4 28 7 7

5 33 5 6.6

6 36 3 6

7 37 1 5.285714


420

example continued

In the example, the relationship between the labor used and the total product (TP) is called the short run production function. Behind the scenes we assume there is a given amount of capital.The marginal product of labor is the additional output forthcoming from the additional unit of labor. Note the first unit of labor has a marginal product of 5.

Note that as the units of labor increases the marginal product first increases, but then begins to diminish after the third unit of labor is employed.


421

example continued



422

The average product of labor is for each amount of labor the output produced divided by the labor amount.




423

TP and MPL, APL

TP or Q

05

10152025303540

0 2 4 6 8

Units of labor given an amount of capital

Tota

l Pro

duct

or Q

uant

ity

of o

utpu

t

Marginal Product and Average Product of Labor

0

2

4

6

8

10

0 2 4 6 8

Units of labor

MPL

, APL MPL

APL


424





425

short run costsIn the short run we will consider the fixed and variable costs of production and how they change as more of the variable input is used.Definitions:Total cost (TC) = Total variable cost(TVC) + Total fixed cost (TFC).Marginal cost(MC) = (change in TC)/(change in output). where change in output = 1 when possible.Average cost (AC) = TC/Q.Average variable cost(AVC) = TVC/Q.Average fixed cost(AFC) = TFC/Q.Note that in the short run fixed costs must be paid whether output is zero or 100,000 units.


426

example

Let’s take the production example we had before and translate the production data into cost data. Say the cost of capital is $50 and the cost of labor is $15 per unit.The next screen shows the continuation of our example.


427

example to illustrate some ideas

Q VC FC TC AVC AFC AC MC

5 15 50 65 3 10 13 3

12 30 50 80 2.5 4.17 6.67 2.14

21 45 50 95 2.14 2.38 4.52 1.67

28 60 50 110 2.14 1.79 3.93 2.14

33 75 50 125 2.27 1.52 3.79 3

36 90 50 140 2.5 1.39 3.89 5

37 105 50 155 2.84 1.35 4.19 15


428

COST Curves

Totals

0

50

100

150

200

0 10 20 30 40

OUTPUT

Dolla

r cos

t

VC

FC

TC

Averages and Marginal

02468

10121416

0 10 20 30 40

OUTPUT

Cost

s pe

r uni

t

AVC

AFC

AC

MC


429

Idealized graph of per unit costs in the short run

$/unit

Q

MC

AC

AVC

Note AVC and AC equal MC when AVC and AC are at their minimum values.


430

When you look back at slide nine at the marginal product and average product curves note that the horizontal axis is measuring labor units used and the curves are inverted u-shaped curves.

When you look back at slide 14 at the marginal cost and various average cost curves note that the horizontal axis is measuring output units and the curves are u-shaped curves.

There is a relationship between these two graphs


431

The marginal cost of production is the change in total cost divided by the change in output.

The marginal product of labor is the change in output divided by the change in labor.

MC = ▲TC/▲Q, and MPL = ▲Q/▲L, so

MC = ▲TC/(MPL ▲L) = price labor/MPL.

Supply, Demand and Equilibrium


433

A basic diagramPrice perunit or $/unit orjust P

Quantity perunit of time orQ

A

B

C

origin

PA

QA

In this chapter we want to ultimately work with a diagram like the one here. The diagram will be our representation of a market for a product during a period of

time -like the market for cups of coffee per day.


434

observation, theory

In the real world we could observe on a given day the price of a cup of coffee and see how many cups are sold. Point A in the diagram on the previous screen, for example, has QA being observed in combination with price PA.We have a theory that the observed combination represented by the point is a point where the supply and the demand for the product are equal - a notion that economists call an equilibrium point.


435

change

We know prices and quantities change over time - like from point A to point B - and we have a theory about this as well. We will see changes in P and /or Q result from changes in economic variables that cause supply and/or demand to shift.But the points we see in the diagram are points where supply and demand are equal - perhaps after shifts.


436

explore

In this chapter we want to explore1) concepts of demand,2) concepts of supply,3) the interaction of supply and demand - equilibrium, and4) the application of taxation in a market for a product.


437

Demand

Demand, in general, refers to how much of a product consumers want during a particular time period. The amount consumers want is influenced by1) the price of the product,2) the consumer desire or taste and preference for the product,3) the level of prices of other goods,4) the level of consumer income, and5) the level of sales taxes or subsidies.


438

The law of demand

The law of demand is our summary statement about how the price of a product influences how much we want. The law is a statement that the price and quantity demanded are inversely related.In a later chapter we will see why economists think the law of demand holds true, but for now we will accept this notion.


439

Change in demand

If any of the items from our list from 2 to 5 should change, then we say there is a change in demand. Economists treat items 2 through 5 differently than the price item. If the price should change we say there is a change in the quantity demanded.

The logic behind this difference is the desire to use graphs as an aid to economic understanding. The graphs used most often are of only two dimensions. Q and P are the two primary variables of interest. Other variables may be of interest and so a different term is used to indicate those situations.


440

change in demand in a graph

P

Q

P1

P2

Q1 Q2

D1 D2

As a consumer if you think about items 2 through 5 in our earlier list, when you see those items as being stable you then have a certain demand for the product. In a graph this means you demand curve is located at a certain place. Let’s say yours is at D1.

If the price should fall from P1 to P2 the movement from Q1 to Q2 is called a change in the quantity demanded - we move along the curve. If an item from our list 2 to 5 should change(and we started at P1) the movement from Q1 to Q2 is called a change in demand - the curve shifts.


441

A sales tax on consumers

Except for the sales tax, we will wait until chapter 4 to really work through our list of concepts that influence how much of a product you and I want to buy.P

Q

D1

P1

Q1

Say that at a certain time there is no sales tax on an item. Then if the price is P1, Q1 is the quantity demanded. We will consider a sales tax one where the consumer pays a tax directly to the government.


442


With a sales tax not only does the consumer have to pay the merchant, but money must be sent to the government as well. The amount paid to the merchant is called the price of the product. The amount the customer ultimately takes out of their pocket for the product is the price plus the tax.Your first inclination, when I say the product now has a lump sum tax of 10 cents per unit on it, would be to say the demand curve should shift up by 10 cents - P is paid to the merchant and the tax is added on and paid to the government. Let’s look at how we really want to handle this situation.


443


Without a sales tax the amount the consumer pays the merchant and the amount taken out of pocket are the same. What really matters to the consumer is how much is taken out of the pocket.Say P1=50 cents and Q1=2 cups of coffee per day. Then before a tax the consumer is willing to pay $1 per day for coffee.Now say a tax of 10 cents per cup is imposed on the consumer. But the consumer wants 2 cups of coffee when $1 comes out of the pocket. With this tax the only way this is going to happen is if the price per cup is now 40 cents.


444


This doesn’t mean the seller will lower the price to 40 cents!!! It just means the consumer will not demand 2 cups unless the price is 40 cents per cup.Thus the demand curve shifts DOWN by the amount of the tax. In our analysis we like to draw the demand curve both before and after the tax.


445

effect of sales tax on the demand curve

P

Q

D1D2

D1 = demand curve before taxD2 = demand curve after tax

Note1) If Pbt is the price before the tax the quantity demanded would be Q1.2) With the tax Q1 will only still be demanded if the price is Pat. Then the

Q1

Pbt = Pat +tax

Pat

consumer will still only have to take out of their pocket Pbt for Q1.


446

Supply

Supply, in general, refers to how much of a product sellers want to make available during a particular time period. This amount is influenced by1) the price of the product,2) the level of costs of inputs to production,3) the level of technology in production, and4) the level of an excise taxes.


447

Law of supply

The law of supply is the statement that the price and the quantity supplied are positively related.We will see about why this is the case later, but let’s just accept this statement for now.


448

Change in supply

If items 2 thru 4 in our list should change the supply curve will shift and we say there has been a change in supply. Note a decrease in supply is a leftward movement of the supply curve. The amount supplied is measured horizontally, i.e., rightward and leftward.P

Q

S2 S1

S2 represents a lower supply.


449

excise tax

An excise tax is a tax on the seller of a product. We treat the tax as a cost of doing business. If there is no tax the seller will offer Q1 for sale when the price is P1. In other words the seller is indicating they need P1 to supply Q1.

Q

S1

P

P1

Q1


450

excise taxIf a lump sum excise tax is imposed then the seller still needs to get P1 for their own efforts in order to supply Q1. This means the price in the market will have to be P1 plus the tax to supply Q1. Thus the supply curve shifts up by the amount of the tax.

Q

S1

P

P1

Q1

P2 = P1 + tax

S2


451

Something seems weird about the sales tax and the excise tax when I compare the two.

The sales tax is paid by the consumer. So prices on the demand curve WILL NOT include the sales tax because consumers know after they take the item they will also have to pay the tax to the government. But, consumers only want to pay a certain amount for a good or service, regardless of taxes or not.

The excise tax is paid by the producer. So prices on the supply curve WILL include the excise tax because after the suppliers get the money they have to send some on to the government and the suppliers still need to get the amount they want for the item sold.


452

Equilibrium

Equilibrium in a market is a situation where1) Buyers can buy all they want at the price considered and2) Sellers can sell all they want at the price considered.

If both situations do not occur there is a force for change in the market. Equilibrium is the absence of a force for change.

Equilibrium in a market occurs where supply and demand cross.


453

EquilibriumP

D1S1

P1

Q1

Any price above P1 is not equilibrium because sellers can only sell the amount buyers will buy and above P1 there is a surplus so sellers have a force for change - lower the price.

Qd QsAt the higher price the quantity supplied is greater than the quantity demanded and since you can only sell what buyers buy, Qs – Qd is a surplus.


454

EquilibriumP

D1S1

P1

Q1

Any price below P1 is not equilibrium because buyers can only buy the amount sellers will sell and below P1 there is a shortage. So, buyers have a force for change - raise or bid-up the price.


455

Change in EquilibriumSteps to analysis1) start out at initial equilibrium,2) see a condition change - item 2 to 5 on demand and/or 2 to 4 on supply change,3) Shift the appropriate curve the appropriate direction,4) at initial price note if excess supply or demand results,5) move to the new equilibrium point, and6) compare the new equilibrium with the initial equilibrium.


456

effect of sales tax on the market

P

Q

P2 + taxP1

P2

S1

D1D2

S1 = supply curveD1 = demand curve before taxD2 = demand curve after taxP1, Q1 = initial equil.P2, Q2 = new equil.

Note1) Q2 < Q1 - lower output2) P2 < P1 - lower market price3) Consumer pays P2 to the seller and pays a tax on each unit purchased to the government,the total paid per unit is P2 + tax.

Q2 Q1


457

effect of sales tax on the market

4) Tax = P2 + tax - P1 + P1 - P2

Amount of increase in per unitpay out made by the consumer.

Amount of decrease in the per unit amountseller receives.


458

effect of excise tax on the market

P

Q

P3P1

P3 - tax

S1

D1

S1 = supply curve before taxD1 = demand curve S2 = supply curve after taxP1, Q1 = initial equil.P3, Q2 = new equil.

Note1) Q2 < Q1 - lower output2) P3 > P1 - higher market price3) tax = P3 - P1 + P1 - P3 + tax = P3 – P1 + P1 – (P3 – tax)

Q2 Q1

S2

increase in amount paidby consumer on per unit basis

decrease in amount seller keeps after the tax, per unit


459

Comparing excise and sales tax

P

Q

S1

D1

Q2 Q1

S2

D2

If the excise tax and the salestax are of the same amount,but only one is imposed,we would end up at Q2.

Pd is what consumers takeout of pocket, Ps is what sellers keep and Pd - Ps is the tax(all on a per unit basis).

Pd

Ps

The economic incidence of a marketplace tax is independent of its legal incidence. In other words, sales or excise taxes have the same real impact on the market.


460

Hey you ever heard of a wedgie, or what is sometimes called a herman? Well, I am not going to talk about that now. I wanted to talk about a wedge. In our supply and demand graph we have seen that when a per unit tax is imposed on the buyer the demand shifts down by the amount of the tax and when a tax is imposed on the seller the supply shifts up by the amount of the tax.

This vertical line here is the amount of the tax. I have shown my right hand as well because I am going to push the line with my hand into a supply and demand graph on the next few slides and WEDGE the tax into the S & D curves. Here goes.


461

Q

P

S

D


462

Q

P

S

D


463

Q

P

S

D


464

Q

P

S

D

So, you can see by the graph, when we wedge the tax into the graph we can see either the demand shifts down by this amount or the supply shifts up by this amount. We end up at the same market quantity and our story is the same as before.


465

The budget constraint

Consumers need income to buy goods and they must pay prices.

These features limit what the consumer can have.


466

Budget constraint or budget line

The budget constraint for an individual shows combinations of x and y that can be attained given a certain income and assuming prices must be paid for the goods.

The constraint will be a line in a graph where the amount of x is measured horizontally and the amount of y is measured vertically.


467


If I = the consumer income in dollars Px = the price per unit of x Py = the price per unit of y x = the amount of x the consumer buys y = the amount of y the consumer buys, then the amount the consumer buys is

I = (Px)(x) + (Py)(y) or y = (I)/(Py) - [Px/Py](x)

Note if x = 0, y = I/Py and if

y = 0, x = I/Px and the slope of the line is - (Px)/(Py).


468

Budget constraint

y

x

(0, I/PY)

(I/Px, 0)

-Px/Py This is the slope – a negative number.


469

Budget constraint

y

x

The slope of the budget line is - Px/Py. Say x = a bag of chips and y = a can of pop. If Px = $1/bag and Py = .50/can, then

- Px/Py = -($1/bag)

($.50/can)

= - 2 cans/bag

2

1

The slope of the budget line indicates that if one bag of chips is given up, 2 cans of pop can be obtained in the market. This occurs at every point on the budget line when prices remain constant in relation to the amount bought.


470

slope

Note on the previous screen that the slope of the budget line is telling us about how much good x is valued in the market in relation to good y.

This implies that the slope of the budget is indicating the market rate of substitution of good x for good y.

The slope of the budget is the relative price of x.


471

Example

Say a consumer has $20 bucks to spend and good x costs $5 per unit and good y costs $4 per unit.The graph of the budget line would be

x(4, 0)

y

(0, 5) The slope is -5/4 = -1.25. This means that if 1 x is given up 1.25 y can be obtained.


472

NOTE

Sometimes a question in the book will have something about showing me a graph. Instead of having you draw the graph electronically you can just tell me about both intercepts and the slope of the line. That way you do not have to draw the graph.


473

Indifference curves

Indifference curves represent a summary of the consumer’s taste

and preferences for various products.


474

There is no accounting for the taste of the consumer. Consumers like what they like(various things influence what they like - advertising, customs...). Consumers derive utility or happiness by consuming goods and services. In economics we summarize the likes or tastes of the consumer by using indifference curves.

An indifference curve shows different combinations of goods that give the same level of utility to the consumer.


475

Diagram used in analysis

good y

good x

The amount of good y a consumer may have is measured vertically

The amount of good x is measured on the horizontal axis.This type of diagram is used extensively when considering the behavior of consumers.


476

Indifference curves - definition

As mentioned earlier, an indifference curve shows various combinations of goods that yield some specific level of utility or satisfaction for the individual.

y

x

A

B

This is one type ofindifference curve. We assume the individual is equally happy at point A or B or any other point on the indifference curve.


477

Indifference curves - feature 1

We assume more goods are preferred to less and thus indifference curves slope downward to the right.

2 1

3 4

y

x

Say the individual is at the point in the middle of the graph. Keep thisin mind as we explorethe following screens.


478


If the individual is at the point in the diagram, then all those points in area 1 and on the boundary are more preferred because those points have either more of both items or more of one and the same amount of the other item compared to the point chosen.

Points in area 3 and the boundary are less preferred to the point in the diagram because the point chosen has more of both items.


479


An individual may think that points in areas 2 and 4 are preferable, less preferred or equally desirable to the point indicated.

Since areas 2 and 4 are the only ones that could have a point of indifference to the one chosen, the indifference curves must have negative slope.


480

slope

In economics we often use graphs and with graphs you can look at the concept called slope. Often in economics the idea of slope will have an economic interpretation. Let’s review the idea of slope.

Slope = rise/run.

With a curve that slopes downward from left to right the slope is a negative number.

With a curve that slopes upward from left to right the slope is a positive number.


481


y

x

A

B

Say the consumer is at point A. If the consumer gives up one unit of x, m units of y must be given back to hold the consumer at a constant level of utility.

You could say the consumer is willing to trade 1 unit of x to get m units of y.

m

1


482


The shape of the indifference curve on the previous screen is said to be convex.

Part of the reason for this is that it is assumed that the amount of good y one receives in return for one unit of x depends on how much of each the individual starts out with.


483

Indifference curves - feature 2y

x

A

B

You can tell that point A has less x than at B. As the individual takes even one less unit of x from either point A or B, some y must be given in return. But more is given in return if point A is the initial point.

The point is the less you have of something(like x atpoint A compared to point B), the more of other things you must be given in return to compensate for the loss of the one unit, assuming the same level of utility is obtained.


484

Indifference curves - feature 2 The marginal rate of substitution(MRS) is the

amount of y given in return for the one unit of x, while maintaining the same level of utility.

We can think of the MRS as a fraction: MRS=absolute value of (change in y)/(change in x) .

In this sense, the MRS is the absolute value of the slope of the curve at various points. Note the slope changes from point to point. In absolute value the fraction gets smaller the farther down the curve one moves. This is another way of saying the curve gets flatter.


485

feature 2

In general, it is assumed that consumers value additional units of a good less and less the more they have of the good. (Or you could say when consumers give up good x they require more and more of good y the less of good x they start with.) The indifference curve gets flatter.

This notion is summarized with the phrase – diminishing marginal rates of substitution.


486


x

Indifference MapEvery point in the graphhas one, and only one,indifference curve running through it.Curves farther out fromthe origin have more utility. So, the consumer can compare every bundle and make a determination of preference or indifference.


487


x

Indifference curves for an individual do not cross. Say they did, like in this diagram. Thenindividual would be indifferent to A and B,indifferent to A and C,and thus by logic should be indifferent to B and C.

AB

C

But C has more of both goods compared to B and thus Cis preferred to B. So the curves can not cross for an individual. Transitivity of preferences holds.


488


Different people can have different general shapes of indifference curves. Some are relatively steep and some are relatively flat.

On the next slide I will put two peoples’ indifference curves and they will cross. Before we said one individual’s curves could not cross.


489


y

x

Mr. A

Mr. B

Note how Mr. A has a steeper curve than Mr. B. From the point where the curves cross if both give up a unit of x, note how Mr. A has to be given more y tomake up for the loss of x than Mr. B. Mr. A is said to have a relatively strong preference for x because he needs much more y in return for the one unit of x given up.


490

A math example of a utility function might be

U = sqrt(XY) – this means utility is a function of the square root of the product of the amount of x and the amount of y a person would get.

To get an indifference curve pick a value of U. Let’s say U = 4. Then some points on the indifference curve would be

X Y

16 1

1 16

4 4

8 2

2 8


491

indifference curve when U = 16

1, 16

2, 8

4, 48, 2 16, 10

5

10

15

20

0 5 10 15 20

X

Y y


492

Utility maximization

The goal of the consumer is to maximize utility given the budget constraint. Let’s see what that

means.


493

y

x

I show the budget line here again. What the consumer attempts to do is find the point on the budget line that will give the maximum utility. I show some arrows to get you to think about moving up and down the line in this search.


494

Here I present a few ideas we think hold in the world and then we see how they show up in the graph.

The consumer wants to maximize the utility, or happiness, that can be achieved when consuming goods and services.

At a given level of happiness the consumer will always give up a unit of a good if on the other good in the market an amount greater than required to maintain the given level of utility is returned. The consumer will also be happier than at the start. As an example, say you are willing to take 0.9 Cokes to give up a Pepsi, and you would be as happy. If in the market when you give up a Pepsi you get 1 Coke back you then you would give up the Pepsi and be happier.


495

A related idea is that

At a given level of happiness the consumer will always take another unit of a good if on the other good in the market an amount less than required to maintain the given level of utility must be given up.

As an example, say you will take another hamburger if you give up 2 hotdogs. If the market only requires you to give up1.5 hotdogs, the you would take the hamburger and you would be happier.

Note: Remember that because of the shape of the indifference curves that the amount you are willing to give up of a product (or an amount you would take) depends on how much you already have and thus changes along the indifference curve.


496

Utility Maximization

The individual would like to get to the highest indifference curve possible, but the budget constraint restricts the individual’s options to the budget line.

On the next slide let’s see what is the best the individual can do. But, before we do remember 1) indifference curves summarize how consumers are willing to trade off good x for y, and 2) the budget line shows how the consumer can trade off good x for good y.


497

Utility Maximizationy

x

a

b

c

u1u2

u3

Because of the budget line u3 can not be reached

u1 can be reached atpoints c and b, but even more utility would beobtained if the individualwent to point a on u2.The utility associated with u2 is the maximum this

personcan achieve given their income and the prices they face.


498


b

Note why b from the previous screen was not the best point. To give up a unit of x and maintain the sameutility the person needed to get back a certain amount of y. But the market actually gives back more ythan the individual requires. This trade is beneficial.The individual would thus give up the unit of xand be happier for the trade.

y

x


499


Note why c from two screens ago was not the best point. To take a unit of x and maintain the sameutility the person is willing to give up a certain amount of y. But the market actually requires the individual to give up less. This is a beneficial trade. The individual would thus take the unit of x and be happier for the trade.

cy

x


500


In the final analysis, the individual maximizes utility when the indifference curve is tangent to the budget line.

Tangent means equal slopes.

a b c

d

Consumer SurplusWhen consumers buy products in the market they may pay less than the full amount they are willing to

pay – they receive consumer surplus.


502

Do you want to buy some eggs?

Who here would buy a dozen eggs for $1.59?

Who would pay $1.29?

Say the actual price of the dozen is $0.89. Do you think the buyers would pay the $1.29 to the grocer when the grocer has a sign out that says $0.89?

So if consumers are willing to pay, in this example, more than $0.89, then they receive an extra benefit in the market called consumer surplus.


503

consumer surplusConsumer surplus is an idea people I know have a hard time accepting. Consumer surplus equals the maximum amount you are willing to pay for an item minus what you have to pay. It seems the hard part is distinguishing between what you have to pay and what you would be willing to pay.

The amount you would be willing to pay is on the demand curve for each unit of the product. In fact the law of demand is an expression that you are not willing to pay as much for additional units as you did for previous units. The amount you have to pay is market determined.


504

Willing to payP

21

18

1512

1 2 3 4

24a

b c

d e f

g h i j

k l m n

When the price is 24, 0 units are demanded. At P=21, 1 unit is demanded. 21 is the maximum price this person would pay for the first unit. Let’s say the market price is 10. Then the surplus on the first unit is 11. The surplus on the2nd....................…,3rd....................... units is?

Q


505

willing to payYou will notice on the previous screen at price 21, the quantity demanded is 1. The area b + d + g + k equals the $21 the consumer would pay for the 1st unit. The area a is under the demand curve but not part of what the consumer would be willing to pay for the first unit. We will add in area a to calculate the consumer surplus. It makes the calculation easier. The second unit would be demanded if the price is 18. The area e + h + i = $18. The area c is under the demand curve but not part of what the consumer would be willing to pay for the second unit.


506

willing to pay

The point I am getting to on the previous screen is if we add in areas like a and c, that are really not a part of what consumers are willing to pay, we have an easier calculation to find out what consumers are willing to pay for a certain number of units. It is simply the area under the demand curve out to a quantity.

P

QQ1

What consumers are willing to pay for the Q1 units


507

Consumer surplus againP

25

10

300 Q

A

B

Area A = .5(300)(25-10) =2250

Area B = 10(300) = 3000

Note consumers would be willing to pay 3000 + 2250for 300 units.But the consumers only have to pay 3000 for the

300 units.So the consumer surplus is area A and equals 2250.

Say with S & D we get the P = 10 and Q = 300.


508

Refresher on areas

The area of a triangle is ½ of the base times the height.

The area of a rectangle, of which the square is a special case, is the base times the height.

We use these ideas from time to time because they assist in the development of economic ideas.


509

consumer surplus again

What do consumers do with the surplus received?

They may spend it on more units of the item in question, they may spend it on other items, or they may save it for a rainy day.

The point here is that the surplus is useful to the consumer!

Cost in Math Form and Perfect Competition in Math Form.


511

Say we have a cost function of the general form

TC = f + aQ + bQ^2 + dQ^3, where the sign ^ means raise to a power.

Note the term f has no Q “hooked” on to it so f represents fixed cost, and all the terms with a Q are part of variable cost:

TFC = f = total fixed cost

TVC = aQ + bQ^2 + dQ^3 = total variable cost.

Now, it is possible that a, b, and d are positive or negative, or even 0.

Looking at averages we have

AFC = f/Q, AVC = (aQ + bQ^2 + dQ^3)/Q = a + bQ + dQ^2,

And ATC = AFC + AVC = TC/Q.


512

To get the marginal cost from a TC of the formTC = f + aQ + bQ^2 + dQ^3, you haveMC = a + 2bQ + 3dQ^2.

Example 1 TC = 100 + Q^2Note f = 100 and a=0, b=a, and d =0.

AFC = 100/Q, AVC = Q and MC = 2Q.

Say this firm operates in a perfectly competitive market where the price is $10.From my notes the production rule says go to the quantity where P = MC, so 10 = 2Q, or Q = 5. The operating rule says only do this if P > AVC. Here AVC = Q and at Q = 5 AVC = 5 and thus P is > AVC. SO the best thing to do is make Q=5.


513

Profit = TR – TC = PQ – [TC/Q]Q = [P – ATC]Q

Here I used a trick that TC times 1 written as Q/Q gives [TC/Q]Q = ATCQ.

Thus, profit = [P – ATC]Q.

In our problem we have [10 – 25]5 = -75. So, the best this firm can do is lose 75. But, note if it shut down it would still have fixed cost of 100 that would have to be paid. So, it is better off operating in the short run while it has the 100 fixed cost.

Example 2 – same cost, but say the price in the market is 20. (note this problem is not exactly like demo problem 8-1)

Produce Q where P = MC: 20 = 2Q, or Q = 10.

Make sure P > AVC: AVC here is 10, so with P > AVC operate.

Profit = [20 – 20]10 = 0.

Demand in Mathematical Terms

Here we want to look at the presentation of demand in math

terms so that we can use the concept in making decisions.


515

Review

We know that how much of a product consumers want depends on 1) the price of the product,2) the consumer desire or taste and preference for the product,3) the level of prices of other goods,4) the level of consumer income, 5) the number of consumers in the market.

In a general mathematical sense we may summarize this with the following

Qx = f(Px, Py, T, M, N) .


516

general math form

On the previous screen

Qx = the amount people want of good x,

f means is a function, note the parentheses here is not a multiplication sign,

Px = the price of good x, Py = the price of good y,

T = a measure of consumer taste, M = consumer income,

N = a measure of the number of consumers in the market.

So, the amount people want depends on or is a function of these influences listed in parentheses.


517

Linear demand

A linear demand curve might be of the form

Qx = a0 + axPx + ayPy + aMM.

Note the a’s with subscripts just means we have a number here. Many books use the greek letter alpha here. The a’s may be positive or negative.

As an example say we have

Qx = 1000 - 3Px + 4Py - .01M


518

Linear demand

Now if Px = 1, Py = 1 and M = 50,000

Qx = 1000 – 3(1) + 4(1) - .01(50,000)

= 1000 – 3 + 4 – 500

= 501.

Once we have the from and coefficient values of the relationship between the variables we can make “predictions” about how much people want based on the value of prices and income and other variables.


519

Market demand

The market demand is the demand from each individual added together. Say in a market we have two buyers. The demand from each is

Q = 10 – 1P, and Q = 20 – 2P, respectively. (you will notice I only have the price term listed. All the other influences are captured in the Q intercept.)

Now, if the price is $1 per unit, the demand is 9 and 18, respectively. So the market demand is 27. Here is how we add the demand functions of each individual to get the market demand : (next screen)


520

Market demand

Q = 10 – 1P

Q = 20 – 2P

Q = 30 – 3P

Notice on the left side on the addition I did not put 2Q. The reason is due to the notation used. The Q for each person is personal, but I just used Q. You can see at a price of 1 the Q is not the same for each person. (We just did this last screen.)

Notice the market demand curve Q = 30 – 3P does add up the demand from each individual at a given price. If P = 1 we have a market demand of 27 (= 9 + 18).


521

Inverse Demand curve

We just saw a market demand curve of

Q = 30 – 3P. I could rewrite this as P = 30/3 – (1/3)Q. When written with P on the left we call the demand curve the inverse demand curve. We write it this way because in a graph we typically have the price on the vertical axis and so the equation follows that convention. In general we write

P = A – BQ.

(Note: do not add individual demand curves when written in inverse form – you do not get what you want.)


522

Nonlinear demand

Demand may not be a linear function. A popular nonlinear form takes the form

Qx = cPxBxPy

ByMBMHBH. An example would be

Qx = 10Px-1.2Py

3M.5H.3 . An interesting thing about this form is if you take the natural log (sometimes written Ln)of each side you get

log Qx = 10 – 1.2 log Px + 3 log Py + .5 log M + .3 log H .

This nonlinear demand is said to be linear in logs.


523

Natural log

On the previous screen you see we have the amount demanded in the form of a natural log. To get the value in the terms you and I are used to you would take the value given and make it the exponent of the term e.

Microsoft excel has the the function ln to put values into natural log form. To get out of natural log form use the exp function.

Qualitative Independent Variables

Sometimes called Dummy Variables


525

In the simple and multiple regression we have studied so far the dependent variable, y, and the independent variable(s), x(s) have been quantitative variables. But the regression can be used with other variables. We will study the case where

The dependent variable, y, is quantitative,

One (or more, in general) independent variable is quantitative, and,

One independent variable is qualitative.

Remember that a qualitative variable is of the type where different values for the variable are just categories. Some examples include gender and method of payment (cash, check, credit card).


526

An example

y = the repair time in hours. The company provides maintenance and it would like to understand why the repair time takes as long as it does. With an understanding of repair time maybe it can schedule employee hours better or improve company performance in some other way.

x1 = the number of months since the last repair service was performed. The idea is that the longer since the last repair the more that will be need to be done. The is a quantitative variable.

x2 = the type of repair service needed. In this example there are only two types of repairs – electrical and mechanical.

So, the company has clients that need repairs and the company is exploring what accounts for the time it takes to make a repair.


527

On the next slide I have a graph where two quantitative variables are on the axes. The two ovals represent the “cloud” of data points. Here the points suggest a positive relationship between months since last repair and repair time. Of course, we will have to test if this is the real case or not, but the graph suggests that is the case.

I have two ovals because it is thought that maybe each type of repair has a different impact on repair time. The different ovals represent what is happening for each type of repair and here I am suggesting that there is a difference in repair time for each level of repair type. Here we will also do a test to see if the different types of repair lead to different repair times.


528

Repair time

Months since last repair


529

The model

Here the regression model is

y = Bo +B1x1 + B2x2. When we estimate the model we use data on y and x1 and x2. Here we make the data for x2 special. We will say that x2 = 0 if the data point is for a mechanical repair and x2 = 1 if the data point is for an electrical repair.

Now, when we look at the model for the two types of repair we get the following: When x2=0

y = Bo + B1x1 + B2(0) = Bo + B1x1, and when x2 = 1,

y = Bo + B1x1 + B2(1) = Bo + B2 + B1x1. The impact of creating x2 as a 0, 1 variable is that when the value is 0 we have one line and when the value is 1 we have another line with a different intercept. The intercept is Bo with the mechanical repair and the intercept is Bo + B2 with the electrical repair.


530


531

Getting and interpreting the results:

The previous slide has the Excel printout for this regression model. The interpretation starts with the F test. The null is that both B1 and B2 are equal to zero. Here the F stat is 21.357 with a p-value (Significance F) = .001. Then we would reject the null with alpha as small as .001 (certainly we reject at alpha = .05) and we go with the alternative that at least one of the beta’s is not equal to zero. In other words, as a package the x’s exhibit a relationship with the y variable.

The next step is to do the t tests on each slope value B1 and B2 (even here we tend to ignore the test on Bo because we typically do not have much data with all the x’s = 0) separately. Here the p-values on both have values less than .05 so we reject the null and conclude each variable has an impact on y.


532

Repair time

Months since last repair

.9305

.9305 + 1.2627

Mechanical y = .9305 +.3876x1

Electrical y = (.9305 + 1.2627) + .3876x1


533

On the previous slide I reproduced the graph I had before, and I added the equations for repair time under each value of x2.

When x2 = 0 we have the line for mechanical types of repair. When x2 = 1 we have the line for electrical types of repair. Ultimately the difference in the two lines here is in the intercept. But, the slope of each line is the same. This means that months since the last repair has the same impact on repair under either type of repair. Since b2 = 1.2627 (really since we rejected the null that B2 = 0) the electrical line has a higher intercept. We can use each equation to predict repair time given the value of months since last repair, and given the type of repair. Of course, if the type is mechanical we use the mechanical line and we use the electrical line for the electrical type.

The next thing we would do is evaluate R square. Here the value is .8592 and this indicates that just over 85% of the variation in y is explained by the x’s.


534

The qualitative variable

In our example we had a qualitative variable with two categories. Note we added 1 x variable for this 1 qualitative variable. The reason is because the 1 variable had 2 categories. Now if the 1 qualitative variable has 3 categories we would have to have 2 x variables. Say we had mechanical, electrical and industrial repair types. We would need x2 and x3 variables, in addition to repair time, x1.With 3 categories we would have 3 lines. When x2 = 0 and x3 = 0 the intercept would be Bo for the mechanical line.When x2 = 1 and x3 = 0 the intercept would b Bo + B2 for the electrical line (assuming the tests had us reject the null).When x2 = 0 and x3 = 1 the intercept would be B0 + B3 for the industrial line.


535

In general, if the 1 qualitative variable has k categories, we add k-1 x’s. When all the x’s are zero we have intercept Bo and the line represents the equation for 1 of the categories and then the other x’s account for the change from Bo the other k-1 category values have.

Summary

1 qualitative variable would have k lines associated with it (assuming tests reject Ho) and we add k-1 x’s of the 0,1 type to account for all the k categories. 1 category is made the “base” category and its line will have intercept Bo and the other categories will have intercept Bo + Bt, where the t would be different for each case of the other categories on the variable.

The budget constraint

Consumers need income to buy goods and they must pay prices.

These features limit what the consumer can have.


537


The budget constraint for an individual shows combinations of x and y that can be attained given a certain income and assuming prices must be paid for the goods.

The constraint will be a line in the graph we saw before – you know the one, the one where the amount of x is measured horizontally and the amount of y is measured vertically.


538


If I = the consumer income in dollars Px = the price per unit of x Py = the price per unit of y x = the amount of x the consumer buys y = the amount of y the consumer buys, then the amount the consumer buys is

I = (Px)(x) + (Py)(y) or y = (I)/(Py) - [Px/Py](x)

Note if x = 0, y = I/Py and if

y = 0, x = I/Px and the slope of the line is - (Px)/(Py).


539

Budget constraint

y

x

(0, I/PY)

(I/Px, 0)

-Px/Py This is the slope – a negative number.


540

Budget constraint

y

x

The slope of the budget line is - Px/Py. Say x = a bag of chips and y = a can of pop. If Px = $1/bag and Py = .50/can, then

- Px/Py = -($1/bag)

($.50/can)

= - 2 cans/bag

2

1

The slope of the budget line indicates that if one bag of chips is given up, 2 cans of pop can be obtained in the market. This occurs at every point on the budget line when prices remain constant in relation to the amount bought.


541

slope

Note on the previous screen that the slope of the budget line is telling us about how much good x is valued in the market in relation to good y.

This implies that the slope of the budget is indicating the market rate of substitution of good x for good y.

Remember the indifference curve slope was indicating how much of good x a person was willing to give up to get more of good y.

The slope of the budget is the relative price of x.

Introduction


543

Introduction

What is managerial economics going to do for you?

Among other things, by studying this course you will gain insight into pricing and output decisions by firms,input mix and production choices by firms, andgovernment intervention in markets.

Note economics is a science where decisions in the presence of scarce resources are studied.


544

Assume

In economics it is assumed that individuals have objectives and goals in mind that guide their actions. For example, businesses attempt to maximize profit and consumers attempt to maximize utility.

What would a manager of a social service agency have as an objective?

Economic Profit

When the term profit is used in economics it is usually a short way of saying economic profit.

Let’s see what this means.


546

Example

Say I am planning to open my own entertainment establishment, called Parker’s Pool Hall. I will have explicit costs for the pool tables, pinball machines, labor and electric I use.

Say these explicit costs add up to $10,000 a year. If the revenue to the firm is $60,000 a year, the accounting profit (revenue – explicit costs) is $50,000.

How do you think I would feel if I gave up a job where I made $40,000 a year and I could have rented out the building where the pool hall is located for $15,000?


547

Implicit costs

Notice the $60,000 in revenue pays the explicit costs of $10,000, pays me the $40,000 I gave up in a job, and only pays $10,000 of the $15,000 in forgone rent.

I end up short $5,000 (I always end up short – slow too!) in the entertainment business, compared to what I was doing before.

The forgone income and rent are examples of implicit costs that economists incorporate into the analysis of profit.


548

Profit

Economic profit = accounting profit – implicit costs

= total revenue – explicit costs – implicit costs

= total revenue – total costs

= profit.

Costs mean all explicit and implicit costs and in economics the term cost really means opportunity cost, or what is given up in a course of action.


549

Profits can be a guiding light!

Resource owners (those having land, labor, capital or entrepreneurial ability) like to make money. When an industry is earning profits (economic profits), resource owners get the message that maybe they should move resources to the industry.

In this sense profits are seen as a mechanism that moves resources to areas that have higher value than where resources are currently being used.

As a manager of business you may get criticized that profits are ugly and outrageous, but profits serve the role of allocating resources to the highest valued use. This is a good thing if you want the world’s resources to go to the place where they are valued most (in terms of willingness to pay).


550

Industry Profit and Five Forces

Michael Porter, a writer of business topics, has put down on paper some ideas about what factors influence the profit an industry can sustain. The following is a listing and brief summary of those ideas.

-Entry – the ability of others to get into an industry will impact the overall level of profit. If barriers to entry can be erected than perhaps profits can be maintained.

-Power of input suppliers – unique inputs tend to be able to get more out of firms and thus influence the level of profits.

-Power of Buyers (of the output) – If there are a few “high-volume” customers they may be able to get low prices and thus drive profits down.

-Industry rivalry – rivalry pertains to influences that exists among the firms within the industry. The greater the rivalry, the lower the profits.


551

-Substitutes and Compliments – The relationship products have with other products can also influence profit levels. The author points out that Microsoft makes more on operating systems (because it sells more units) when hardware is cheaper and thus more folks can buy computers.

Understanding Markets

Who are the players in the market system and what influence do

they have on price?


553

Transactions – two sides

Every transaction has two sides – the buying side and the selling side. Other names used are the consumer and producer sides.

A market is where the consumer and the producer interact.

The consumer would like to PAY LOW PRICES (given all else the same).

The producer would like to RECEIVE HIGH PRICES.

In every transaction there is a struggle between the desires of producers and consumers in terms of the market price. The market is a mechanism that balances out the two desires.


554

Bargaining Power

The power that consumers and producers have over the price is influenced by relationships that exist between

consumer and producer

consumers and other consumers, and

producer and other producers.

Let’s explore these ideas on the next few screens, OK?


555

Consumer-Producer Rivalry

Consumers like to pay low prices, but consumers can not offer too low of prices because eventually producers would not make the good available.

Producers like high prices, but producers can not require too high of prices because eventually consumers would not purchase the good.

The market price is the price that balances out the opposing forces.


556

Consumer-Consumer Rivalry

Consumers like to pay low prices. But in a world of scarcity (wants being greater than resources available to satisfy all those wants) consumers are pitted against each other in an attempt to capture the goods and services they want. This leads consumers to BID-UP prices in the presence of a relatively large amount of consumers.

Think about professional sports. Owners are the frontline consumers of the athletes. Years ago when one owner had the right to resign the player forever the player received much less than occurs in a world a free agency.


557

Producer-Producer Rivalry

Producers like high prices. But, if there are many producers of a product then each, in an attempt to gain buyers, will tend to lower the price to attract those consumers from other producers.

Think about fast-food establishments in an area. As a casual observation, it seems to me the more producers you have in an area, the lower the prices. This may take affect by using coupons or other special deals, but the producers try to get your business.


558

Prices

Later in the course we will think about why prices turn out the way they do, and the rivalry among producers and consumers and among themselves will play a key role.

A topic like this is often called price theory within the economics community because a primary concept of study is the price of products.

Time Value of Money

Decisions made today have consequences today and in the future. The time value of money

concept is an aid in evaluating the future in terms of today’s value.


560

Time line

Now 1 2 3 4 5 n

Now is time zero, or when the decision is made. Each following number is an “end of period” concept. We have the end of the first period, end of the second period and so on until the end of the nth period.


561

Interest Rate Growth

If you have $1 today and can earn an interest rate of 10% by the end of the first year then you will have $1.10.

The$1.10 is calculated as the amount you start the period with plus the product of what you start the period with times the rate of interest that period.

If F is the amount at the end of the period, P is the amount at the beginning of the period and i is the rate of interest during the period, then in general we have

F = P + Pi = P(1 + i).


562

Growth in general

If you start out with P and wait one period at rate i we just saw you have F = P(1 + i). Now, if you again earn i, by the end of the second period you would have

F = P(1 + i) + P(1 + i )i (start period with + start period with times i)

= P(1 + i)(1 + i)

= P(1 + i)2.

In general, at the end of n periods, you have

F = P(1 + i)n.


563

Present Value

The present value concept uses the growth process we just studied, but the focal point is the present. As an example, what amount do you need today if you want $1.10 at the end of the period and you can earn 10% during the period. You need P = F / (1 + i) = 1.10 / (1 + .1) = $1.00

In general if you want to have F n periods from now and you can earn i each period , then today you need

P = F / (1 + i)n.

Note, the present value of an amount today would mean n = 0 and so P = F because anything raised to the power zero equals 1.


564

Discount Rate

The present value P of a future amount F n periods from now at interest rate i is

P = F / (1 + i)n.

The interest rate i in this context is often called the discount rate. It is the rate at which we “discount” future values to place them in terms of today’s value.

Do not confuse this with the discount rate in the context of monetary policy. The Federal Reserve charges banks the “discount rate” when those banks borrow from the Fed.


565

Example

say you are offered the opportunity to get paid $1 at the end of the first period and another $1 at the end of the second period. You know you can earn 10% over the next two years. The catch is that to get the pay-outs you have to give up $1.50. Should you do it?The present value of the future payments is

{1 / (1 + .1)} + {1 / (1 + i)2}= {1/1.1} + {1/1.21}= .91 + .83 (rounding to two digits)=1.74.

Since the future stream of payments has a present value of $1.74 you should do it. You basically trade $1.50 for $1.74. What a deal!


566

Net Present Value

The net present value of an opportunity is the present value of all the benefits of the opportunity minus the present value of all the costs of the opportunity.

On the last screen, the NPV of the opportunity was

$1.74 - $1.50 = $0.24.


567

Apply NPV

Rules for behavior

1) Take an opportunity if the NPV > 0.

2) Choose the opportunity among competing choices that has the highest NPV (firms maximize profit).

3) The value of the firm is the net present value of the future profit stream.


568

Caution

Much of what we will do in this course is think about what to do in one period and we will think about the rules of behavior in that context. It seems we will ignore the time value of money. We are not ignoring the concept.

As an example, we will think about how much a firm should produce this period. Should it make 1, 2, 3, or more units this period? This period it should make the profit maximizing amount. The rules we come up with for this type of decision can be used in any time period. There is no time dimension in much of what we do. BUT, if there is a time dimension, use the time value of money!

Marginal AnalysisA major tool or way of thinking in economics is marginal analysis. Basically, the tool says to get to the “optimal” position think about

the next move.


570

Driving Analogy

Did you drive 100 mph today?

When you think about driving there are benefits and costs.

Benefits: it can be exhilarating, you get there quicker so you can stay where you are longer and enjoy that situation, and there are probably more.

Costs: risk of injury, penalties for driving over speed limit, and there are probably more.

Many choose to drive instead of walk because the benefits of driving outweigh the costs. But how fast should we drive?


571

Driving Analogy

Now think about increasing the speed at which you drive 1 mph at a time, please (). We usually don’t even think about it out of the driveway until we hit the speed limit. Then we start to think about cops in the area giving tickets, how fun it is to push the exhilarator (accelerator), the injuries that might happen, etc…

As we push our total speed higher and higher, the economic way of thinking would have use write down the marginal benefit and marginal cost of each mile per hour faster. Drive a mile per hour faster if the marginal benefit is at least as great as the marginal cost.


572

General Analysis

We will see more later, but essentially it is thought that the marginal benefits of an activity decline the more we do of the activity and the marginal costs of an activity rise the more we do of an activity. With this in mind, on the next screen I will have a graph with MB and MC on the vertical axis, while on the horizontal axis I will have the TOTAL amount of the activity.

So, while we increase the total activity on the horizontal axis, on the vertical axis we measure the marginal benefit and cost of the additional unit.


573

Graphical Interpretation

MB,MC

amount or Q

MC

MB

Q*

go don’t


574

Activity Rule

Engage in an activity up to the point where the marginal benefit equals the marginal cost. The logic here is that people are maximizers – they want the most benefit net of costs.

Q* is the optimal amount in the graph. Before this point each unit added has a MB > MC and so adding these units adds more to benefit than cost and makes the total net higher. Always add a unit if MB > MC on that unit. If more than Q* is done then on those units the MB < MC and thus the net amount is lowered. We do not want that.

You will notice that when the Q* unit was added MB = MC. Nothing on the net was added or lost. But our rule is go to point where MB = MC.


575

Calculations of marginal amounts

Total Revenue is price times quantity.

Marginal revenue is the typical benefit we have for firms in a market. MR is the change in total revenue when we change output, usually by one unit.

MR = Change TR divided by change in output.

Marginal cost is the change in total cost divided by the change in output.

Isoquants

An isoquant is a curve or line that has various combinations of

inputs that yield the same amount of output.

In this chapter we want to explore ideas about production of output from using inputs and then look at how much that production will cost.


577

Production function

Here we will assume output is made with the inputs capital and labor. K = amount of capital used and L = amount of labor. The production function is written in general as Q = F(K, L),where Q = output,and F and the parentheses are general symbols that mean output is a function of capital and labor.The output, Q, from the production function is the maximum output that can be obtained form the inputs.

Two screens from now we will see some isoquants. Note: on a given curve L and K change while Q is fixed.


578

Time Frame

In production, we have said that firms have the ability to use both capital and labor.

When you consider the fact that capital is basically the production facility – the building, equipment, machines and the like – you can get the feeling that it is probably less easy to change the capital than it is to change the amount of labor used.

When you look at how long it takes to change the amount of capital in production, during that time when capital can not be changed in amount the time period of production is said to be the SHORT RUN. When all inputs can be changed we are in the LONG RUN.


579

Long run

Labor

Capital On a curve we have different combinations of L and K that give the same amount of output. Curves farther out in the northeast direction have more output. Later we will say more about what the firm uses as a guide to choice of position in the graph. The position chosen will have implications for the amount of labor demanded.


580

Short Run

Capital

Labor

K*

In the short run the firm would have a given amount of capital, say K* here. Production would occur along the dotted line.


581

Marginal Rate of Technical Substitution - MRTS

Capital

Labor

Change in K Change in L

On the next slide I will refer to a change with the use of a triangle.

slope =


582

MRTS

The slope of the curve at a point is

K/ L

Now, if the marginal product of an input is defined as the change in output divided by the change in the input, the slope can be manipulated to be:

K Q and since K = 1

L Q Q MPK

So the slope is MPL/MPK and is called the MRTS (in absolute value) and it is a measure of the rate at which inputs can be substituted and output remains the same.


583

A few slides back I showed an isoquant. I also put a tangent line at a point on the curve. The slope of a curved line is really the slope of a tangent line.

You will notice that as you move along the curved line from left to right that the slope of a tangent line gets smaller (in absolute value).

Production and Costs in the Short Run


585

Overview

In this section we want to 1) Think about how production might occur and change as different amounts of inputs are used in the production process, and 2) Translate the production data into cost data. In other words, we will want to understand how the cost of producing various units of output might change as different amounts of inputs are used.


586

Fixed/variable inputs

Inputs can be classified as either fixed or variable.

A variable input is one that can be changed as the level of output is changed .A fixed input is one that can not be changed as the level of output is changed.

We often think of labor as a variable input and capital or land as a fixed input.


587

Short run/long run



588

Short run

Labor

Capital

K=2

1 2 3 and so on

Q = 76

Q = 248

Q = 492

Note here that as K = 2, if L = 1, Q = 76 and

if L = 2, Q = 248, and

if L = 3, Q = 492, and so. On the next slide I show this information and more. Note: the numbers are made up

and not based on any specific mathematical function.


589

Quantity of L TP or Q MPL APL

0 0

1 76 76 76

2 248 172 124

3 492 244 164

4 784 292 196

5 1100 316 220

6 1416 316 236

7 1708 292 244

8 1952 244 244

9 2124 172 236

10 2200 76 220

11 2156 -44 196


590

example continued

In the example, the relationship between the labor used and the total product (TP), or output, is called the short run production function. Behind the scenes we assume there is a given amount of capital.The marginal product of labor is the additional output forthcoming from the additional unit of labor. Note the first unit of labor has a marginal product of 76.

Note that as the units of labor increases the marginal product first increases, but then begins to diminish after the third unit of labor is employed.


591

example continued



592

The average product of labor is for each amount of labor the output produced divided by the labor amount.




593

TP and MPL, APL

Marginal Product and Average Product

-100

0

100

200

300

400

0 5 10 15

Quantity of Labor

MP

and

AP

TP or Q

0

500

1000

1500

2000

2500

0 5 10 15

Quantity of Labor

Tota

l Pro

duct

of O

utpu

t


594





595

short run costsIn the short run we will consider the fixed and variable costs of production and how they change as more of the variable input is used.Definitions:Total cost (TC) = Total variable cost(TVC) + Total fixed cost (TFC).Marginal cost(MC) = (change in TC)/(change in output). where change in output = 1 when possible.Average cost (AC) = TC/Q.Average variable cost(AVC) = TVC/Q.Average fixed cost(AFC) = TFC/Q.Note that in the short run fixed costs must be paid whether output is zero or 100,000 units.


596

example

Let’s take the production example we had before and translate the production data into cost data. Say the fixed costs is $1000 per unit of capital and we had two units before in our example, and the cost of labor is $400 per unit.The next screen shows the continuation of our example.


597

QL Q MPL APL TFC TVC TC

0 0 2000 0 2000

1 76 76 76 2000 400 2400

2 248 172 124 2000 800 2800

3 492 244 164 2000 1200 3200

4 784 292 196 2000 1600 3600

5 1100 316 220 2000 2000 4000

6 1416 316 236 2000 2400 4400

7 1708 292 244 2000 2800 4800

8 1952 244 244 2000 3200 5200

9 2124 172 236 2000 3600 5600

10 2200 76 220 2000 4000 6000

11 2156 -44 196 2000 4400 6400


598

QL Q MPL APL TFC TVC TC AFC AVC ATC MC

0 0 2000 0 2000

1 76 76 76 2000 400 2400 26.32 5.26 31.58 5.26

2 248 172 124 2000 800 2800 8.06 3.23 11.29 2.33

3 492 244 164 2000 1200 3200 4.07 2.44 6.5 1.64

4 784 292 196 2000 1600 3600 2.55 2.04 4.59 1.37

5 1100 316 220 2000 2000 4000 1.82 1.82 3.64 1.27

6 1416 316 236 2000 2400 4400 1.41 1.69 3.11 1.27

7 1708 292 244 2000 2800 4800 1.17 1.64 2.81 1.37

8 1952 244 244 2000 3200 5200 1.02 1.64 2.66 1.64

9 2124 172 236 2000 3600 5600 0.94 1.69 2.64 2.33

10 2200 76 220 2000 4000 6000 0.91 1.82 2.73 5.26


599

COST Curves

Total cost curve

01000200030004000500060007000

0 1000 2000 3000

TP or Q or output

Do

llars

of

Co

st

TFC

TVC

TC

Costs per unit

05

1015

2025

3035

0 500 1000 1500 2000 2500

Quantity of Output

Dolla

rs p

er u

nit


600

Idealized graph of per unit costs in the short run

$/unit

Q

MC

AC

AVC

Note AVC and AC equal MC when AVC and AC are at their minimum values.


601

When you look back at the marginal product and average product curves note that the horizontal axis is measuring labor units used and the curves are inverted u-shaped curves.

When you look back at the marginal cost and various average cost curves note that the horizontal axis is measuring output units and the curves are u-shaped curves.

There is a relationship between these two graphs. When you move to the right by adding labor in the one graph you are moving to the right in the other by having output increased.


602

How much output should the firm make? How much of the variable labor should be hired?

At this stage of our study we can say in general that additional units of output should be made if the additional revenue on those units is at least as great as the cost on those units. Even if the additional revenue is equal to the additional cost nothing has been lost, so we say produce units until the marginal revenue equals the marginal cost. Now, if we assume all the units are sold at the same price, then the additional revenue per unit sold is the price of the output. In this case MR = P.


603

The marginal cost of production is the change in total cost divided by the change in output.

The marginal product of labor is the change in output divided by the change in labor.

MC = ▲TC/▲Q, and MPL = ▲Q/▲L, so

MC = ▲TC/(MPL ▲L) = price labor/MPL.

So MR = MC implies P of output = price labor/MPL on the last unit of output made or on the last unit of labor hired. This can also be seen as

P of output times MPL = price labor.

So a rule of thumb is make output until MR = MC, or from a different point of view, hire labor up to the point where the value of the marginal product, VMP (this is P of output times MPL) = the wage (the price of labor).


604

QL Q MPL APL TFC TVC TC AFC AVC ATC MC

P outpu

t Wage VMP

0 0 2000 0 2000

1 76 76 76 2000 400 2400 26.32 5.26 31.585.26 3 400 228

2 248 172 124 2000 800 2800 8.06 3.23 11.292.33 3 400 516

3 492 244 164 2000 1200 3200 4.07 2.44 6.51.64 3 400 732

4 784 292 196 2000 1600 3600 2.55 2.04 4.591.37 3 400 876

5 1100 316 220 2000 2000 4000 1.82 1.82 3.641.27 3 400 948

6 1416 316 236 2000 2400 4400 1.41 1.69 3.111.27 3 400 948

7 1708 292 244 2000 2800 4800 1.17 1.64 2.811.37 3 400 876

8 1952 244 244 2000 3200 5200 1.02 1.64 2.661.64 3 400 732

9 2124 172 236 2000 3600 5600 0.94 1.69 2.642.33 3 400 516

10 2200 76 220 2000 4000 6000 0.91 1.82 2.735.26 3 400 228


605

On the previous slide assume price of output is $3 per unit, and the wage is $400.

Note 9 units of labor is desired because VMP is at least as great as the wage, but not on 10 units.

Also, 2124 units of output should be made, but not more because P of output is at least as great as the MC, but not on more units.

Production and Costs in the Long Run


607

The long run

• The long run is the time frame longer or just as long as it takes to alter the plant.

• Thus the long run is that time period in which all inputs are variable.


608

Isocost lines

An isocost line includes all possible combinations of labor and capital that can be purchased for a given total cost.In equation form the total cost is

TC = PLL + PKK,where TC = Total cost,

PL= the wage rate,L = the amount of labor taken,PK = the rental price of capital, andK = the amount of capital taken. This

equation can be re-expressed asK = TC/ PK - (PL/ PK) L.


609

example

As an example say labor is $6 per unit and capital is $10 per unit. Then if we look at a total cost of $100 we see various combinations of inputs:L = 10 and K = 4 or L = 0 and K = 10 or L = 16.67 and K = 0, amoung others.

On the next screen we can view the isocost line in a graph.


610

graph of isocost lineK

L

This is the isocost line at $100. If we wanted to see higher costs we would shift the line out in a parallel shift and a lower cost we have a shift in.


611

cost and outputK

L

On this slide I want to concentrate on one level of output, as summarized by the isoquant. Input combination L1, K1 could be used and have cost summarized by 4th highest isocost shown. L2, K2 would be cheaper, and L*, K*

K1

K2

K*

L1 L2 L*is the lowest cost combination of inputs to produce

the given level of output. Here the cheapest cost of the output occurs

at a tangency point between an isocost and isoquant.


612

cost and outputK

L

On this slide I want to concentrate on one level of cost, as summarized by the isocost line. Input combination L1, K1 could be used and have this cost but more output would be obtained if L*, K* were used.

K1

K*

L1 L*Here, the most output for a given cost occurs at a

tangency point.


613

cost and output

On the last two screens we have seen the tangency of an isoquant and isocost line shows either1) the cheapest way to produce a certain level of output, or2) the most output that can be obtained for a given amount of cost. These two things are different sides of the same coin and profit maximizing firms would be expected to reach the tangency positions in the long run.


614

Tangency

In the long run when a firm is able to change all inputs we see the firm will go to a point where the slope of an isocost line is tangent to a isoquant. This means the slopes are equal.

Thus, slope of isocost = (PL/ PK) = MRTS = slope of isoquant.

Remember we said MRTS can be shown to be the ratio of marginal products of labor to capital. Thus

PL/PK = MPL/MPK means MPK/PK = MPL/PL. This is a statement that the “bang for the buck” should be the same for both inputs. In other words the additional output for each input per dollar spent should be equal across inputs

when all is said and done.


615

If you happen to be at a point where the ratios are not equal take more of the input that has the higher ratio because its marginal product will diminish with a greater amount taken. You will probably have to take less of the other input.


616

Expansion pathK

L

Once we have a unit cost of capital and labor we can draw many isocosts, each one that is farther out has a higher cost. We can see the tangency of each isocost with an isoquant (output level).In the long run the firm will be at one of the points of

tangency. When connect all those points we have the expansion path. In the long run the firm will be on the expansion path.


617

The Short Run and the Long Run and seeing the connection between the two.

The exception to reaching the tangency in the long run would be the short run when the amount of some input can not be changed to reach the tangency. In the long run all inputs can be changed in amount and thus the tangency point could be reached.


618

short runK

L

Here the cheapest way to produce the output level as depicted in the isoquant would be to hire L*, K*. But the firm has committed to having K1 units of capital. Thus the cost of this output is indicated by the fourth highest isocost line.

K1

K2

K*

L1 L2 L*We could follow K1 out and see costs of other levels

of output(by putting in more isoquants).


619

As you follow along K1 maybe one output level will occur where that short run point is exactly the same as the long run point. In that one case the cost level is the same in both the short run and the long run.

Remember the output level shown on the previous screen in the short run with K1 has a higher cost to produce that output than would occur in the long run.

So, in the long run, you make the cost of a certain level of output the lowest by not only adjusting labor to the right amount but capital to the right amount. But, if in the short run you are not at the right amount of capital then you will produce the output at a higher cost because in the short run you are stuck at a certain level of capital.


620

On the next slide I have two short run average cost curves. Each one represents the average cost with different amounts of the fixed input capital. SO, maybe ATC1 could have 1 unit of capital and ATC2 could have two units of capital. There really should be lots more of these curves but I show two to get to the next point.

If output will be less than Q in the long run, then in the short run costs might be too high if we have two units of capital. But, in the long run capital would be switched to 1 unit. Similarly, output above Q has lowest cost when made with two units of capital.


621

To get Long Run GraphsATC

Q

ATC1

ATC2

Q


622

Long Run continued

• When we switch from one unit of capital to two units, we have the long run because all inputs are then variable.

• But with the two units we would have short run curves for that level of capital.

• Now we have two sets of cost curves, one for one unit of capital and one for two units of capital.


623

Interpretation

• If output is going to be less than Q1 in the long run then only one unit of capital would be wanted because those units would be produced cheapest with one unit of capital.

• Greater than Q1 would be produced cheapest with two units of capital.


624

Interpretation

• The long run curve is parts of the short run curves. For each range of output the long run curve is the segment of the short run curve that is the lowest, representing the cheapest way to produce that range of output in the long run. The final long run curve is smooth. Let’s see.


625

Smooth long run curveATC

Q

Each point on the long run curve is really just a point off the lowest short run curve at a level of output.


626

Reason for long run shape

• The long run cost curve is said to be u - shaped, just as in the short run, but for a different reason. In the short run we had diminishing returns. In the long run we have economies of scale.


627

Reason continued

• The basic idea of economies of scale is that at least for a while when the plant size is increased the average cost curve is pushed down, implying average costs are lowest in a bigger plant. It may be that further increases in plant size push the average cost curve back up. This would technically be called diseconomies of scale.


628

Long Run

• Another way to view the long run is to think about different short run situations and put them together. Think of a short run with one capital unit. Think of one with two capital units, and so on.

• We would have a similar table of numbers and graphs as we did in the short run example when only one unit of capital was available.

Some Additional Cost Concepts


630

The author suggests that a good function to represent total cost has the general form

TC = f + aQ + bQ^2 + cQ^3,

Where the key ^ means raise to power,

f represents fixed cost,

Q represents the level of output that can vary, and

a, b, and c are numbers, sometimes called constants.

The average cost (AC OR ATC) = TC/Q = f/Q + a + bQ + cQ^2, the average variable cost is a + bQ + cQ^2, the average fixed cost is f/Q and the marginal cost = a + 2bQ + 3Q^2.


631

Sometimes firms make more than one type of good and one type of cost function to represent the total cost of making both goods would be

TC = f + aQ1Q2 + Q1^2 + Q2^2.

The marginal cost with respect to Q1 would be

MC1 = aQ2 + 2Q1, and with respect to Q2

MC2 = aQ1 + 2Q2.


632

Economies of Scope.

This is when you buy Scope in a really big bottle.

Economies of scope are present whenever it is less costly to produce a set of different goods in one firm than it is to produce that set in two or more firms.

Example of two goods in the set. Add up the cost of good 1 in one firm and the cost of good 2 in another firm then subtract the cost from making both in one firm.


633

In notation form we have

TC(Q1, 0) + TC(0, Q2) – TC(Q1, Q2).

If this expression > 0 we have economies of scope,

If < 0 we have diseconomies of scope, and

If = 0 we do not have economies of scope.

The degree of scope economies is

Sc = {TC(Q1, 0) + TC(0, Q2) – TC(Q1, Q2)} / TC(Q1, Q2).

Why do scope economies exist?

Particular outputs share common inputs. Example: advertising diet coke with lemon twist also helps classic coke because the brand names are the same.


634

Cost complementarities – when increasing the production one good it lowers the marginal cost of producing the other good.

Example: Say a multiproduct firm has

TC = 100 -0.5Q1Q2 + Q1^2 + Q2^2

In terms of scope economies

If Q2 = 0 TC1 = 100 + Q1^2 and if Q1 = 0 TC2 = 100 +Q2^2,

Then TC1 + TC2 – TC = 100 + .5Q1Q2 which >0 for Q1 and Q2 greater than 0. So economies of scope exist.

In terms of cost complementarities

MC1 = -.5Q2 + 2Q1 so if Q2 goes up MC1 goes down, and

MC2 = -.5Q1 + 2Q2 so if Q1 goes up MC2 goes down. Thus there are cost complementarities.


635

If in the example on the previous screen if the firm divested itself of product 2 its cost would become

TC = 100 +Q1^2 and its MC would be 2Q1. This MC is more than under the case of cost complementarity.

Chapter 6

The Organization of the Firm


637

Last chapter we said the firm works to make output as cheap as possible. There we focused mainly on transforming inputs to output. Here we add to more ideas:

1) The firm must obtain the inputs in the least costly way, and

2) The firm must ensure that maximum effort is given by all involved in the firm. (Is maximum 100%? Probably not, we would all go bonkers. But, maximum is a high level of effort.)

Some guide named Ronald Coase has a story called “Nature of the Firm.” In the story he basically said a firm will internalize an operation if it is cheaper than doing the operation external to the firm. This chapter is based on this story.


638

Methods of Getting Inputs

1) Spot Market – buyers and sellers meet in the open market, make a deal and move on. There is no formal relationship between the buyer of the input and the seller.

2) Have a contract – have a formal agreement between the buyer and the seller.

3) Vertically Integrate – As a maker of output you also make your own inputs.

Transaction Costs

When getting an input, firms incur costs in excess of the actual amount paid to the input supplier. These costs include searching for sellers, negotiating terms of trade and other investments and expenditures required to get and use the input.


639

Some investments firms make are specialized in nature. An example would be where as a supplier you have to have a certain knowledge base and that knowledge is only required by 1 buyer.

Transaction costs may be high with specialized investment because of

1) Costly bargaining to hammer out details

2) Underinvestment – supplier may buy less than best tools to do the job because supplier can not be sure buyer of input will be around long enough for input supplier to get most out of the tools.

3) Opportunism

Example: Buyer of an input likes to specify that supplier has “quality” inputs. Moreover, the buyer spends $10 investigating the supplier to make sure it is okay. After the investigation the $10 is a sunk cost. While the input supplier may normally sell


640

the input for $100, on this new buyer it may try to get between $100 and 110 because the supplier knows the buyer can buy the input elsewhere at $100, but it will also have to spend $10 to varify the other seller has quality.

Problems of Spot Exchange

If acquisition of input requires substantial specialized investments there is likely to be high bargaining costs. Perhaps opportunism and underinvestment would happen as well.

As we look at the world around us specialized inputs are probably not traded much on the spot market.

Problems of contracts

Contracts may overcome underinvestment and opportunism, but the negotiation costs could be high.


641

Problem of vertical integration

Vertical integration overcomes the costs of negotiating with a middleman, but it increases the degree of complexity of the organization.

Author suggestion:

If an input is not very specialized buy it on the spot market. If an input is specialized contract when bargaining is not very complex. Otherwise, vertically integrate.


642

Owner –Manager Problems

Many firms have managers who run the firm, but the managers are not the owners of the firm. The manager likes income (and will get it if the owners are happy), but the manager also likes leisure. Owners don’t like the managers having too much leisure.

The situation described here is 1 type of Principal – Agent problem. The general problem is an agent working on behalf of the principal has interests that differ from the principal and thus agents may not always do what is in the best interest of the principal.

Ways the owner-manager problem may be overcome

1) Give managers pay incentives so that they act like owners.

2) Managers may recognize if they earn a good reputation as a good manager then they can advance in the company or become a “free agent” and make more money later.


643

3) Managers may be motivated by the possibility that if they under-perform the company will be overtaken by new owners who will replace them with new managers.

Manager-worker problem

Another principal-agent problem occurs between managers and workers. The manager is now the principal. How does the manager get the worker to not shirk (take too much leisure)?

Ways to overcome the problem

1) Profit sharing for workers.

2) Revenue sharing like tips and wages.

3) Piece rates – you get paid by how much you produce.

4) Time clocks and spot checks.


644

So, there you go. We have explored some issues that deal with the cost of doing business. The hope is that if we are sensitive to these issues than perhaps we can have the firm produce its output level at the lowest possible cost.

The Nature of Industry


646

Later we will study industries called perfect competition, monopoly, monopolistic competition, and oligopoly. The differences in these industry types has to do with factors such as how many sellers there are in the industry, or market, technology and cost consideration, demand conditions and how easy it is to enter an industry.

Let’s explore some of these topics next.

Measuring Market Structure


648

Concentration ratios

In the real world of business we see the number of firms varies from industry to industry. In an attempt to find a numerical measure to indicate which industries are more like monopoly – one firm - and which are more like perfect competition – many firms, concentration ratios were devised.

Concentration ratios typically use sales as the concept used in the numerical measure.


649

Concentration ratios

CRn is the sales added across the n largest firms in an industry divided by the total industry sales(and then multiply the result by 100 to be in percentage terms). For example, CR4 is the sales of the 4 largest firms added together divided by total sales in the industry(generally, more than 4 firms).

Examples

a) Monopoly industry –> CR4 = 100,

b) Industry with 4 firms of equal size (25% of sales for each) -> CR4 = 100.

Can you tell which of the examples above has only one firm by just looking at the CR4? Of course not!


650

More examples:

c) 10 firms, each with 10% of market -> CR4 = 40,

d) 4 firms, each with 10%, and 30 firms, each with 2% -> CR4 = 40.

Here we have two examples of industries where the CR4 is the same. But we see the remaining firms after the top 4 are very different in each example. You would see this by looking at the CR8, but not all the time. So, another measure has been added and the measure considers all the firms in an industry. The measure is the HHI


651

Herfindahl-Hirschman Index – HHI

To get the HHI we need the market share of each firm in percentage terms. Then we square the market share of each firm. After this, simply add the squared market share of each firm to get the final number.

Examples

a) Monopoly -> HHI = 1002 = 10,000. This is as big as you can get.

b) 4 firms with 25% each -> HHI = 252 + 252 + 252 + 252 = 2500

c) 10 firms each with 10% -> HHI = 10 times 102 = 1000.

d) 4 firms with 10%, 30 firms with 2% -> HHI = 4 times 102 plus 30 times 22 = 400 + 120 = 520.


652

Another way to get this is to take the market shares in fractional terms, square each share, add them all up and multiply by 10000.

HHI

The closer the HHI is to 10,000 the more the industry is like a monopoly. The closer to 0 the more the industry is like a competitive industry.

Issues with CR4 or HHI

How do we define a market? At issue is how narrow or broad do we define the industry. Is aluminum foil and waxed paper in the same market? What about that plastic wrap that gets all stuck together before you cover the food? Should that be included with the aluminum foil and waxed paper?

The issue raised has to be settled before we can even calculate the CR4 or the HHI.


653

The Census Bureau looks at firms that have similar production processes and considers them to be in the same market. But, this method may not be useful if consumers do not consider different products with similar production processes to be substitutes for each other.

The cross price elasticity of demand

The cross price elasticity of demand is defined as the percentage change in the demand for good x given the percentage change in the price of good y.

Example

If the price of Pepsi (and only Pepsi in this example) goes up we would expect the demand for Coke to rise. So the cross price elasticity of demand is positive for substitutes and we would expect goods in the same market to have a high numerical value for the cross price elasticity.


654

Geography

Most studies have considered concentration ratios for the country. Local ratios need to be considered.

If you look at the services of real estate agents, then concentration ratios at the national level are probably small. But, in many towns there is only one agent. Local ratios could be large.

Ratios at the national level do not include foreign firms that actually compete. This means that some industries will appear more concentrated toward monopoly when, in fact, if you include the foreign firms the ratios would be lower.


655

Vertical integration

Goods and services are the end of a process of transforming inputs into those goods and services. Just think of a loaf of bread. The wheat needed to be grown. Then the wheat is sent on to millers. The miller sends on the “stuff” to the baker. From the baker the item might go to a distributor and then the retailer. The more that one firm is involved in all stages of the production process, the more vertically integrated the firm is said to be.

With this in mind, there are some industries that are not vertically integrated and this would suggest low concentration. But this could be misleading because all the firms in the “stream” of production are tied to the main product.


656

The authors of our text use the example of Coke and Pepsi. There are many bottlers around the country and this leads to low concentration. But in the soft drink industry you and I know Coke and Pepsi are the dominant players.

So, what have we done here? We listed numerical measures of concentration designed to show what type of market structure an industry might have. Plus, we indicated some ideas we need to be aware of as we look at these measures.


657

http://www.usdoj.gov/atr/public/guidelines/horiz_book/toc.html

The link above is to a web site at the Department of Justice dealing with horizontal mergers – companies in the same line of business. Note section 1.5.

Market Conditions

Firms in an industry will have a demand for its product, while at the same time there is a demand for the product from all the firms as a group. With each there is an elasticity of demand.The Rothschild index is the elasticity of the total market - Et divided by the elasticity of the firm - Ef.If there are not many substitutes for a firm’s product you would expect the index to be 1 and if there are many substitutes you would expect the index to be closer to 0.




658

Entry into Industry

Major League Baseball has a specific barrier to entry into the league. You have to get the approval of the other owners in the league. This is a significant barrier.

Patents may limit the number of firms that can operate in an industry, as can capital requirements.

The notion of a barrier to entry is significant because if there is an ability to restrict others then maybe existing firms can enjoy long term profits without fear of others stepping in and taking some of those profits.

Lerner Index


660

Lerner IndexL = (P – MC)/P. This is a measure of the exercise of monopoly power.In perfect Comp. the L = 0 because (as we will see) P = MC.

The Lerner Index = 0 in competition and is larger for Monopoly situations. The term P – MC is often called the Monopoly mark-up.

By math we see

LP = P – MC, or MC = P – LP = (1 – L)P, or

P = [1/(1 – L)]MC, 1/(1 – L) is the mark-up factor. If L = 1 MC = P.


661

As a manager, this current section is designed to have you look at the world around you and observe some things. In the future you will learn about models of the world so you can put into perspective what you are observing. Along the way you will learn about rules of behavior. Behavior in this sense is what price should you charge for your services and what output level should you attempt to sell.

Cost of Living


663

cost of living

On the next several slides we want to explore the economic concept called the cost of living. We typically look at a price index to help us understand the cost of living.In order to do this let’s first think about some examples of consumer optimum points.

Say that you have income of $20, the price of x is $3, the price of y is $4.Now if you spent all of your income on x you could buy 6 2/3 x or if you spent all your money on y you could buy 5 y. Note that each time an additional unit of x is purchased, 3/4 of a y must be given up.


664

cost of livingy

x

(0, 5)

(6 2/3, 0)

From the previous screen I have taken information about the budget line and have drawn in the budget line. Plus I have added the fact that when the consumer faces this budget line they end up purchasing the basket (4, 2).

(4, 2)

We know that when the consumer ends up at point (4, 2) the are as happy as they can be at this time. In fact they are at a point of tangency between the budget line and their highest possible indifference curve.


665

cost of livingy

x

(0, 5)

(6 2/3, 0)

In this diagram you can see the optimum point for the consumer.

(4, 2)


666

cost of livingy

x

(0, 5)

(6 2/3, 0)

Now let’s say that there are some changes in the world. The price of x becomes 4(it used to be 3), and the price of y becomes 2(used to be 4). Now the new budget line would have: 1) if all income(no change in this example) is spent on y, 10 y could be bought.2) 5 x could be bought if all is spent on x.

(4, 2)

In this example the original optimum point could also be purchased at the new prices: (4)(4) + (2)(2) = 20.


667

cost of living

new

old

x

y

In this diagram I put just the new and the old budget lines. Note that the same original basket can be purchased under either set of prices. With the new budget we know the consumer will not end up to the right of the original basket because any of those baskets on the new budget could have been purchased by the consumer under the

old set of prices, but the consumer didn’t buy them. Therefore, they could not have been preferred to the basket.


668

cost of living

new

old

x

y

When I put in the indifference curve tangent to the old budget line you can see the individual will not end up at the original basket

under the new budget because it isn’t tangent there now. You know the consumer will not end up on the new

budget line way up in the upper left - also left of the indifference curve. Those points are less preferred because they have to be on a lower indifference curve.


669

cost of livingy

x

(0, 5)

(6 2/3, 0)

We conclude that in this example the consumer will actually end up on a higher indifference curve at the later prices compared to the earlier prices. Thus, the consumer is happier under the new prices than under the old prices.

(4, 2)

Note this is a special example because the consumer can buy the same basket under either set of prices.


670

cost of living

Now in this example we had original basketx = 4 and y = 2.Under the original prices of Px = 3, Py = 4 the cost of living at the original basket was (3)(4) + (4)(2) = 20.

The consumer price index looks at the cost or ‘price’ of a basket of goods over time. If we look at the original basket and original prices in this example we see the cost of living is 20.

Now the new prices are Px = 4, Py = 2. The cost of the original market basket is still 20 = (4)(4) + (2)(2).


671

cost of living

In this example the consumer price index would show no change in consumer prices.What is interesting about this example is that although one price went up and one went down, the original basket cost stayed the same- no CPI change - BUT the level of happiness for the consumer went up.In this sense you could say that the CPI is a misleading indicator of the cost of living. It measures the cost of a basket of goods - not the cost of a level of happiness. Since the consumer ends up happier in our example (at the same cost), the cost of having the original happiness went down.Thus, the CPI overstates the cost of maintaining a given level of happiness.


672

steak and potatoes

potatoes

steak

Note in this example the order of preference for the baskets of goods(steak, potatoes)(2, 2) is preferred to(2, 1) is preferred to(1, 2) is preferred to(1, 1)


673

steak and potatoespotatoes

steak

Now say in some year Ps = $2 and Pp = $1 and the consumer has $4 of income. The budget line is drawn in and the optimum for the consumer is 1 steak, 2 potatoes.


674

steak and potatoespotatoes

steak

In a later year let’s say prices change such that steak is lowered to $1 and potatoes rise to $2.The new budget line is the dashed line.

Note at the new pricesmore steak is bought when steak is at a lower

price and less potatoes are bought when potato prices went up.


675

steak and potatoes

Also note on the previous screen that after the price change the consumer is better off.

Now let’s look at the original basket (as is done with the consumer price index). At the old prices the basket cost $4. Under the new prices the basket costs $5. We can see from the consumer preferences that this old basket is less preferred than the new basket.The consumer price index would indicate a 25% increase in prices and the consumer is still better off. Why?


676

steak and potatoes

The CPI follows the cost of fixed basket of goods over time.Consumers do not buy a fixed basket of goods over time. They tend to shift to goods that have prices lowered and away from goods that have had price increases.In this regard the CPI overstates the true impact of inflation. It measures inflation of a fixed basket of goods. What would really be good is to look at the cost of buying a fixed level of happiness. This method can not be devised. So we live with a measure that has problems and recognize what those problems are.

Price changes and total revenue changes


678


When we look at the collection of consumers in the market, at this time in our study we assume each consumer pays the same price per unit for the product.

Also at this time in our study the total expenditure of the consumers in the market would equal the total revenue (TR) to the sellers.

So, here we look at the whole demand side of the market in general.


679

Elasticity and total revenue (TR) relationship

P

Q

P1

Q1

TR in the market is equal to the price in the market multiplied by the quantity traded in the market. In this diagram TR equals the area of the rectangle made by P1, Q1 and

the horizontal and vertical axes. We know from math that the area of a rectangle is base times height and thus here that means P times Q. The rectangle here is TR.


680


We will want to look at the change in values of a variable and in order to do so we want to have a consistent measure of change. In this regard let’s say the change in a variable is

the later value minus the earlier value.

Thus if the price should change from P1 to P2, then the change in price is

P2 - P1, or similarly if the TR should change the change in TR is

TR2 - TR1.


681


P

Q

P1P2

Q1 Q2

Now in this graph when the price is P1 the TR = a + b(adding areas) and if the price is P2 the TR = b + c.

The change in TR if the price should fallfrom P1 to P2 is (b + c) - (a + b) = c - a.

Similarly, if the price should rise from P2 to P1 the change in TR is a - c. I will focus on price declines next.

a

b c


682


P

Q

P1P2

Q1 Q2

Since the change in TR is c - a, the value of the change will depend on whether c is bigger or smaller, or even equal to, a. In this diagram we see c > a and thus the change in TR > 0.

This means that as the price falls, TR rises. I think you will recall that in the upper left of the demand the demand is price elastic. Thus, if the price falls in the elastic range of demand, TR rises.

a

b c


683

Elasticity and TR

You will note on the previous screen that I had c - a. In the graph area c is an indication of the change in TR because we are selling more units. The area a is an indication the change in TR when there is a price change. We have to bring the two together to get the change in TR.

Thus a lower price has a good and a bad.Good - sell more units.Bad - sell at lower price.


684


P

Q

P1P2 Q1

Q2

Now in this graph when the price is P1 the TR = a + b(adding areas) and if the price is P2 the TR = b + c.In this diagram we see c < a and thus the change in TR < 0.

I think you will recall that in the lower right of the demand the demand is price inelastic. Thus, if the price falls in the inelastic range of demand, TR falls.

ab

c


685


P

Q

P1P2

Q1 Q2

Now in this graph when the price is P1 the TR = a + b(adding areas) and if the price is P2 the TR = b + c.In this diagram we see c = a and thus the change in TR = 0.

I think you will recall that in the middle of the demand the demand is unit elastic. Thus, if the price falls in the unit elastic range of demand, TR does not change.

a

b c


686

Okay, let’s see if you understand this section.

If the price of a product falls will the firm lose revenue?

In general we say the answer depends on what the elasticity of demand is for the product. Revenue will be lost only if the demand is inelastic and the price falls. If you like to memorize stuff, here is a table for you:

Demand is P P

Elastic TR TR

Unit elastic TR TR

Inelastic TR TR

Call this symbol the no change symbol.

Income and substitution effects


688

Here we want to explore some more of the detail of a price change on the demand for a good. Here is the basic idea. Say the price of x falls. When this happens we think two things are at work: an income effect and a substitution effect.

The income effect: If initially we buy the same amount of x as we purchased before, since x has a lower price we will have more of our own income left and so it will feel like we have more income. We saw when we have more income we want more normal and less inferior goods. So, the income effect of a price change means if the price is lowered we could want more or less of the good.


689

The substitution effect: The sub effect is an indication that as the price of a good falls we want more of the good and we use it in substitution for other goods.

In economics we like to show the income and substitution effects in the diagram of consumer utility maximization.


690

change in price - optimal point changey

xx1

y1

Say the consumer starts out at x1, y1. If the price of x should fall the budget line rotates out in a counterclockwise fashion. The dashed line above x1 is similar to the one in the income change diagram. Except here we do not think the consumer

will end up to the left of the dashed line when there is a price decline.


691


The reason we feel the consumer will not end up to the left of the dashed line is twofold:when the price falls1) at the initial amount of x purchased the consumer feels richer and we saw this may make them buy more or less of x(income effect of a price change),2) x becomes relatively cheaper and we feel people move toward now relatively cheaper products and away from now relatively more expensive items(substitution effect of a price change).


692


So, the income effect means more or less x given a price decline, and the substitution effect means more x given a price decline.Now if the good is an inferior good1) the income effect says less x2) the substitution effect says more x.

The only way we could end up to the left of the dashed line on the previous screen is if the income effect operating with an inferior good is larger than the substitution effect. Economists have felt this rarely, if ever, happens.


693


y

xr s t

Focusing only on good x here, say we start at point r. With a price decline in x this consumer would end up at point t. But I have also shown point s. Here is how to think about this point: after the price fall think about the consumer losing enough income so that the initial

utility level could be obtained.


694


The movement from r to s highlights the substitution effect because the consumer had the income effect of the price change taken away. The movement from s to t is the income effect.


695

The demand curveP

x (usually we put Q)

P1

P2

Q1 Q2(r t)

From 2 screens ago we saw a pricedecline had us move from point r to t. When we put this info into a price, quantity graph we see the demand curve is downward sloping.


696

The demand curve

You and I already knew the demand curve was downward sloping, but now we also know it is because we think substitution effects outweigh income effects. Plus we know at each point along the demand curve the consumer is maximizing their utility given the situation they find themselves in. We also know now that at lower prices the consumer reaches a higher level of satisfaction. This was not always obvious along just the demand curve.


697


y

xt s r

Focusing only on good x here, say we start at point r. With a price increase in x this consumer would end up at point t. But I have also shown point s. Here is how to think about this point: after the price increase think about the consumer getting enough income so that the initial utility level could be obtained.

r to s sub effect

s to t income effect


698

To highlight the income and substitution effects of a price change we put in an intermediate point. Essentially what we did was say after the price change let’s show a hypothetical change in income to get the consumer back to the original indifference curve that they started with.

(Lower price, take income away, higher price, give income back.)

The movement along the original indifference curve is then the substitution effect. Then take the income change back out to see the income effect.

Impact of Change in Income

Here we want to consider the change consumers will make if

they experience a change in income.


700

change in income.

Note that the budget line is a summary of the baskets of goods that a consumer can buy. The consumer ultimately picks the basket that is able to be purchased and gives the individual the most satisfaction or happiness.

For the next few slides let’s just think about the budget line and not about consumer utility maximization.


701


y

x

Remember on the budget line we are measuring the amount of x and y the consumer can buy given their income and given the fact that prices must be paid.x1

y1

I have illustrated one basket the consumer can buy. With the price of x = Px and the price of y = Py the consumer here could buy x1, y1.


702

change in income - budget changey

x

There are many ways to think about how the budget line would change given an income change, but one way to think about it would be to pick a given amount of x, say x1. Before the income

x1

y1

change say that once x1 is bought that leaves only y1 of y. Now if there is an income increase, after x1 is bought that would leave more money to spend on y and thus y2 could be bought.

y2


703


From the previous screen we can see more y can be bought if there is more income available, but how much more depends on the prices of x and y and it depends on the income change.

But, as income rises more y can be bought, given an amount of x is bought. Thus the budget line shifts out in a parallel fashion if income grows and by a similar logic shifts in parallel if there is an income decline.


704


Now that we know how the budget changes given an income change, let’s see how the consumer optimum changes(given that taste and preferences do not change).


705


x

Say the consumer starts out at point a - x1, y1 gives maximum satisfaction. Note I have extended a line above point x1.Now with more income the budget line shifts out. The consumer will end up either

x1

y1

to the right or the left of the dashed line. If the consumer ends up to the right, more x is wanted with more income. If the consumer ends up to the left of the dashed line then less x is wanted when more income is obtained.

a


706


A normal good is one where that as the consumer gets more income more of the product is demanded (or less income means less of the good is demanded).

An inferior good is one where as the consumer gets more income less of the product is demanded (or less income means more of the good is demanded).


707

Income consumption pathy

xx1 x2

y1

When we look at several consumer optimum points at various levels of income and then trace out the points with a line we get the income consumption path. Here both goods are normal goods. Would the income consumption path be downward sloping if only one of the goods were inferior?

a


708

Engel curve - normal goody

xx1 x2

y1

In the right hand picture we can see an income increase and from the left graph we take the new x, x2, and draw it in with the new income level. The Engel curve for a normal good is upward sloping. What about for an inferior good?

a

income

x

x2x1

I1 I2


709

Note that the second graph on the previous slide had income on the horizontal axis and the quantity of x on the vertical. This is different than most graphs you have probably seen in econ.

Mrs. Engel’s boy thought this idea up – to study how changes in income change our consumption patterns.

Indifference curves

Indifference curves represent a summary of the consumer’s taste

and preferences for various products.


711

De gustibus non est disputandum

There is no accounting for the taste of the consumer. Consumers like what they like(various things influence what they like - advertising, customs...). Consumers derive utility or happiness by consuming goods and services. In economics we summarize the likes or tastes of the consumer by using indifference curves.

An indifference curve shows different combinations of goods that give the same level of utility to the consumer.


712

Diagram used in analysis

good y

good x

The amount of good y a consumer may have is measured vertically

The amount of good x is measured on the horizontal axis.This type of diagram is used extensively when considering the behavior of consumers.


713

Indifference curves - definition

As mentioned earlier, an indifference curve shows various combinations of goods that yield some specific level of utility or satisfaction for the individual.

y

x

A

B

This is one type ofindifference curve. We assume the individual is equally happy at point A or B or any other point on the indifference curve.


714


We assume more goods are preferred to less and thus indifference curves slope downward to the right.

2 1

3 4

y

x

Say the individual is at the point in the middle of the graph. Keep thisin mind as we explorethe following screens.


715


If the individual is at the point in the diagram, then all those points in area 1 and on the boundary are more preferred because those points have either more of both items or more of one and the same amount of the other item compared to the point chosen.

Points in area 3 and the boundary are less preferred to the point in the diagram because the point chosen has more of both items.


716


An individual may think that points in areas 2 and 4 are preferable, less preferred or equally desirable to the point indicated.

Since areas 2 and 4 are the only ones that could have a point of indifference to the one chosen, the indifference curves must have negative slope.


717

slope

In economics we often use graphs and with graphs you can look at the concept called slope. Often in economics the idea of slope will have an economic interpretation. Let’s review the idea of slope.

Slope = rise/run.

With a curve that slopes downward from left to right the slope is a negative number.

With a curve that slopes upward from left to right the slope is a positive number.


718


y

x

A

B

Say the consumer is at point A. If the consumer gives up one unit of x, m units of y must be given back to hold the consumer at a constant level of utility.

You could say the consumer is willing to trade 1 unit of x to get m units of y.

m

1


719


The shape of the indifference curve on the previous screen is said to be convex.

Part of the reason for this is that it is assumed that the amount of good y one receives in return for one unit of x depends on how much of each the individual starts out with.


720


x

A

B

You can tell that point A has less x than at B. As the individual takes even one less unit of x from either point A or B, some y must be given in return. But more is given in return if point A is the initial point.

The point is the less you have of something(like x atpoint A compared to point B), the more of other things you must be given in return to compensate for the loss of the one unit, assuming the same level of utility is obtained.


721

Indifference curves - feature 2 The marginal rate of substitution(MRS) is the

amount of y given in return for the one unit of x, while maintaining the same level of utility.

We can think of the MRS as a fraction: MRS=absolute value of (change in y)/(change in x) .

In this sense, the MRS is the absolute value of the slope of the curve at various points. Note the slope changes from point to point. In absolute value the fraction gets smaller the farther down the curve one moves. This is another way of saying the curve gets flatter.


722

feature 2

In general, it is assumed that consumers value additional units of a good less and less the more they have of the good. (Or you could say when consumers give up good x they require more and more of good y the less of good x they start with.) The indifference curve gets flatter.

This notion is summarized with the phrase – diminishing marginal rates of substitution.


723


x

Indifference MapEvery point in the graphhas one, and only one,indifference curve running through it.Curves farther out fromthe origin have more utility. So, the consumer can compare every bundle and make a determination of preference or indifference.


724


x

Indifference curves for an individual do not cross. Say they did, like in this diagram. Thenindividual would be indifferent to A and B,indifferent to A and C,and thus by logic should be indifferent to B and C.

AB

C

But C has more of both goods compared to B and thus Cis preferred to B. So the curves can not cross for an individual. Transitivity of preferences holds.


725


Different people can have different general shapes of indifference curves. Some are relatively steep and some are relatively flat.

On the next slide I will put two peoples’ indifference curves and they will cross. Before we said one individual’s curves could not cross.


726


y

x

Mr. A

Mr. B

Note how Mr. A has a steeper curve than Mr. B. From the point where the curves cross if both give up a unit of x, note how Mr. A has to be given more y tomake up for the loss of x than Mr. B. Mr. A is said to have a relatively strong preference for x because he needs much more y in return for the one unit of x given up.


727

A math example of a utility function might be

U = sqrt(XY) – this means utility is a function of the square root of the product of the amount of x and the amount of y a person would get.

To get an indifference curve pick a value of U. Let’s say U = 4. Then some points on the indifference curve would be

X Y

16 1

1 16

4 4

8 2

2 8


728

indifference curve when U = 16

1, 16

2, 8

4, 48, 2 16, 10

5

10

15

20

0 5 10 15 20

X

Y y

Budget

Here we explore the combinations of income and leisure the

individual can obtain


730

Budget constraint

The budget constraint for an individual shows combinations of income and leisure that can be attained.

The constraint will be a line in a diagram where we put the hours of leisure on the horizontal axis and income on the vertical axis. When an individual takes more leisure here we are assuming that less time is spent as labor.


731

Budget constraint

income

leisure

(0, 24)

(24, 0)

This budget line is drawn assumingthe wage rate is $1. In one day, one could have 24 hours of leisure and no income, or no leisure and $24 income, or any other combo on the line.


732

Budget constraint

income

leisure

(0, 24)

(24, 0)

Note how the slope of the budget line isthe negative of the wage rate. Forevery unit of leisuregiven up, $1 would be earned as income.slope=(change in inc) (change in leis.)

=1/-1= -1 = -wage.


733

Budget constraint

income

leisure

(0, 24)

(24, 0)

(0, 48)

If the wage should rise,to say $2 per hour, the budget constraintrotates clockwise. Thepoint on the vertical axis now has to indicate$48 in income if one worked all day.The slope of the newbudget is - $2.


734

Budget constraint

income

leisure

(0, 24)

(24, 0)

nonlabor income

If the individual has nonlabor income, the budget line shiftsup by the amount of nonlabor income. The slope remains as was - remember the slope is the negative of the wage rate.


735

Let’s come up with the equation for the budget constraint.

The dollar volume of income – y - we can undertake is made up of our income from work and any nonlabor income we have. If the wage is w, h is the number of hours we work, and the nonlabor income is Z, then

y = wh + Z.


736

y = wh + Z

Say T = 24 hour day, then the amount spent in work is 24 minus the time spent in leisure (l). So,

y = w(24-l) + Z

Note:

1) If l=0, meaning all time is spent working, y = 24w + Z.

2) If l = 24, meaning all time spent in leisure, y = Z.

3) If Z = 0, meaning no nonlabor income, y = w(24-l)


737

Budgets when wage = $2

0

10

20

30

40

50

60

70

0 10 20 30

Leisure

Inco

me

budget V= 0

budget V = 10

Note here that when the nonlabor income changed the budget shifted out in a parallel fashion.


738

The budget line represents the most of income and leisure the individual can get. The individual can be inside the budget, but not outside it (meaning farther out in the northeast direction from the budget.)

Next we will bring together the budget line and the indifference map for an individual and explore what the connection is between the two.

To Supply Labor or Not to Supply Labor

This is the question to which we turn.


740


The individual would like to get to the highest indifference curve possible (because then they would maximize utility – that is the utility they can obtain), but the budget constraint restricts the individual’s options to the budget line.

On the next slide let’s see what is the best the individual can do.


741

Utility Maximizationincome

leisure

a

b

c

u1u2

u3

Because of the budget line, u3 can not be reached

u1 can be reached atpoints c and b, but even more utility would beobtained if the individ.went to point a on u2.

The utility associated with u2 is the maximum this personcan achieve given the wage rate.


742


b

Note why b from the previous screen was not the best point. To give up a unit of leisure and maintain the same utility the person needed to get back a certain amount of income. But the market actually gives back more income than the individual requires for the same level of utility. This trade is beneficial. The individual would thus give up the unit of leisure and be happier for the trade.

C

L


743


Note why c from two screens ago was not the best point. To take a unit of leisure and maintain the sameutility the person is willing to give up a certain amount of income. But the market actually requires the individual to give up less. This is a beneficial trade. The individual would thus take the unit of leisure and be happier for the trade.

c


744


In the final analysis, the individual maximizes utility when the MRS=wage(this means the indifference curve is tangent to the budget line).Distance cb is the amount of labor this individual would supply. Distance ad is the amount of income they would have.

a b c

d


745

At the same wage, why two people supply different amounts of labor

Note the solid line indiff.curve is for the workaholic. At the workaholics optimalpoint, the leisure lover finds it beneficial to take on more leisure because or their willingness to give up much more inccom to get moreleisure than the market requires.

Note that at each personsoptimal pointMRS=wage.

A workaholic is a person with a relatively weak preference for leisure because little income is needed to give up a unit of leisure

Changes in wage and the work decision

here we explore the income and substitution effects of a wage

change.


747

Change in the wage rate

a

b

c

d

Before the wage rate increasethe person does best at pointa. After the wage rate increase the individual willbe happier but what is notclear is if 1)they will work

more, as they would at area b, 2) they work the same amount as, as at point c, 3) they work less, as at area d.Economic theory does not indicate which move will bepreferred for any individual, but we have some generalrules called the income effect and the substitution effectthat help us understand which move a person makes.


748

Income effect

The basic idea of the income effect is that as the wage rate rises(falls), even if the person worked the same amount as before the wage increase, they would have more income. Now when people obtain more income they tend to want more goods and services(at least those kinds we call normal). Leisure is one of those goods we would like more of and this pulls the person toward area d on the previous screen.


749

Income effect in a graph

The way we look at the incomeeffect is to not change the wage,but to give the person more (nonlabor) income and see howthey react. Since we assumeleisure is a normal good the person will take more leisure.leisure

income


750

Substitution effect

The basic idea of the substitution effect is that as the wage rate rises, the price of leisure rises. As the price of anything rises you and I tend to look for something else in substitution for the thing that has had an increase in price.

This means we would want less leisure as the price of leisure(the wage rate) rises. On slide 2 this means we would move more toward area b.


751

Substitution effect in a graph

k j

Start out on the indifference curve tangent to the budget line above point j. An increase in the wage rotates the budget clockwise. Now if we take away non-labor in the amount so that the person ends up with the same utility with which they started, then we would be at the point above k – a tangency.

leisure

income

sub. effect is from j to k.


752

income effect in a graph

k j

To see the income effect we start at point k and give back income so that we are on the new wage budget line.

leisure

income

happen, then the income effect would be stronger than the substitution effect and the person would want more leisure as the wage rose.

If the income effect had us move to this area of the budget, a place that could, in theory,


753

Change in the wage rate again

a

b

c

d

The graph here is the same one as on slide 2. At the initial wage a is still the best point for the person.After the wage increase:

Area d will be where the individual ends up if the income effect is stronger than the opposing sub. effect. Area b will be where the individual ends up if the income effect is weaker than the sub. effect. An the individual will endup at point c if the two forces are equal.


754

Supply curve of labor

wage

labor supply

In this diagram we see theperson supplys more labor at higher wages.This would be like endingup at point b in the previous diagram.


755

Supply curve of labor with a backward bend

wage

labor supply

Here the backward bend of the supply curve is the result of a wage increase moving the individual to area d on slide 8. We think this only happens when the wage is already fairly high.

Nonparticipation and other examples in the labor market


757

Nonparticipation - not in the labor market

income

hours

A

24

Note:1)nonlaborincome isavailable2) Wage is relativiely low

Starting at point A, if the person thinks of “buying” another unit or leisure, the amount they are willing to pay is higher than what they have to pay. So they buy another unit. This moves the person down to a point of all leisure.

I1 I2 I3 I4

The flat budget line implies the amount of inc.given up for onemore unit of leisure is low.


758

Nonparticipation - not in the labor market

income

hours

A

24

I1 I2 I3 I4

ab

c

Starting at a the person has utility I1. They would give up ac to get one more unit of leisure and be as happy. But they only have to give up ab. The individual takes another unit of leisure and is happier for it

Analogy time: say you are truly willing to give up $10 for something. But you only have to give up, say $5. You do it and are happier.


759

So, for the person on the previous slide, the wage in the market is so low that the individual is willing to give up income and take leisure up to the point that they do not work at all.


760

Reservation wage

The wage implied by this budget is tangent to the indiff. curve at the 24 leisure point. This is the highest wage at which theindividual chooses not to work.A wage just a wee bit higher would be the lowestwage at which the individual would work.

You could say the reservation wage is the value of leisure because if the wage is higher, then leisure will be given up.


761

Retirement

Let’s consider a retirement plan that pays individual a certain amount - provided they do notwork any hours. Their budgetis the horizontal line at a.At various wage rates we see how much leisure the individualwould have with the same income as in retirement.

a

If the indiff. curves are relatively steep, as in graph, people retire. They are willing to give up much income inexchange for more leisure. If indiff. curves are relatively flat, (workaholics, remember)people may work, even at lower total pay compared to retirement income.


762

Standard workday - 8 hour shift and underemplolyent

b a

Say a company will only let employees work 8 hour days. Point a has 16 hours of leisure and thus 8 hours of work. The person involved would like less leisure, but can not get to point b because of the employer restriction. This implies the worker is underemployed.

income

leisure


763

Standard workday - 8 hour shift and uoveremploymentt

a b

Point a has 16 hours of leisure,the amount an employer may require. The person involved would like more leisure. This implies the worker is overemployed.


764

Premium pay versus straight pay

You may be familiar with the concept of getting paid time and a half if you work overtime. This is called premium pay. This changes the budget line to have a kink like below:


765


Once the person decides how much they want to work given the overtime pay, we can think of another pay scheme that gives them one wage for all hours, but they could have same pay as with the overtime scheme.

a At point a the individual has a certain income level and this could occur fromeither budget line.


766


a b

Under the overtime payment plan the person wants to work amount implied by point a.

If a standard one rate is paid, theperson could work the samehours and receive the same pay,but they find it better to work less.

The employer would have to offer a really high wage and thus income to get the worker to work as much as under the overtime pay scheme.

Price ceiling

This is an example of government intervention in a market.


768

price ceilingP

S1

D1

QQ1

P1

A price ceiling is a maximum legal price. The government enacts one when it is felt the market price is too high. So an effective legal maximum must be below the equilibrium price. Price can then not legally get to P1.

Pc



769

price ceilingWith the price ceiling we see:1) lower price Pc,

2) lower quantity supplied - from Q1 to Qs. This is really also the amount traded. The amount traded has fallen because buyers can only buy what sellers sell.

3) Higher quantity demanded - Q1 to Qd.

4) shortage = Qd - Qs.


770

full economic price

On the previous slide I mentioned in point 1 that the price falls. But, let’s think some more about this. Since there is a shortage at the lower price, some method needs to be worked out to decide who gets to buy the items. Maybe people wait in line after having arrived early. This is costly. Consumers will actually pay, by waiting, up to the price on the demand curve above the point of trade with the price ceiling. We see this on the next slide.

So, the market price falls with a ceiling, but with the shortage created consumers end up “spending more.” Maybe another way they pay is having to bribe the sellers by paying the full Pf to the sellers.


771

Full priceP

S1

D1

QQ1

P1

Pc

Qs Qd

Pfa

b c

d e

Consumers will spend up to Pf to get the item since at Qs, the amount sellers will make available, the price on the demand curve is Pf.

f


772

Note on the previous screen

Before that ceiling was imposed consumer surplus was the areas a+b+c and producer surplus was d+e+f.

After the ceiling the full price consumers pay is Pf and they only get Qs units. So their surplus ends at only a. Consumers lost b and c. If the consumers bribed sellers, as I mentioned before, the at least area b is lost to the consumer but gained by the seller. Area c though is totally lost to the consumer.

Similarly the sellers will lose out on e because with the ceiling less is sold.

Areas c and e are called the deadweight loss of the ceiling because they used to be captured by the participants and are then lost to all because less units are traded.


773

price ceilingP

S1

D1

QQ1

P1

This screen is a repo of a previous screen. Imagine you are sitting at P1, do it! Where do you look for the ceiling? Down! Why not up?

A ceiling above P1 would cause a surplus and we know with a surplus the price will fall. It would fall to P1.

Pc


Price ceilings above equilibrium are not binding

Or are not effective!

Utility maximization

The goal of the consumer is to maximize utility given the budget constraint. Let’s see what that

means.


775

y

x

I show the budget line here again. What the consumer attempts to do is find the point on the budget line that will give the maximum utility. I show some arrows to get you to think about moving up and down the line in this search.


776

Here I present a few ideas we think hold in the world and then we see how they show up in the graph.

The consumer wants to maximize the utility, or happiness, that can be achieved when consuming goods and services.

At a given level of happiness the consumer will always give up a unit of a good if on the other good in the market an amount greater than required to maintain the given level of utility is returned. The consumer will also be happier than at the start. As an example, say you are willing to take 0.9 Cokes to give up a Pepsi, and you would be as happy. If in the market when you give up a Pepsi you get 1 Coke back you then you would give up the Pepsi and be happier.


777

A related idea is that

At a given level of happiness the consumer will always take another unit of a good if on the other good in the market an amount less than required to maintain the given level of utility must be given up.

As an example, say you will take another hamburger if you give up 2 hotdogs. If the market only requires you to give up1.5 hotdogs, the you would take the hamburger and you would be happier.

Note: Remember that because of the shape of the indifference curves that the amount you are willing to give up of a product (or an amount you would take) depends on how much you already have and thus changes along the indifference curve.


778


The individual would like to get to the highest indifference curve possible, but the budget constraint restricts the individual’s options to the budget line.

On the next slide let’s see what is the best the individual can do. But, before we do remember 1) indifference curves summarize how consumers are willing to trade off good x for y, and 2) the budget line shows how the consumer can trade off good x for good y.


779

Utility Maximizationy

x

a

b

c

u1u2

u3

Because of the budget line u3 can not be reached

u1 can be reached atpoints c and b, but even more utility would beobtained if the individualwent to point a on u2.The utility associated with u2 is the maximum this

personcan achieve given their income and the prices they face.


780


b

Note why b from the previous screen was not the best point. To give up a unit of x and maintain the sameutility the person needed to get back a certain amount of y. But the market actually gives back more ythan the individual requires. This trade is beneficial.The individual would thus give up the unit of xand be happier for the trade.

y

x


781


Note why c from two screens ago was not the best point. To take a unit of x and maintain the sameutility the person is willing to give up a certain amount of y. But the market actually requires the individual to give up less. This is a beneficial trade. The individual would thus take the unit of x and be happier for the trade.

cy

x


782


In the final analysis, the individual maximizes utility when the indifference curve is tangent to the budget line.

Tangent means equal slopes.

a b c

d

Determinants of elasticity of demand

Different products have different elasticity values. It is thought there are factors that lead to

certain elasticity values.


784

Different elasticitiesP

Q

We see the same price change along both curves, but the flatter curve has a greater quantity response. If you worked out the elasticity, you would see the flatter curve is more elastic than the steep curve in any price range.


785

Determinants of elasticity

• Some determinants are– The number of substitutes a product has,– The % of the consumer budget the item costs,– Time.


786

# of Subs.

• The more substitutes an item has the more likely the quantity demanded will respond to a price change.

• Thus, the more subs. there are the greater the elasticity.


787

% of consumer budget

• The greater the % of your budget the greater is the elasticity.

Let’s use milk as an example. Milk purchases by the typical consumer likely takes a relatively small percentage of the budget for a consumer. Changes in the price elicit almost no change in the quantity demanded.

A few years back the government taxed yachts and this raised the price of yachts. The Gov thought rich people would go on buying. Many buyers though said I’ll keep my current yacht longer because this increase is too much of my budget. The price change had a significant on the quantity demanded.


788

Time

• The longer the time period since the price change, the more elastic demand tends to be. To a certain extent because the longer time since the price change the more time we have to find substitutes. With home heating fuels if the price goes up in short term we buy but in long term we buy less and wear a sweater or search for other methods.

Elasticity from mathematical demand curves

Before we saw linear and nonlinear demand curves. We return to them to get elasticity

values from them.


790

Linear demand

A linear demand curve might be of the form

Qx = a0 + axPx + ayPy + aMM.

To evaluate the price elasticity of demand from a certain point on the demand curve you would need to have a Px and Qx point to start from. The elasticity is then axPx / Qx

As an example say we have

Qx = 1000 - 3Px + 4Py - .01M and we start at

Px = 1 and Q = 300. Then around the price = 1 the Ed = -3(1)/300 = -.01


791

Linear demand

Cross price and income elasticities are found in a similar way.

Note: take the coefficient of the relevant term, multiply by the original value of the relevant price or income and divide by the starting quantity.

Say when Py = 2 Qx = 400. From the previous screen, the cross price elasticity would be 4(2)/400 = .02 so we have an example of substitutes.


792

Nonlinear demand

Demand may not be a linear function. A popular nonlinear form takes the form

Qx = cPxBxPy

ByMBMHBH. An example would be

Qx = 10Px-1.2Py

3M.5H.3 . An interesting thing about this form is if you take the natural log (sometimes written Ln)of each side you get

log Qx = 10 – 1.2 log Px + 3 log Py + .5 log M + .3 log H .

This nonlinear demand is said to be linear in logs.


793

Nonlinear demand

When the nonlinear demand is written in natural log form the coefficients in the equation are themselves elasticities. From the previous screen the price elasticity of demand is –1.2, the cross price elasticity is 3, and the income elasticity is .5.

So from the previous screen good x is elastic in the range investigated, is a normal good and in regard to good y is a substitute.

Other demand elasticities

There are other elasticities besides the own price elasticity of

demand. Let’s see a few here.


795

demand shifters

We saw that things like taste and preference, price of other goods, income and the number of buyers shift the demand curve if they change. How much do they shift the demand curve?

We use other elasticity concepts as an indication of how much the curve will shift given a change in one of these factors.


796

cross price elasticity of demand

Edxy = % change in Qdx / % change in Py.


If the value is negative we have complements and if positive we have substitutes.

If the absolute value is between 0 and 1 the cross elasticity is inelastic, if = 1 unit elastic and if greater than 1 elastic.


797

income elasticity of demand

Edxm = % change in Qdx / % change in M.


If the value is negative we have an inferior good and if positive we have a normal good.

If the absolute value is between 0 and 1 the income elasticity is inelastic, if = 1, unit elastic, and if greater than 1, elastic.


798

applied problem

Say the cross price elasticity for Coke with respect to the price of Pepsi is 1.7. This means for every 1% Pepsi raises price the demand for Coke will go up 1.7%.

Say Coke exec’s hear Pepsi is going to raise price by 2.5%. How much will Coke exec’s expect demand to rise?

1.7 = 1.7= x/2.5 or x = 1.7(2.5) or 4.25%


799

Elasticity of supply

The elasticity of supply is used to indicate the percentage change in the quantity supplied given a percentage change in price.

The elasticity of supply is calculated in a manner similar to the other elasticities we have seen and has a similar interpretation in terms of the range of values the elasticity might take, i.e. elastic, inelastic and unit elastic.

Monopoly Pricing and Output

We study the pricing and output decision of the monopoly firm.


801

Price and output decision for the monopolist in the short run

The amount of output the monopolist should sell in the short run is the amount where MR = MC(as long as P>AVC), just as in the case of the competitive firm.

The price charged would then be the price on the demand curve above the quantity where MR = MC.


802

Logic of MR = MC rule$

Q

D

MR

MC

a b c

The Q = b is the Q whereMR = MC. But look at Q = a. Atthat point, Q could be increased and more would be added torevenue than to cost and thus profit would rise. We know this because the MR > MC for these Q.

Now let’s look at a Q greater than where MR = MC, like at point c. More has been added to cost than to revenue and thus profit would fall. We know this because MC > MR at this Q.


803

What price?$

Q

MC

D

MR

P*

Q*

At Q*, where MR = MC, P* is the price on the demand curveconsumers are willing to pay for Q* and thus this is the price charged by the monopolist.


804

Qualification$

MC

D

MR

P*

Q*

ATC

AVC1

AVC2

AVC1

AVC2

Note that the ATCis above the demandcurve, so the firm will lose money. In the short run, the question is whetherthe firm should shutdown or continue to operate. Let’s go to the next screen and say moreabout this.


805

continueIf the real AVC is AVC1, then the firm should not follow the MR = MC rule. At this level of output, P < AVC. It should not operate at all and lose less money by not operating than if it tried to operate.

The situation is that only some of the variable costs are being covered and none of the fixed costs are being covered. The firm should not operate and only lose its fixed cost.


806

continue 2

If the real AVC is AVC2, then the firm should operate,even though there is still a loss. The P > AVC, and this means the revenue from operating covers all of thevariable costs and some of the fixed costs. This is better than not operating and losing all the fixed costs.

Note that in the long run if ATC > P (at the Q where MR = MC) the monopoly will continue to lose money andshould in that case cease operating.


807

Quiz 1 – not a real quiz$

MC

D

MR

P*

Q*

ATC

Is this monopoly firmearning a profit? If so,draw in the graph therectangle that represents the profit.


808

Quiz 2 not a real quizMC

D

MR

P*

Q*

AVC

$ ATC

Is it possible for a monopoly to lose money?

Indicate in the graphhow much thismonopoly is losing byindicating the lossrectangle.

Monopoly

Here we see what a monopoly is and its revenue potential.


810

Overview

Monopoly means one seller.

In perfect competition many sellers were price takers. Any one seller could not influence the price of the product in the market. The competitive firm could only choose what amount to sell.

A monopoly firm will have to determine both how much to sell and at what price.


811

Review p $

Market Q Firm Q

P=MR=D

In a competitive market, the market demand curve represents the demand of all consumers in the market. At the equilibrium price in the market, the firm must merely sell what it wants at this price. The firm is a price taker and we say the demand for a firm is horizontal or perfectly elastic.

D

S


812

MonopolyFor a monopoly firm the demand is the same as the market demand we see in competition. The demand is downward sloping to the right, what is called less than perfectly elastic.

Since the monopolist is the only seller, it is natural they face the market demand curve.

The situation of monopoly is often called imperfect competition.


813

Maximize profitSince the monopolist is the only seller in the market, the monopolist must decide what price to charge andhow much to sell.

When the monopolist sells, she is worried about profit. The goal is to maximize profit. But, in order to maximize profit, the pattern of revenues and costs at various output levels must be understood. The pattern of cost was the topic of an earlier chapter. Now we look at the pattern of revenue.


814

Market demand P

Q

142

132

3 4

In the market, the way consumers will take a greater quantity demanded is to have a lower price in the market. As an example, if the pricein the market is 142, consumers will have a

quantity demanded of 3. But the quantity demanded will be 4 when the price is 132.


815

Marginal revenueMarginal revenue is the change in total revenue when there is a change in output. Let’s continue with the example we introduced before.

If the P = 142, Qd = 3 and TR = 426.If the P = 132, Qd = 4 and TR = 528.Thus, the marginal revenue(MR) of the 4th unit is 102.

The price needed to get the 4th unit was 132, but the MRis only 102. Why the difference between P and MR? (It wasn’t like that for the competitive firm.)


816

InterpretationWhen the price is lowered from 142 to 132 the amount sold rises. In fact, the 4th unit sold brings in 132 in revenue. But this isn’t all we need to look at to have MR. Since the monopolist must sell to all consumers at the same price, the first 3 units now get sold at 132 as well. That means revenue on those three units will not included 10 per unit when the price is lowered.

Continuing with the example,

MR(of the 4th unit) = 132 - (142-132) 3 = 102


817

interpretationP

Q

142

132

3 4

a

bc

Area a + b = 142 times 3 = 426 = TR when P = 142Area b + c = 132 times 4 = 528 = TR when P = 132

MR = c - a = 132 - (142-132)(3) = 102

area c is the gain in revenue from sellingmorearea a is the loss inrevenue from selling at a lower price.


818

Let’s do another exampleWhen P = 132, Qd = 4.When P = 122, Qd = 5.

When P = 132, TR = ...................When P = 122, TR = ...................

So the 5th unit is sold when P = 122, but the MR of the

5th unit = ...........................................

Again we see P>MR.


819

MR from areas to heightP

Q

a

b c

P

Q

In the above diagram we think ofMR as area c - a and we get a number.

height = MR

In the bottom graph we can think of the numberas a height. Note still theMR is lower than the priceon the demand curve.

On the next screen we will see the whole MRcurve.

D

D


820

Monopoly MR in a graph$

Q

D

4

132

102

I do not have a prooffor you, but you can see in this diagramthat MR is also a straight line that startsat the same place asdemand in the upperleft, but is always below demand becauseP>MR. Like at Q = 4, MR = 102 and P = 132.

Note that a good way to draw in MR is to first draw demand and then put MR through the Q axis halfway out to the demand curve. I put an X at that point.

Multiplant Monopoly

Here we study the situation where a monopoly sells in one market

but makes the output in two facilities.


822

multiplant monopolist

The type of monopolist we will consider here is one that produces output in two facilities, but sells the output in one market.The questions we want to answer are:1) How much output to sell in the market,2) What price to charge in the market,3) How much of the total output should come from each of the facilities?


823

firm level marginal cost

Each facility will have a marginal cost schedule. The first unit of output out of each facility will have a MC value, of course. Say the first plant has a MC = 3 for the first unit and plant 2 has a MC = 4 for the first unit. The first unit the firm sells should come form plant 1.Now say the second unit from plant 1 has a MC = 3.5. The second unit the firm sells should come from plant 1 as well. If the third unit from plant 1 has a MC = 4.25, then the third unit the firm should sell should be the first unit from plant 2. In a graph this is accomplished by horizontally adding the plant level MC’s to get the firm level MC.


824

Firm level marginal cost

MC1 MC2

$ MC firm

equal


825

decision time

MC1 MC2

$ MC firm

D

MR

Pm

Q1 Q2 Q = Q1 + Q2


826

analysis

The firm will sell the level of output where firm level MC = MR,charge the price on the demand curve at this level of output,recognize the MR at the optimal Q is a firm level MR now and each plant should produce the amount where MR = MC.Since the firm level MR drives the revenue side of things, don’t sell additional units that have higher MC than MR. Thus plants have MC’s that are equal and also equal to MR.


827

In general, when the inverse demand isP = A – BQ, the MR isMR = A – 2BQ. Example: Say demand is P = 70 – 0.5Q, then MR = 70 – Q.

Note in the example that B = 0.5 and 2B = 2(0.5) = 1.

So, this is just a rule you will use in working with a monopoly. You have to put the demand in this inverse form to apply the rule.


828

Decision in Math Terms

Say we have demand in inverse form of

P = 40 – Q.

Plus say the total cost in each plant is (with subscripts)

TC1 = Q1 + Q12,

TC2 = 4Q2 + 0.5Q22.

The MR for the firm is: MR = 40 – 2Q. The MC at each plant is MC1 = 1 + 2Q1,

MC2 = 4 + Q2.


829

Decision in Math Terms There are several ways we could proceed at this time to answer the questions we set out above. I have chosen the path that is consistent with using the graph we saw before. Next you will see a crucial step.

Re-express each MC in Q form as

MC1 = 1 + 2Q1, as Q1 = .5 MC1 - .5

MC2 = 4 + Q2, as Q2 = MC2 – 4.

Now, the Q’s add up to Q and on the right side we add to get Q = 1.5MC – 4.5 (you ignore the subscripts on the MC terms and add them together.)


830

Output and Price for the Firm

Re-express the MC for the firm as

MC = (2/3)Q + 3. We have MR = 40 – 2Q. Thus the level of output to maximize profit occurs where MR = MC and we have

40 – 2Q = (2/3)Q + 3, or Q = 37(3/8) = 13.875. The price to charge is on the demand curve

P = 40 – 13.875 = 26.125. Note at the optimal level of output the MR = 40 – 27.75 = 12.25.


831

Production in each plantThe MC in each plan, again, is

MC1 = 1 + 2Q1,

MC2 = 4 + Q2.

With MR = 12.25 at the optimal output, set each MC = 12.25 to see how much to make in each plant:

Plant 1 1 + 2Q1 = 12.25, or Q1 = 5.625 and

Plant 2 4 + Q2 = 12.25, or Q2 = 8.25.

Note the two Q’s add up to what we saw before.


832

Profit

The profit for the firm is 258.1875.

Find this by looking at the TR and TC in each plant.


833

Demo problem 8-6

P = 70 - .5Q is demand,

So MR = 70 – Q because of rule we saw before.

Say MC1 = 3Q1 and MC2 = Q2. Then

Q1 = [1/3]MC1 and Q2 = MC2.

Q1+ Q2 = Q 4/3MC and MC = [3/4]Q

Make the Q where MR = MC, so

70 – Q = [3/4]Q, or 70 = [7/4]Q, or Q = 40. Set this Q into the demand to get the price P = 70 -0.5[40] = 50. The value of MR at Q = 40 is 30 so in each plant MR = MC gives

In plant 1 30 = 3Q1, or Q1 = 10 and in Plant 2 30 = Q2.

Multiple Regression

Here we add more independent variables to the regression.

In this section I focus on sections 13.1, 13.2 and 13.4


835

Let’s begin with an example of simple linear regression. A trucking company is interested in understanding what is going on with the time the drivers are on the road. Travel time is the dependent variable. It seems that travel time (how long it takes to make the days deliveries) would be influenced by miles traveled, the independent variable.

I have the simple regression results from such a study on the next slide.


836

Note the estimated equation is

y (time) = 1.27 + .068x(miles).

The p-value on the slope coefficient (miles line) is .0041 and since it is less than .05(say that is alpha we use) we reject the null of a zero slope and conclude there is a relationship between miles driven and travel time.

R square = .66 and thus 66% of the variation in y is explained by x.

Miles time (hours)


837

So, we had a significant relationship between x and y and the r-square was .66. This r square is not bad, but the company may think that with only 66% of the variation in travel time explained by miles driven, maybe other variables will explain the variability as well. Another variable that could explain the travel time is the number of deliveries that are made.

In a multiple regression we can add another variable to the initial X variable we had included.

In Excel you just include in the definition of X two (or more columns) variables Note you may want to have the Y variable in the last column of the right or the first column on the left because the X’s need to be included together in contiguous columns. I have a multiple regression output on the next slide.


838


839

Math formThe multiple regression form of the model is:

Yi = B0 + B1 x1 + B2x2 + … + e,whereB0 is the Y intercept of the line, Bi is the slope of the line in terms of xi, and e is an error term that captures all those influences on Y not picked up by the x’s. The error term reflects the fact that all the points are not directly on the line.

So, we think there is a regression line out there that expresses the relationship between x’s and Y. We have to go find it. In fact we take a sample and get an estimate of the regression line.


840

When we have a sample of data from a population we will say in general the regression line is estimated to be Ŷi = b0 + b1 x1 + b2x2 + …, where the ‘hat’ refers to the estimated, or predicted, value of Y.

Once we have this estimated line we are right back to algebra. Ŷ values are exactly on the line.

Now, for an each value of x we have data values, called Y’s, and we have the one value of the line, called Ŷ. This part of multiple regression is very similar to simple regression. But our interpretation will change a little.


841

From the multiple regression output we see the coefficients section means the estimated regression line is estimated to be

Ŷ = -.8687 + .0611x1 + .9234x2.

From the simple regression we had

Ŷ = 1.2739 + .0678x1. You will note the variable x1 does not have the same value in each case.

In the simple regression case the .0687 is the increase in the mean value of Y for each unit increase in x1, but we could not control all the other factors at work in influencing Y. In the multiple case the .0611 is the increase in the mean value of Y when x1 increases by 1, but we have controlled for the influence that x2 has on Y by including x2 in the equation.

Each slope or net regression coefficient measures the mean change in Y per unit change in the particular x, holding constant the effect of the other x variable.


842

Problem 3 page 471

a) The formal model is

Y = Bo + B1(foreimp) + B2(Midsole) + e and the estimates equation is

Ŷ = -0.027 + 0.791X1 + 0.605X2.

b) Since the p-value on each slope is less than alpha = .05 (something I saw more about later), we can interpret each slope separately in the following way.

For each unit increase in foreimp, the mean value of Y increases by 0.791, holding constant the value of midsole. For each unit increase in midsole, the mean value of Y increases by 0.605, holding constant the value of foreimp.

Multiple Regression Interpretation


844

Correlation, Causation

Think about a light switch and the light that is on the electrical circuit. If you and I collect data about someone flipping the switch and the lights going on and off we would be able to say that there is correlation from a statistical point of view. In fact, you and I know we can say something even stronger. We can say in this case there is causation.

In the world of business (and other areas) we want to find relationships between variables. We would hope to find correlation and if we have a compelling theory maybe we could say we have causation.


845

Example

Say we are interested in crop yield on a farm. What variables are correlated with crop yield? You and I know the amount of water has been shown to have an impact on yield, as has fertilizer and soil type, among other things. In a multiple regression setting, if

Y = yield,

x1 = water amount, and x2 = amount of fertilizer, the a multiple regression would be of the form

Y = Bo +B1x1 + B2x2 + e and our estimated regression would be of the form

Ŷ = bo +b1x1 + b2x2.


846

r square

r square on the regression printout is a measure designed to indicate the strength of the impact of the x’s on y. The number can be between 0 and 1, with values closer to 1 meaning the stronger the relationship.

r square is actually the percentage of the variation in y that is accounted for by the x variables. This is also an important idea because although we may have a significant relationship we may not be explaining much. From the yield example the more variation we can explain then the more we can control yield and thus feed the world, perhaps. Or maybe in business setting the more variation we can explain the more profit we can make.


847

F Test

In a multiple regression, a case of more than one x variable, we conduct a statistical test about the overall model. The basic idea is do all the x variables as a package have a relationship with the Y variable? The null hypothesis is that there is no relationship and we write this in a shorthand notation as

Ho: B1 = B2 = … =0. If this null hypothesis is true the equation for the line would mean the x’s do not have an influence on Y. The alternative hypothesis is that at least one of the beta’s is not zero, written H1: not all Bi’s = 0. Rejecting the null means that the x’s as a group are related to Y.

The test is performed with what is called the F test. From the sample of data we can calculate a number called the F statistic and use this value to perform the test. In our class we will have F calculated for us because it is a tedious calculation.


848

F

Under the null hypothesis the F statistic we calculate from a sample has a distribution similar to the one shown. The F test here is a one tailed test. The farther to the right the statistic we get in the sample is, the more we are inclined to reject the null because extreme values are not very likely to occur under the null hypothesis. In practice we pick a level of significance and use a critical F to define the difference between accepting the null and rejecting the null.


849

F

To pick the critical F we have two types of degrees of freedom to worry about. We have the numerator and the denominator degrees of freedom to calculate. They are called this because the F stat is a fraction.

Numerator degrees of freedom = number of x’s, in general called k.

Denominator degrees of freedom = n – k – 1, where n is the sample size. As an example, if n = 10 and k = 2 we would say the degrees of freedom are 2 and 7 where we start with the numerator value. You would see from a book the critical F is 4.74 when alpha is .05. Many times the book also has information for alpha = .025 and .01.

Area we make = alpha

Critical F


850


851

F

In our example here the critical F is 4.74. If from the sample we get an F statistic that is greater than 4.74 we would reject the null and conclude the x’s as a package have a relationship with the variable Y.

On the previous slide is an example and the F stat is 32.8784 and so the null hypothesis would be rejected in that case.

Area we make = alpha =.05 here

4.74 here


852

F

P-value

The computer printout has a number on it that means we do not even have to look at the F table if we do not want to. But, the idea is based on the table. Here you see 32.8784 is in the rejection region. I have colored in the tail area for this number. Since 4.74 has a tail area = alpha = .05 here, we know the tail area for 32.8784 must be less than .05. This tail area is the p-value for the test stat calculated from the sample and on the computer printout is labeled Significance F. In the example the value is .0003.


4.74 here 32.8784


853

SOOOOOOO,

Using the F table,

Reject the null if the F stat > critical F in the table, or

If the Significance F < alpha.

If you can NOT reject the null then at this stage of the game there is no relation between the x’s and the Y and our work here would be done. So from here out I assume we have rejected the null.

t tests – After the F test we would do a t test on each of the slopes similar to what we did in a simple linear regression case to make sure that each variable on its own has a relationship with y. There we reject the null of a zero slope when the p-value on the slope is less than alpha. The t test for each regression coefficient is equivalent to testing for the contribution of each independent variable.


854

Multicollinearity

Can you say multicollinearity? Sure you can. Let’s all say it together on the count of 3. 1, 2, 3 multicollinearity! Very good class, now listen up!

Multicollinearity is an idea that volumes have been written about. We want to have a basic feel for the problem here.

You and I want x variables that help explain Y. The reason is so that we can predict and explain movement in Y. As an example, if we can predict and explain crop yield maybe we can make yield higher so that we can feed the world!

So, we want x’s that are correlated with Y. This is a good thing. But, sometimes the x’s will be correlated with each other. This is called multicollinearity. The problem here is that sometimes we can not see the separate influence an x has on Y because the other x’s have picked up the influence due to their correlation.


855

From a practical point of view multicollinearity could have the following affect on your research. You reject the null hypothesis of no relationship between all the x variables and Y with the F test, but you can not reject some or all of the separate t tests for the separate slopes. Don’t freak out (yet!).

Let’s think about crop yield. Some farmers have water systems. The more it rains in a summer the less water the farmers directly apply. (Okay, maybe I am ignorant here and farmers here can use all the water they can apply – its an example.) If you included both inches of rain and water applied there is a correlation between the two. This may make it difficult to see the separate impact of either the rain or the water from the system.

If the x’s (the independent variables) have correlations more extreme than .7 or -.7 then multicollinearity could be a problem


856


857

Problem 4 page 471, problem 14 page 476 and 26 on page 481

On the previous slide I have an Excel printout.

a)The model for the problem is

Cost = Bo + B1(sales) + B2(# of orders) + e and the estimates line is Ŷ = -2.728 + 0.0471X1 + 0.0119X2.

b) For each unit increase in sales, the mean value of Y increases by 0.0471, holding constant the # of orders. For each unit increase in# of orders, the mean value of Y increases by 0.0119, holding constant the value of sales.

c) While the value for bo = -2.728 we really do not look at it for much meaning because in the data there are no sales values = 0 and no # of orders = 0. This is like extrapolation we saw before – this is risky to interpret outside the range of the values of the x’s.


858

d) To predict we use Ŷ = -2.728 + 0.0471X1 + 0.0119X2 and note the data for sales use 400 because data is in thousands. So, we have Ŷ = -2.728 + .0471(400) + .0119(4500) = 69.662.

(Not doing e and f)

Prob 14

a) The critical value of F with 2 and 21 degrees of freedom is 19.45. Our Fstat from the printout is 75.13 so we can reject Ho: B1=B2=0 and conclude that there is a significant relationship between the x’s and the Y variable.

b) The p-value here is the value under the heading Significance F and has value 3.0429E-10. The E-10 part means move the decimal 10 places to the left. Thus the p-value is 0.00000000030429 which is way less than alpha so we can reject the null and conclude the same thing we did in part a.


859

c) r2 or R square = .8759 and means that 87.59% of the variation in costs is explained by the variation in sales and the variation in the number of orders.

d) Not doing

Prob 26

Not doing a

b) Note the p-values for both sales and # of orders are both less than alpha = .05 so each variable makes a significant contribution to the model and both should be included in the model.

Multiple Regression Interpretation


861

Correlation, Causation

Think about a light switch and the light that is on the electrical circuit. If you and I collect data about someone flipping the switch and the lights going on and off we would be able to say that there is correlation from a statistical point of view. In fact, you and I know we can say something even stronger. We can say in this case there is causation.

In the world of business (and other areas) we want to find relationships between variables. We would hope to find correlation and if we have a compelling theory maybe we could say we have causation.


862

Example

Say we are interested in crop yield on a farm. What variables are correlated with crop yield? You and I know the amount of water has been shown to have an impact on yield, as has fertilizer and soil type, among other things. In a multiple regression setting, if

y = yield,

x1 = water amount, and x2 = amount of fertilizer, the a multiple regression would be of the form

y = Bo +B1x1 + B2x2 + e and our estimated regression would be of the form

y hat = bo +b1x1 + b2x2.


863

F Test

In a multiple regression, a case of more than one x variable, we conduct a statistical test about the overall model. The basic idea is do all the x variables as a package have a relationship with the y variable? The null hypothesis is that there is no relationship and we write this in a shorthand notation as

Ho: B1 = B2 = … =0. If this null hypothesis is true the equation for the line would mean the x’s do not have an influence on y. The alternative hypothesis is that at least one of the beta’s is not zero. Rejecting the null means that the x’s as a group are related to y.

The test is performed with what is called the F test. From the sample of data we can calculate a number called the F statistic and use this value to perform the test. In our class we will have F calculated for us because it is a tedious calculation.


864

F

Under the null hypothesis the F statistic we calculate from a sample has a distribution similar to the one shown. The F test here is a one tailed test. The farther to the right the statistic we get in the sample is, the more we are inclined to reject the null because extreme values are not very likely to occur under the null hypothesis. In practice we pick a level of significance and use a critical F to define the difference between accepting the null and rejecting the null.


865

F

To pick the critical F we have two types of degrees of freedom to worry about. We have the numerator and the denominator degrees of freedom to calculate. They are called this because the F stat is a fraction.

Numerator degrees of freedom = number of x’s, in general called p.

Denominator degrees of freedom = n – p – 1, where n is the sample size. As an example, if n = 10 and p = 2 we would say the degrees of freedom are 2 and 7 where we start with the numerator value. You would see from a book (maybe page 672 of a stats book) the critical F is 4.74 when alpha is .05. Many times the book also has a table for alpha = .025 and .01.

Area we make = alpha

Critical F


866


867

F

In our example here the critical F is 4.74. If from the sample we get an F statistic that is greater than 4.74 we would reject the null and conclude the x’s as a package have a relationship with the variable y.

On the previous slide is an example and the F stat is 32.8784 and so the null hypothesis would be rejected in that case.


4.74 here


868

F

P-value

The computer printout has a number on it that means we do not even have to look at the F table if we do not want to. But, the idea is based on the table. Here you see 32.8784 is in the rejection region. I have colored in the tail area for this number. Since 4.74 has a tail area = alpha = .05 here, we know the tail area for 32.8784 must be less than .05. This tail area is the p-value for the test stat calculated from the sample and on the computer printout is labeled Significance F. In the example the value is .0003.


4.74 here 32.8784


869

SOOOOOOO,

Using the F table,

Reject the null if the F stat > critical F in the table, or

If the Significance F < alpha.

If you can NOT reject the null then at this stage of the game there is no relation between the x’s and the y and our work here would be done. So from here out I assume we have rejected the null.

T tests

After the F test we would do a t test on each of the slopes similar to what we did in a simple linear regression case to make sure that each variable on its own has a relationship with y. There we reject the null of a zero slope when the p-value on the slope is less than alpha.


870

Multicollinearity

Can you say multicollinearity? Sure you can. Let’s all say it together on the count of 3. 1, 2, 3 multicollinearity! Very good class, now listen up!

Multicollinearity is an idea that volumes have been written about. We want to have a basic feel for the problem here.

You and I want x variables that help explain y. The reason is so that we can predict and explain movement in y. As an example, if we can predict and explain crop yield maybe we can make yield higher so that we can feed the world!

So, we want x’s that are correlated with y. This is a good thing. But, sometimes the x’s will be correlated with each other. This is called multicollinearity. The problem here is that sometimes we can not see the separate influence an x has on y because the other x’s have picked up the influence due to their correlation.


871

From a practical point of view multicollinearity could have the following affect on your research. You reject the null hypothesis of no relationship between all the x variables and y with the F test, but you can not reject some or all of the separate t tests for the separate slopes. Don’t freak out (yet!).

Let’s think about crop yield. Some farmers have water systems. The more it rains in a summer the less water the farmers directly apply. (Okay, maybe I am ignorant here and farmers here can use all the water they can apply – its an example.) If you included both inches of rain and water applied there is a correlation between the two. This may make it difficult to see the separate impact of either the rain or the water from the system.

If the x’s (the independent variables) have correlations more extreme than .7 or -.7 then multicollinearity could be a problem


872

r square

r square on the regression printout is a measure designed to indicate the strength of the impact of the x’s on y. The number can be between 0 and 1, with values closer to 1 meaning the stronger the relationship.

r square is actually the percentage of the variation in y that is accounted for by the x variables. This is also an important idea because although we may have a significant relationship we may not be explaining much. From the yield example the more variation we can explain then the more we can control yield and thus feed the world, perhaps. Or maybe in business setting the more variation we can explain the more profit we can make.

Price Floor

This is another example of government intervention in a

market.


874

price floorP

S1

D1

QQ1

P1

A price floor is a minimum legal price. The government enacts one when it is felt the market price is too low. So an effective legal minimum must be above the equilibrium price so price can not get down to P1.

Qd Qs

Pf

a b c

d e

The downward arrow is here to suggest price can not get below Pf.


875

price floorWith the price floor we see:1) higher price Pf,

2) lower quantity demanded - from Q1 to Qd. This is really also the amount traded. The amount traded has fallen because sellers can only sell what buyers buy.

3) Higher quantity supplied - Q1 to Qs.

4) surplus = Qs - Qd.


876

One thing we notice with the floor is a surplus is created. What happens to the goods that are made and not purchased?

Maybe the government will buy them – the government would have to pay (Qs – Qd)times Pf to buy the surplus.

Maybe the government will ask producers not to make them.

Public Goods


878

A public good is one that is nonrival and nonexclusionary in consumption.

Nonrival means that when you consume the good it does not diminish the availability for me to consume the good. An example would be radio signals. When turn on your radio it does not stop me from doing the same and listening to the same station.

Nonexclusionary means that when the good is provided no one can be excluded from consuming it. Once radio waves are out there they are out there for all.

Most goods and services we have (implicitly) considered this term are private goods that do not have the characteristics mentioned here.


879

Demand

In the private good case we said the market demand was the horizontal summation of each individual’s demand. The logic there was that at a given price each consumer decided how much to consume on there own.

For the public good, all consumers consume the same amount, although each may be willing to pay a different amount for additional units of the good. Constructing the demand for a public good then is NOT the horizontal sum. It is the vertical sum. This means that at each quantity we have to see how much in total consumers as a group are willing to pay.


880

Say the demand for each of three people is, respectively,

p1 = 30 – q1, p2 = 30 – q2, p3 = 30 – q3(note we have identical demands, although this may not always be the case).

As a private good you add the demands horizontally by first re-expressing the demands in “Q” form, like

q1 = 30 – p1, q2 = 30 – p2, q3 = 30 – p3, and then total demand is

Q = q1 + q2 + q3 = 90 – 3p.

Note if p = 1 the total market demand is 87 and each individual will demand 29 units.


881

In the public good case the total demand is

P = p1 + p2 + p3 = 90 – 3q.

Note if q = 1 the total amount folks are willing to pay is 87 and each person is willing to pay 29.

Q

$

30

90

Each individual’s demand

Total demand


882

Say that each unit of the public good and be supplied at a MC = 54. Note that each individual alone does not value even 1 unit enough to cover the MC. But, as a group, the three have evaluations of the product above or equal to the MC up to 12 units. We see this by setting 90 – 3q = 54, or q = (90 – 54)/3= 12.

Q

$

30

90

MC = 54

12

18

12 units is considered the socially optimal level of output. These units are valued as much or more as what it cost to make the units.

Note each person would pay 18 for each of the 12 units, while they would be willing to pay more than 18 on some of those units so each person gets

Consumer surplus = .5(30 – 18)12 = 72, for a total of 3(72) = 216.


883

Let’s think about one of the three saying they have no value from the public good (which is untrue, but how can we know for sure?).

The demand would then only be p = 60 - 2q and set equal to MC = 54 we would have solution q = (60 – 54)/2 = 3. So only 3 units of the public good would be provided. The two who pay would each pay 27 per unit ( p = 30 – 3) and each would have consumer surplus = .5(30 – 27)3 = 4.5 for a total from the 2 = 9.

Now, the one who said they have no need for the public good actually gets a benefit or consumer surplus = .5(30 – 27)3 + 27(3) = 85.5. The individual has an incentive to be a free rider because they benefit more (85.5 to 72), while as a group the total consumer surplus is smaller (216 to 94.5).

Each individual may chose to be a free rider and then no units of the good will be produced.


884

The logic of this lesson suggests that there is a legitimate reason for the government to tax to raise funds to provide some public goods. Of course, there will probably always be debate on which public goods the government should provide.

Demonstration problem 14-4 is a neat problem in that our work environment might sometimes be a situation where folks will be free riders. The example there is that workers what a more desirable work environment. Maybe the workers want the parking lot to look better and so they may plant shrubs. Some may really get value from the shrubs but not want to pay.

Regression

A review and summary of our work up to this time with some examples – the examples are on the Excel file listed on the web right below

this file – Please be sure to hit the tabs for sheets 1, 2 and 3.


886

The model

When we look at two quantitative variables we often wonder if the two variables are related in some way. As an example I am sure you are aware of the relationship between the weight of a person and the amount of calories they ingest each day. Given all other factors being at a certain level, the more calories the higher the weight.

Now, in general when y is the dependent variable and x is the independent variable, we say the relationship between the variables is of the form

y = Bo + B1x

and we note that it could be the case that B1 = 0 and therefore there is no relationship between the two variables.

So, our basic question is, are the two variables in the population related?


887

The following is the progression of ideas you may want to follow as you investigate the relationship between two variables.

1) We take a sample from the larger population because it is often time consuming and expensive to do a census.

2) Create a scatterplot of the data and even include the estimated regression line. The plot gives us our first glimpse of the relationship between the variables. Caution, we can not rely on the graph alone.

If the points in the plot are upward sloping from right to left we say there is a positive relationship. If the points are downward sloping we say there is a negative relationship and if there is no slope we say there is no relationship.


888

3) Run the regression and get the estimated regression line, which we note in general as

y hat = bo + b1x and bo and b1 are read off an Excel regression output under the coefficients section.

4) The null hypothesis is that even if the sample has a scatterplot suggesting a relationship we will say there is no relationship and thus Ho: B1 = 0. The alternative is that there is a relationship of some kind and thus Ha: B not equal to 0. (We typically do a two-tailed test here.)

If the p-value on the slope > alpha we can not reject the null hypothesis and we conclude there is no relationship between the variables. Our analysis would be over. But, if the p-value < alpha we reject the null hypothesis and conclude there is a relationship between the variables in the population.


889

In our examples on the accompanying Excel program you see that examples 1 and 2 suggest we reject the null if alpha = .05 and we can not reject the null on example 3. Our work would be done with example 3. So, on example 3, even tough the sample suggests a positive relationship, there is not enough evidence in this case to suggest the relation is different from B1 = 0.

5) r2 (read r squared of r square) is the percentage of the variation in the y variable that is explained by the x variable.

Why is this important? The y variable is usually one we are very interested in – like college graduates starting salary – and as we look across individuals we notice not everyone gets the same starting amount – there is variability. r2 as a number is a measure of the % of the variation in y that is explained by the x variable. The value of r square ranges from 0 to 1 and the closer the value is to 1 the stronger is the relationship between the variables.


890

6) r and the sign of b1

Remember we are really concerned with the population relationship. We take a sample and test the null of no relationship. If we reject the null we say there is a relationship. What kind of relationship is there? We go with what the sample suggests is the relationship.

In example 1 we had a negative value of b1 and so we would say there is a negative relationship. In example 2 we had a positive b1 and we would say there is a positive relationship. (Remember in example 3 we concluded there was no relationship.)

The correlation coefficient r is the square root of r square and can also be used to assess the strength of the relationship. The r can range from -1 to 1, but if you calculate it by taking the square root of r square from the Excel output you would think it ranges from 0 to 1. You would have to take the square root of r square and give it resulting value the same sign as the slope estimate.


891

The closer the value or r to -1 or 1 suggests a stronger relationship between x and y. For example 1 we would have a negative r and for example 2 we would have a positive r.

The Basics of Regression


893

Remember back in your prior school daze some algebra? You might recall the equation for a line as being y = mx + b. Or maybe you had the form y = a + bx. Maybe you even had another form. Did you?

Notice how the y term is on the left of the equal sign. It looks like y is all by itself, but actually it is called the dependent variable. The value of y depends on the value of x. x is the independent variable.

On the right side the variable x has a coefficient with it called the slope. The slope can be negative or positive, or even zero.

The term that is on the right with no x hooked to it is called the y-intercept, or intercept for short. The intercept can be positive, negative or zero.


894

x

y

This height is called the intercept.

Here I show three different lines with the same intercept. But, different lines could have different intercepts. Intercepts can even be negative.


895

x

y

The dot on the line is represented by an x value and a y value.

1

?

Say we move from a dot one unit away in the x direction. The slope then tells us how far we have to go in the y direction to get back to the line.

Note on the upward sloping (to the right) curve when we went over to the right on x we have to go up on the y variable. On the flat line we wouldn’t move in the y direction at all, and on the downward sloping line we would move down to the line.

1

2

3


896

Now, in algebra, we might have a specific line with the form

y = 60 + 5x. Then we can say, when

x= y=

0 60

1 65

2 70

3 75 and so on. In algebra every point fits exactly on the line.


897

Now, let’s use an example to see how what we have just been thinking about is related to statistics. Say a chain of pizza joints has stores in many college towns. And say it is wondering if the sales in these towns are related to the size of the college in terms of student population.

Sales would be the y variable because sales are thought to depend on the population. The student population would be the x variable.

On the next screen I have data from 10 of the stores. Note each row is a store and we have on each line the population and the sales. Then we put each store as a dot in the scatter diagram.


898

Restaurant Population Sales1 2 582 6 1053 8 884 8 1185 12 1176 16 1377 20 1578 20 1699 22 149

10 26 202

0

50

100

150

200

250

0 5 10 15 20 25 30

Population in 1000's

Sales

in $1

000's

Do the dots fit exactly on a line like in algebra? No, but maybe a line can be put into the data so that the line can be used to represent the data.


899

Math formIt is thought that in the population the variable x and y are related in the following general form:

y = B0 + B1 x + e,whereB0 is the y intercept of the line, B1 is the slope of the line, and e is an error term that captures all those influences on y not picked up by x. The error term reflects the fact that all the points are not directly on the line.

So, we think there is a regression line out there that expresses the relationship between x and y. We have to go find it. In fact we take a sample and get an estimate of the regression line.


900

Later we will see a method to get an estimate, but for now say we have the method.When we have a sample of data from a population we will say in general the regression line is estimated to be ^

y = b0 + b1 x, where the ‘hat’ refers to the estimated value of y.

Once we have this estimated line we are right back to algebra. y hat values are exactly on the line.

Now, for an each value of x we have data values, called y’s, and we have the one value of the line, called y hat.


901

At each x a deviation, or residual is the data value minus the y hat value. The method we use to find the line is called the (ordinary) least squares method.

From the data of our example I tell you the least squares method gives the equation

y hat = 60 + 5x (look like the algebra you saw before?)

Now, go back to the slide with the data. Create a y hat, or values of y on the line, column (you don’t have too, but think about it). You get this column by taking the population values for x in each row and plug into the line to get the y hat. The difference between the sales values and the y hat values are the deviations to which I refer.


902

ordinary least squaresThe typical method used to pick the line through the data is called the ordinary least squares line. This method is the one that minimizes the sum of squared deviations of the data points to the line. The line has desirable properties(not proven here):1) It is unbiased - if many samples were taken, the average of the intercepts and slopes from the samples would be the population intercept and slope.2) It is consistent - ‘large’ samples would give the population intercept and slope as well.


903

One last point in this section. When you see the scatterplot like the one I had before, you should look at the pattern in the dots.

Look at the dots from left to right. 1) if the dots go up hill, suggesting a positive slope, you should get the feel that the sample suggests the relationship between the variables is then beginning to look like a positive relationship – this means the two variables tend to move in the same direction. The means higher values for x go with higher values for y. 2) If the dots go down hill the sample is suggesting there is a negative relationship between the variables. 3) If the dots are flat the sample is suggesting there is no relationship between the variables.

More Regression Information


905


906

On the previous slide I have an Excel regression output.

The example is the pizza sales we saw before.

The first thing I look at is the coefficients. See cell b28 has the word coefficient. We take the information below and write the equation as

y hat = 60 + 5x. This is the estimated regression equation. The intercept is 60 and the slope is 5.

Remember x = population of students and y = sales.


907

Hypothesis test about the population slope B1.

Remember we have taken a sample of data. In this context we have taken a sample and estimated the unknown population regression.

Our real point in a study like this is to see if a relationship exists between the two variables in the population. If the slope is not zero in the population, then the x variable has an influence on the outcome of y. Now, in a sample, the estimated slope may or may not be zero. But the sample provides a basis for a test of the true unknown population slope being zero.

For the test we will use the t distribution.


908

The t-distribution

At this stage of the game I am going to have you accept some of the following without much proof.

The t-distribution is like the normal except for two notable features. 1) t-distributions tend to be wider (show more variability) than z distributions. 2) the t-distribution does not have one standard like the normal distribution. Each t-distribution is unique, based on its degrees of freedom.

Admittedly, degrees of freedom is a term without much meaning to you, but in the context of simple regression equals the sample size minus 2.


909

Many books have t-tables. Or you could do a Google search. Go to the upper tail area being .025. If you run down the column with your finger you will notice at the bottom the number 1.96. So, when the degrees of freedom is really large, the t is like the z. But, with other degrees of freedom on the t-distribution, you have to go out farther than 1.96 to get to .025 in the upper tail. This is what I mean be t-distributions being wider.

The t-values in this table are critical values for tests of hypotheses.

Back to our hypothesis test about the slope. The null hypothesis is that B1 = 0, and the alternative is that B1 is not equal to zero. Since the alternative is not equal to zero we have a two-tailed test.

Our example has a sample size of 10, so the degrees of freedom is 8. A level of significance of .05 means we want .025 on each side for a two tail test. From t-table the critical t is 2.306.


910

Back on the computer output we see the calculated t in cell d30. The t stat from the sample is the slope divided by the standard error. Notice the t is 8.6167. Since this is bigger than the critical t we reject the null and conclude the slope is not zero in the population. Thus in the population of all company stores, sales are influenced by populations of students in the college towns.

Excel prints the p-value for the test. For the slope we have 2.55E-05. E notation of the form E-05 means move the decimal in the number 5 places to the left. So our p-value is 0.0000255. This is a two-tailed p-value. Since this is less than .05, it is an alternative way to reject the null hypothesis. This method can be used without looking at the t-table.


911

In cells f30 and g30 you have the 95% confidence interval for the slope. The interval is (3.6619, 6.3381). So you can be 95% confident the true unknown population slope is in this interval.

A few slides back I wrote ,” From the t-table the critical t is 2.306.” The margin of error in the confidence interval is the critical value times the standard error: (2.306 ).5803 = 1.3381 for an interval for the slope 5 – and + 1.3381.

In cell b17 you see the R square value of 0.9027. Sometimes this is called r2, and its real name is the coefficient of determination. The coefficient of determination is a statistic used to see how well the data points “hug” the regression line. The value can be anywhere from 0 to 1. If all the data points actually touch the line then R square would be 1. If the value is 0 the points are not close to the line at all.


912

The square root of the coefficient of determination is the correlation coefficient ( called r). Remember the correlation coefficient was an indicator of the direction and strength of the relationship between two variables.

The correlation coefficient could be anywhere from minus 1 to 1. Negative values meant a negative relationship and positive values meant a positive relationship. There we said the closer to 1 or minus 1 the stronger the relationship.

If R square = 1, r = 1 and the relationship is as strong as you can get.

If R square = .9, r = .94 and you still have a pretty strong relationship.

If R square = .5, r = .71 and you would still be in the strong relationship neighborhood.


913

Well, in this section I have tried to go over some of the basic regression ideas. The point again is that we are studying two variables together and trying to establish if the two variables are related or not.

Why should we care if two variables are related? As a person in business it might help the bottom line. As another example, say it can be established that the size of the advertising budget has an impact on sales. This could help us determine the right size budget.

I have a claim that one day I will try to back up by using regression. I claim that recycling of paper makes states in the country have less trees. Each state probably recycles a different number of pounds of paper and has a certain amount of tree population growth or destruction. With tree population as the dependent variable, I would expect the slope coefficient on pounds of paper recycled to be negative. In other words, the more recycling, the less trees. (ITS an econ story, but anyway.) Regression can be used in social policy analysis. Anyway, that’s all for now.

Hypothesis test of the slope


915

X x

Y y

Null hypothesis Alternative hypothesis


916

ON the previous slide I have two graphs with some points in each (ignore the ovals for now, please). Imagine there are more points in the same basic area as those shown.

Now, we use stats to help us understand the world and in the context of regression we think variables are related. Examples would be that income depends on years of school, or weight depends on net calories consumed, or gpa depends on hours studied per week.

IN each example the thinking is that one variable changes value from one person to the next because each person does not have the same value of another variable – not all people have the same income because not all people have the same years of schooling.

There is a tradition in statistics to say initially that there is no relationship between two variables (even if our research and theorizing suggests there is). The null hypothesis is then that the slope of a regression line between the two variables is zero. This would mean the data are the graph on the left.


917

In stats we take a sample from a population and make calculations – here we calculate the regression coefficients. We take a random sample, which means every data point has an equal chance of being picked.

Now if you look at the graphs again and this time look at the ovals. Say the ovals represent the data points that make it in our sample. If you just focus on the ovals could you tell which graph the data came from? No, both samples suggest a positive relationship between x and y.

Now in regression we assume the slope in the population is zero and use the sample slope as a basis for a test of hypothesis about the population slope. Under the hypothesis of a zero slope if the slope we get has a low probability of occurring then we reject the null and conclude the population slope is not zero.

Look back at the graph on the left. Could we get a random sample that would only include points in the oval? Yes we could, but is seems more likely the random sample would include other points, like in upper left. So we have a low probability of getting the sample and thus the slope. When we have a low probability result (.05 is chosen as low) we reject the null and conclude the population is probably more like the alternative.

An example


919

Airline Percentage on time Complaints

Southwest 81.8 0.21

Continental 76.6 0.58

Northwest 76.6 0.85

US Airways 75.7 0.68

United 73.8 0.74

American 72.2 0.93

Delta 71.2 0.72

America West 70.8 1.22

TWA 68.5 1.25

Here is some data on airlines. We have the percentage of flights on time and the number of complaints per 100,000 passengers.

What do you think happens to the number of complaints the greater the percentage of flights on time? I would think the complaints would fall.


920

00.20.40.60.8

11.21.4

65 70 75 80 85

% on time

Com

plai

nts

per 1

00,0

00

pass

enge

rs

complaints

The scatterplot suggests higher the % on time the lower the number of complaints per 100,000 passengers.


921

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.882607408

R Square 0.778995837

Adjusted R Square 0.747423814

Standard Error 0.160817904

Observations 9

ANOVA

df SS MS F Significance F

Regression 1 0.638118768 0.638118768 24.67361157 0.001624211

Residual 7 0.181036788 0.025862398

Total 8 0.819155556

CoefficientsStandard

Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 6.017831995 1.052259699 5.718960823 0.000721093 3.529634972 8.506029019 3.529634972 8.506029019

% on time -0.0704144 0.01417572 -4.967253927 0.001624211 -0.103934628 -0.036894173 -0.103934628 -0.036894173


922

ON the previous screen I put a circle around the coefficients on the bottom left of the screen. We use them to write the equation as

y hat = 6.02 – 0.07x, where y = complaints per 100,000 passengers and x is % of flights on time.

Just to the right of the circle I have a rectangle around the t stat and p-value for the slope. Since the p-value is less than .05 we can reject the null hypothesis of a zero slope and we conclude that the percentage of flights on time has an influence on the number of complaints per 100,000 passengers. Since the slope is negative we would say the more flights on time means less complaints.

IN the rounded rectangle on the previous page toward the top left you see the R-square. You really only what to look here after you see the slope is not zero. When the slope is not zero the R-square tells us the percent of the variation in y explained by the x variable. Here this means that 77.9% of the variation in complaints is explained by the % of flights on time. This is a good R-square. Can you think of what else would lead to complaints? Maybe bad snacks on the flight, or rude flight attendants.

Excel and Regression


924


925

On the next screen you can see I typed in the data for an schooling / income study. I even put in labels in the first row.


926


927

On the main menu at the top, go to the tools option. When you click on tools you want to see the tool called data analysis. Excel does not always show this option. If you do not see data analysis, hit the Add-Ins option. From the pop-up menu there check the Analysis Toolpak.

When this is completed you should be able to go back to tools on the menu at the top and hit data analysis. You would then see a screen similar to what comes next in these slides. You will have to scroll down in the list to get to “regression.”


928


929

On the next screen you will see what excel asks you to put in to get the regression results.


930


931

For the example I had on slide 4,

For the Input y range put b1:b6, the cells the data is in.(y is the dependent variable – the variable I am most interested in understanding.)For the Input x range put a1:a6.(x is the variable we think will help us predict and explain y.)Check labels box. (Only check the labels box if you have a label in the data set like I do.)

Check confidence level box - keep at 95%

Check output range and a9 in open box. (I like to have the output next to the data set. You can go to a new worksheet if you want.)


932

When you say ok to the regression dialog box Excel will do its thing and have the results highlighted. Keep the results highlighted, but you will need to adjust the column widths to be able to read the output. Open the Format menu, choose ‘column’ and select ‘autofit selection.’

Then un-highlight the cells and look at your results.

If you print the results you may want to change the page to landscape.Sometimes in the output you will see a number followed by E and some other stuff. E-06 means take the number given and move the decimal place six places to the left. Similarly, E+06 means move the decimal 6 places to the right.

Duopoly again

Here we look at the Stackelberg leader/follower model


934

The Cournot model was a simultaneous game in the sense that each player did not know what the other did before their own action.

The Stackelberg duopoly model is sequential in that one player will act, the other will see the action and then act.

As an example, let’s use the same demand and cost conditions as we used in the Cournot example:

P = 100 – 2Q, or = 100 - 2(q1 + q2), and MC = 10 for both.

Firm 1 is the leader in the example. There are industries where we have leaders. In cars it is still probably GM. What about in software? Computer Chips?


935

Firm 1 being the leader thinks that with the market demand firm 2 will take what ever part of the market firm 1 leaves behind. In the sense of Cournot, firm 1 understands that firm 2 has a best response function indicating what firm 2 should make. As before in the Cournot case, the best response function firm 2 has is found by:

MR = MC for firm 2, giving

100 - 2q1 - 4q2 = 10, or q2 = (90/4) - (2/4)q1,

Firm 1 then thinks that since firm 2 will follow in this way I (firm 1) will put this into the demand and see what is my best option where MR = MC.


936

P = 100 - 2q2 - 2q1, is market demand

P = 100 – 2[ (90/4) - (2/4)q1 ]- 2q1, by sub. of q2 from firm 2,

= 55 - q1.

Firm 1 MR = MC is then

MR = 55 – 2q1 = 10 = MC, or

q1 = 22.5.

Then the follower will have

q2 = (90/4) - (2/4)22.5 = 11.25. Total output in the market is 33.75 and thus the market price is (from the demand curve) 100 – 2(33.75) = 32.5.


937

Summary:

P Q profit

Monopoly 55 22.5 1012.5

P. Comp 10 45 0 for each firm

Duopoly - Cournot 40 30 450 for each firm

Doupoly – Stack. 32.5 33.75 506.25 for leader

253.13 for foller

So, the Stackelberg Duopoly leads the industry closer to the competitive solution than did the Cournot solution. This seems ironic because usually, when we have one leader firm, the leader gets criticized. But here it leads to better result, short of competition.

Supply and Demand


939

In economics we use a model of supply and demand in an attempt to understand market outcomes for a good or service. Of particular interest are two basic questions:

1) What determines the price of a product, and

2) What determines the quantity of a product sold.

Before I get into this I want to present something totally different. I want to talk about the weather. In particular, I want to talk about the highest temperature in Wayne, Nebraska on each and every day. At the bottom I have a graph of the highest temperature on each day for the year 2006 (I made up the data, but do you think it covers the basic idea?)

Day of the year

Highest temperature on the day

J F M A M J J A S O N D


940

Notes about graph:1) The long term we see the highest temperature occurred sometime in July or August.

2) When you look at any three or four day period (a shorter time frame than the whole year) you see ups and downs of the highest temperature.

Why does the highest temperature each day follow the pattern I have shown?

The accepted answer comes from the science areas of astronomy and physics. In these sciences there are theories about how the earth is tilted and how it rotates around the sun. These ideas provide us with our understanding of the pattern of daily high temperatures.


941

Now, instead of thinking about the weather we could consider a market. There is a market for corn, wheat, Mt. Dew in a 20 ounce bottle, Microsoft stock, and many more. Some folks use a graph similar to the one I had with the weather example. The vertical axis variable may be the price of the product or the quantity (number of units) of the product traded.

Our study of supply and demand is the scientific way folks go about explaining the pattern of price movements and/or quantity traded movements.

When we study supply and demand we use a different graph than the one I have used so far. But it is related. Let’s turn to that graph next.


942

Price, P

Quantity, Q

Along this axis we measure the price per unit of a product. At the bottom we start at zero and move our way up.

Along this axis we measure quantity in units of a good or service. On the left we start at zero and as we go right we go to larger amounts.


943

Price, P

Quantity, Q

We could look at any point in the graph and at that point we can get a feel for the quantity at that point and the price at that point. This point would correspond to the other graph in that this point is for a certain day. On other days we could be a a different point and we want to build a theory of that movement.Price

at the point

Quantity at the point


944

Price, P

Quantity, Q

In economics, often times the only point you need to focus your attention on is where two curves cross.


945

Price, P

Quantity, Q

D1D2

If a curve should shift – here the demand shifts – you can focus your attention on the new intersection.


946

Price, P

Quantity, Q

D1D2

1) Note here that when the demand shifted we would say it shifted because of a change in demand

2) Note here that after the curve shifted, we will move along the new demand curve and call the movement a change in the quantity demanded.


947

So, we have gotten warmed up to the model of supply and demand. Now we want to look at

1) The demand side of the market,

2) The supply side of the market,

3) The interaction of supply and demand and how these determine the price in the market and the quantity traded in the market, and

4) Changes in supply and demand and how that leads to price and quantity traded changes.


948

P

Q

D

Demand in general refers to how much of a product consumers want to buy. In the graph here you should note two things.

1) The demand curve is downward sloping as you look at the graph from left to right, and

2) The demand curve is in a certain position or location that could change.

Let’s think about each of these points in more detail.

When we say the demand curve is downward sloping we say this is a reflection of the law of demand. The law of demand is a statement that when the price of the product changes the quantity demanded moves in the opposite direction.

So, if the price should rise, the quantity demanded will fall, and if the price should fall the quantity demanded will rise.

Law of Demand – Price and quantity demanded are inversely related.


949

Let’s consider one more thing about the law of demand. Let’s take an example from our life. Any music CD costs about 15 bucks, give or take a few $’s. At that price you and I could probably buy more than we do, but we would have to give up other things (like milk and cookies, what were you thinking?) to get even more CD’s. In order to get us to demand an even greater quantity the price has to be lowered and we therefore do not have to give up as much of the other things we enjoy.

It works the other way as well. If the price becomes higher we have a lower quantity demanded because at the higher price we have to give up too much of other things we like and so we reduce our quantity demanded for the CD’s.


950

P

Q

D

But, If the price was lower than P1 you see there would be movement down the demand curve. Some folks would say that since they do not have to give up as much other stuff to get more units here, they are happy to demand a greater quantity.

So, the price of the product is a major determinant of how much of a product consumers want. But there are other things that have an influence as well.

P1

Q1

In the graph at P1, although folks could probably buy more of the product, quantity demanded is only Q1 because folks have decided they do not want to give up other things to get more of Q.


951

P

Q

D

P1

Q1

A few slides back I mentioned that we need to pay attention to the position or location of the demand curve and that maybe the location could change.

What I now want to make explicit is that Q1 was demanded at P1 with the understanding that other things that influence demand are held constant. If these other things should change then at P1 the amount people want could change and the demand would shift.

Let’s go back to our CD example. We said if the price was P1 folks would demand Q1 units. But, if people get more income it is likely they can afford more things and thus the demand for CD’s would shift to the right.


952

So, on the previous slide we see the demand curve would shift right when a people’s income would go up. Similarly we would expect the demand curve would shift left if people’s income should fall.

People’s income is a factor that leads the demand curve to be in a certain location. This means if income should change the demand curve will shift to a new location.

Other factors that lead to a shift in the demand include the price of related goods, consumer taste and preference, and the number of consumers in the market.

On the next slide is a table that will list how the demand curve will shift given a change in a factor of demand. Note the table does not include the price of the product itself. If the price changes there is a movement along the demand curve and we say there is a change in the quantity demanded.


953

Factor of demand change demand shifts toIncome increase for normal good rightIncome decrease for normal good leftIncome increase for inferior good leftIncome decrease for inferior good rightComplementary good price increase leftComplementary good price decrease rightSubstitute good price increase rightSubstitute good price decrease leftIncrease in consumers in market rightDecrease in consumers in market left

Please note that when a factor changes in such a way that demand shifts to the right we could also say demand has increased and if a factor changes in such a way that demand shifts to the left we could also say demand has decreased.


954

P

Q

S

Supply in general refers to how much of a product producers want to sell. In the graph here you should note two things.

1) The supply curve is upward sloping as you look at the graph from left to right, and

2) The supply curve is in a certain position or location that could change.

Let’s think about each of these points in more detail.

When we say the supply curve is upward sloping we say this is a reflection of the law of supply. The law of supply is a statement that when the price of the product changes the quantity supplied moves in the same direction.

So, if the price should rise, the quantity supplied will rise , and if the price should fall the quantity supplied will fall.

Law of Supply – Price and quantity supplied are directly, or positively, related.


955

Let’s consider the story about why the supply curve is upward sloping. Production of a good or service takes time and producers have lots of things they would like to do. When the price of a good is low producers look at their options and conclude at a low price that they will make a few units but then do something else because there is not a big payoff to production. But, if the price is higher they do not mind giving up other things to produce here because they will get more for their efforts.


956

P

Q

S

In the graph at P1, although producers could probably make more of the product, quantity supplied is only Q1 because producers have decided they do not want to give up other things to make more of Q.

But, If the price was higher than P1 you see there would be movement up the supply curve. Some producers would say that since they get more for producing this item they give up doing other stuff and they are happy to supply a greater quantity of this good.So, the price of the product is a major determinant of how much of a product producers want to make. But there are other things that have an influence as well.

P1

Q1


957

P

Q

S

A few slides back I mentioned that we need to pay attention to the position or location of the supply curve and that maybe the location could change. What I now want to make explicit is that Q1 was supplied at P1 with the

understanding that other things that influence supply are held constant. If these other things should change then at P1 the amount producers want to make could change and the supply would shift.As an example, say the company is making candy and the price of sugar, a major input to the product, goes up. Then at P1, since it costs more to make a unit of candy, the producer will make less because there is less profit to be made per unit. Producers would rather do something else.

P1

Q1


958

So, on the previous slide we see the supply curve would shift left when the price of an input to the production process went up. Similarly the supply curve would shift right when the price of an input falls.

The price of an input is a factor that leads the supply curve to be in a certain location. This means if the input price should change the supply curve will shift to a new location.Other factors that lead to a shift in the supply include the state of technological sophistication used in production (what I call the state of technology), the number of sellers and the price sellers expect to see in the future.On the next slide is a table that will list how the supply curve will shift given a change in a factor of supply. Note the table does not include the price of the product itself. If the price changes there is a movement along the supply curve and we say there is a change in the quantity supplied.


959

Factor of supply change supply shifts toInput price increase leftInput price decline rightIncrease in state of technology rightDecrease in state of technology leftIncrease in expected future price leftDecrease in expected future price rightIncrease in producers in market rightDecrease in producers in market left

Please note that when a factor changes in such a way that supply shifts to the right we could also say supply has increased and if a factor changes in such a way that supply shifts to the left we could also say supply has decreased.


960

Price, P

Quantity, Q

Now that we have considered supply and demand separately we will bring the two together and see how buyers and sellers interact in a market.

S

D


961

Price, P

Quantity, Q

Notice at this price P1 the quantity demanded equals the quantity supplied.

S1

D1

P1

Q1


962

Price, P

Quantity, Q

Notice that when you look at any price above where the curves cross, like at Pa, the quantity supplied is greater than the quantity demanded – a surplus

S1

D1

Pa

Qd Qs


963

Price, P

Quantity, Q

Notice that when you look at any price below where the curves cross, like at Pb, the quantity supplied is less than the quantity demanded – a shortage

S1

D1

Pb

Qs Qd


964

Notice on the previous three slides that I have put the subscript 1 on the labels for the supply and demand curves. I do this to have you understand that when we consider the interaction of supply and demand we initially have supply and demand located in place because the factors that can shift these curves are fixed at a certain level for the time being. Later these curves can shift, but for now we have them fixed in place.

Theory of Price Change

1) When the price is above P1 in our graphs from the previous slides we see Qs > Qd, meaning we have a surplus. All buyers at this price (as recognized by the amount on the demand curve) would get to buy, but not all sellers would get to sell. This surplus of items means some sellers have an incentive to change. They would lower the price so that they do not have any left over items.


965

2) When the price is below P1 in our graphs from the previous slides we see Qs < Qd, meaning we have a shortage. All sellers at this price (as recognized by the amount on the supply curve) would get to sell, but not all buyers would get to buy. This shortage of items means some buyers have an incentive to change. They would bid up the price in an attempt to get the item.

3) When the price is P1 we see Qs = Qd. All buyers and sellers are able to buy and sell, respectively, what they want at this price. Neither group has an incentive to change.

Item 3) here defines equilibrium in the market. Take this to mean you should focus your attention on were the curves cross. But items 1) and 2) help us understand why the price will change when conditions in the world change. Let’s turn to this next.


966

Price, P

Quantity, Q

For any market story this is where you mind should be, on this graph with all the knowledge you have in these notes. Slides 16 and 22 mention how supply or demand could change.

S1

D1

P1

Q1


967

Price, P

Quantity, Q

Here we have a demand increase. Slide 16 should remind you how a demand increase can happen. Note at the initial price P1 Qs = Q1 but demand is now Qd.

S1

D1

P1

Q1

D2

Qd


968

Price, P

Quantity, Q

At P1, since Qd > Qs, we have a shortage and with a shortage the price will rise. The price will rise to P2.

S1

D1

P1

Q1

D2

Qd

P2


969

Price, P

Quantity, Q

Note as the price rises due to the shortage both a) the quantity supplied rises from Q1 to Q2 and b) the quantity demanded falls from Qd to Q2. The shortage is gone.

S1

D1

P1

Q1

D2

Qd

P2

Q2


970

Let’s summarize what is on the last 4 slides.

1) We have the market at some starting point. Note the equilibrium price and quantity traded, P1 and Q1.

2) The demand increases creating a shortage.

3) The shortage means the price will rise.

4) The shortage is eliminated because with the higher price the a) quantity supplied rises and b) the quantity demanded falls (from the new higher level).

Overall, the increase in demand resulted in

1) An increase in the market price, and

2) An increase in the quantity traded in the market.


971

Price, P

Quantity, Q

From this starting point let’s now look at the story of a supply increase.

S1

D1

P1

Q1


972

Price, P

Quantity, Q

Here we have a supply increase. Slide 22 should remind you how a supply increase can happen. Note at the initial price P1 Qd = Q1 but supply is now Qs.

S1

D1

P1

Q1

S2

Qs


973

Price, P

Quantity, Q

At P1, since Qs > Qd, we have a surplus and with a surplus the price will fall. The price will fall to P2.

S1

D1

P1

Q1

S2

Qs

P2


974

Price, P

Quantity, Q

Note as the price falls due to the surplus both a) the quantity supplied falls from Qs to Q2 and b) the quantity demanded rises from Q1 to Q2. The surplus is gone.

S1

D1

P1

Q1

S2

Qs

P2

Q2


975

Let’s summarize what is on the last 4 slides.

1) We have the market at some starting point. Note the equilibrium price and quantity traded, P1 and Q1.

2) The supply increases creating a surplus.

3) The surplus means the price will fall.

4) The surplus is eliminated because with the lower price the a) quantity demanded rises and b) the quantity supplied falls (from the new higher level).

Overall, the increase in supply resulted in1) An decrease in the market price, and

2) An increase in the quantity traded in the market.


976

What have we learned? Among other things

1) The price and quantity traded in a market are determined by the interaction of supply and demand.

2) The price and quantity traded in a market will change if there is a change in supply or demand.

Economics all

Documents

introduction pgpse notes

rational people

services people

scarce resources

market economy

marginal costs

social costs

principles of economicssociety