The Theory of Consumer Choice Part I. Class Business Homework 1 is due Wednesday, June 26 th. Make sure you read Chapter 1 of The Armchair Economist for.

The Theory of Consumer ChoicePart I

Class Business Homework 1 is due Wednesday, June 26th.

Make sure you read Chapter 1 of The Armchair Economist for Monday!

The Right Thing to Do

The Trolley Problem Suppose you find yourself near some train tracks. A trolley is racing down the tracks, and next to you is a lever that

will switch the tracks and send the trolley down another path. Playing on the tracks are some kids. If you pull the lever, the trolley will go down a track with only one kid on it.

There is no doubt that if you pull this lever, that one kid will die. If you do not pull the level, the trolley will go down a track with five kids on it.

There is no doubt that if you do not pull this lever, all five kids will die.

What do you do?

The Trolley Problem Part 2 Suppose that you are standing on top of a bridge, watching as a trolley is racing toward some kids playing on the tracks.

On the bridge with you is a very fat man. If you push the fat man off the bride, onto the tracks, he will surely die, but he

will also surely stop the trolley, for he is a very fat man. If you do not push the fat man, the trolley will continue past the bridge and

kill five children playing in the trolley’s path.

What do you do?

The Trolley Problem Part 3 Suppose that you are a doctor with five very sick patients. Each patient is in need of a transplant. One needs a heart, the second a kidney, the third a liver, the fourth a lung, and the fifth also needs a kidney.

A man walks into your office with a minor health issue, but while running some tests you realize that he would be a viable donor for all five of your other patients.

If you cure this man of his minor health issue and send him on his way, there is no doubt your other five patients will die.

If you kill this man and take his organs, all five of your other patients will surely live.

What do you do?

Ethics There are two prominent theories about how one ought to act: Deontology: Decisions should be made according to a set of rules. Categorical Imperative: A proposition that declares a certain action to be

necessary. “Act only according to that maxim whereby you can at the same time will that it

should become a universal law without contradiction.” Contractarianism: We must construct a social contract that governs behavior. John Rawls: Do the constructing behind a “veil of ignorance” in the “original

position.” Natural Rights: Human beings have absolute, natural rights. John Locke: Natural right to defend “Life, health, Liberty, or Possessions.”

Consequentialism: Morality depends on the outcome. Utilitarianism: Maximize happiness and reduce suffering. Jeremy Bentham: “It is the greatest happiness of the greatest number that is the

measure of right and wrong.”

Hedonic Calculus The philosopher Jeremy Bentham (1748-1832), and his student John Stuart Mill (1806-1873) are considered the fathers of Utilitarianism.

Bentham suggested counting up units of pleasure and pain based on the following dimensions:

Intensity: How strong is the pleasure? Duration: How long will the pleasure last? Uncertainty: How likely is it that the pleasure will occur? Propinquity: How soon will the pleasure occur? Fecundity: The probability that the action will be followed by sensations of the

same kind. Purity: The probability that it will not be followed by sensations of the opposite

kind. Extent: How many people will be effected? Benthamite Francis Edgeworth imagined the intensity could be

measured by a machine, which he called the “hedonometer”.

No Relic of the Past Daniel Kahneman and his co-authors have tried to estimate how much people enjoy various activities.

Fun with Jeremy Bentham Bentham’s will requested that his head be mummified and his skeleton preserved, and put on display. His wished were granted and you can see him at University College London.

Modern Economics Most consider the birth of economics as a field of study to be Adam Smith’s The Wealth of Nations.

Smith was a moral philosopher concerned with how people ought to behave.

His studies led him to evaluate why some had more than others.

Economics remained closely associated with moral philosophy through the 19th century.

I think it is a great error that the authors of our textbook decided not to mention any of this.

“There is no such thing as philosophy-free science; there is only science whose philosophical baggage is taken on board without

examination.” – Daniel Dennett

Utility In modern parlance, Utilitarianism asks us to maximize “utility”.

What exactly is utility measuring? In economics, utility is synonymous with “happiness” or “well-

being”. We assume that people know what makes them happy, and how

happy it makes them.

The burgeoning field of neuroeconomics has been looking for something more concrete than these abstract concepts.

Many studies have looked at neurochemical responses to economic decisions. Some postulate that were talking about surges in neurotransmitters like dopamine.

The Economic Concept of Utility Economics, historically, has been a science used by consequentialists to determine and relate consequences.

Our methods sought to simultaneously offer both positive and normative analysis.

Utility: Assuming that it is measurable, the total satisfaction a person receives from a given level of consumption or from an activity. Almost always, economists think of utility as a mathematical function:

Properties of Utility: Completeness: All possible combinations can be processed by the function. Transitivity: If you prefer A to B and B to C, then you prefer A to C. Nonsatiation: More is preferred to less.

An Example of Utility Suppose we wanted to divide five hours of our time between listening to Billy Joel or the music of legendary film composer John Williams.

B is the number of hours spent listening to Billy Joel. W is the number of hours spent listening to John Williams.

If we divide the time evenly,

If we give up 1 hour of Billy Joel, how much Williams would we need to make us just as happy?

Indifference Different combinations of goods can make us equally as well off. We might calculate that our well-being is just as higher whether

we go for pizza or for Chinese food. We might be just as happy buying 3 oranges and 2 apples as we

are buying 1 orange and 6 apples.

Evaluating where people are indifferent cant help us to determine how people end up choosing what they get.

Every Combination Math is nice in that it allows us to be both complete and consistent.

John W

illia

ms

Billy Joel

We can graph this function at a constant utility to see all of the possible consumption bundles that make us that happy.

Changing Utility

Increasing our utility alters the equation, and shifts this curve.

Remember that this curve shows all of the possible values for B and W.

John W

illia

ms

Billy Joel

𝑈=13.75𝑈=13.80𝑈=13.85𝑈=13.90𝑈=13.95𝑈=14.00𝑈=14.05𝑈=14.10𝑈=14.15𝑈=14.20𝑈=14.25𝑈=14.30𝑈=14.35𝑈=14.40𝑈=14.45𝑈=14.50𝑈=14.55𝑈=14.60𝑈=14.65𝑈=14.70𝑈=14.75

Indifference Curves Indifference Curves plot all of the market baskets (combinations of goods) a consumer views as being equally satisfactory.

ICs hold utility constant, but allow the composition to change. Due to the laws of mathematics, the same composition cannot

yield two different utilities. 2.5 hours of John Williams and 2.5 hours of Billy Joel always gives 13.75 utils. The important conclusion of this proposition is that indifference curves

cannot cross.

W

B

W

B

W

B

Trade-Offs In order to maintain a constant level of well-being, every loss must come with a corresponding gain.

The rate at which we replace losses is called the marginal rate of substitution, and it measures our willingness to trade one good for another.

Utility B W

13.75 1 4.25

13.75 1.5 3.5

13.75 2 2.9375

13.75 2.5 2.5

13.75 3 2.15

From the choice of (2.5, 2.5) we can gain 0.5 hours of Billy Joel by giving up 0.35 hours of John Williams, or we can give up 0.5 hours of Billy Joel and gain 0.4375 hours of John Williams.

These trades leave us exactly the same in terms of welfare.

Marginal Rate of Substitution

The marginal rate at which we would give up hours of John Williams to get hours of Billy Joel is 9 hours of Joel for 7 hours of Williams.

From a starting point of 2.5 hours spent on each, we would be just as well off listening to 1.29 hours more of Billy Joel and 1 hour less of John Williams

This is the slope of the indifference curve.

Utility B W

13.75 1 4.25

13.75 1.5 3.5

13.75 2 2.9375

13.75 2.5 2.5

13.75 3 2.15

From the choice of (2.5, 2.5) we can gain 0.5 hours of Billy Joel by giving up 0.35 hours of John Williams, or we can give up 0.5 hours of Billy Joel and gain 0.4375 hours of John Williams.

These trades leave us exactly the same in terms of welfare.

Slope of the Curve

The rate at which we are willing to trade one good for another marks the slope of our indifference curve.

This will turn out to be a big help later on.

Utility B W

13.75 1 4.25

13.75 1.5 3.5

13.75 2 2.9375

13.75 2.5 2.5

13.75 3 2.15

John W

illia

ms

Billy Joel2.5

2.5

2

2.94

1.5

3.5

3

2.15

1

4.25

Slope = 9/7

Marginal Rate of Substitution The marginal rate of substitution (MRS) is a measure of an individual’s willingness to trade one good for another.

The MRS represents our marginal benefit of consuming a particular good.

We value 1 hour of John Williams at 1.29 hours of Billy Joel. Value is determined relative to our other options. This value

represents our benefits of gaining additional units of a good.

Most indifference curves exhibit a diminishing marginal rate of substitution.

When you have something in abundance, you are not willing to give up much to get more of it.

When you don’t have much of something you want, you will give up a lot to get it.

The Utility Approach Let’s go back to Billy and John:

We can get the marginal rate of substitution if we allow utility to vary as well.

Our previous approach held utility constant. This approach holds the quantity of each good constant in turn. By this method:

The Utility Approach

B W Utility

2.5 2 11.5

2.5 2.5 13.75

2.5 3 16

B W Utility

2 2.5 12

2.5 2.5 13.75

3 2.5 15.5

𝑀𝑈𝑊=∆𝑈∆𝑊

=16−13.753−2.5

=4.5 𝑀𝑈 𝐵=∆𝑈∆𝐵

=15.5−13.753−2.5

=3.5

𝑀𝑅𝑆𝑊𝐵=𝑀𝑈𝑊

𝑀𝑈𝐵

= 4.53.5

=97

Indifference CurvesApplications and Examples

Introducing the Composite Good A composite good is a number of goods treated as a group. Usually we use this to express all off the other opportunities that

we have.

Ex. If we are evaluating how much pizza to buy, the composite good represents all of the other things we could spend that same money on. XThis is a clever convention that allows us to analyze how we choose without restraining ourselves to a single alternative.

Changing Attitudes We all have different tastes that can be represented by indifference curves. When we really like something, we need a lot of something else to get us

to give some of it up. This makes the MRS very steep, and the indifference curve tilts towards

our favored good.

Jurassic Park

U1

X

Worthless Things As we become less and less concerned about one of the goods we are consuming, the IC becomes flatter.

Jurassic Park 2

U2

X

A Deep Dislike There are some goods which we may actually dislike. In order to offset getting more of the economic bad, we need more of the economic good.

Jurassic Park 3

U3

X

Perfect Substitutes The shape of our indifference curve can be inferred by what we know about the relationship between two goods.

What would an indifference curve between two perfect substitutes look like?

BP G

as

Shell Gas

U1

For most people, gas stations are perfect substitutes for each other.

What does this trade-off look like?

Perfect Compliments Perfect compliments are consumed in equal proportion to each other.

We only get utility from one if we a matching unit of the other.

Rig

ht

Shoe

Left Shoe

U1

Getting an additional right shoe affords us no additional utility.

We are indifferent between 2 pairs of shoes and 2 pairs of shoes plus one extra right shoe.

Indifference Curve Basics Indifference curves visualize our preferences for certain things. By comparing them to composite goods, we see what trade-offs

we have to make.

We gain utility as an indifference curve moves away from the origin. Higher utility means we are better off. Importantly, though, indifference curves for the same person

cannot cross.

The slope of the indifference curve, the marginal rate of substitute, measures the marginal benefit of our consumption.

The Budget Constraint

The Budget Constraint Our choices depend not only on our preferences, but also on our wealth.

We only have so much money to buy things with.We have to split that income among all of the

things we want. Everything we want has a price.

And so we are limited to the following:

Returning to our composite good convention, we can examine our budgetary possibilities be comparing it to a single good representing all of our other alternatives.

+1

Graphing our Budget Constraint Imagine we are at the grocery store deciding how much Diet Wild Cherry Pepsi to buy.

Pepsi costs $3 a 12-pack. The composite good costs $1.

12-Packs of Pepsi

All other goods (X)

Total money spent.

0 15 15

1 12 15

2 9 15

3 6 15

4 3 15

5 0 15

Pepsi

X

15

5

The Budget Constraint represents all of the affordable bundles of

goods. -3

The slope of the budget constraint is the ratio of

prices.

𝐼𝑛𝑐𝑜𝑚𝑒¿𝑃 𝑋𝑋+¿𝑃𝑌𝑌1−

The Price Ratio The Price Ratio is the slope of the budget constraint. A price ratio of -3 tells us that if we want to get one 12-pack of

Pepsi, we have to give up three units of the composite good. The price ratio measures the marginal cost of getting one more

unit of a good in terms of the value of the alternatives.

Because prices are usually fixed, the budget constraint is often a straight line.

This is not always true, however, and some of the most interesting problems involve unusual budget constraints.

Changes in Income The budget constraint holds income constant.

Therefore, when income changes, the budget constraint shifts.

The intercepts of this line are always income divided by price.

Pepsi

X

𝐼=$1𝐼=$2𝐼=$3𝐼=$ 4𝐼=$5𝐼=$6𝐼=$7𝐼=$8𝐼=$9𝐼=$10𝐼=$11𝐼=$12𝐼=$13𝐼=$14𝐼=$15𝐼=$16𝐼=$17𝐼=$18𝐼=$19𝐼=$20

Changes in Price Suppose Pepsi goes on sale, and now costs only $2 a 12-pack.

12-Packs of Pepsi

All other goods (X)

Total money spent.

0 15 15

1 12 15

2 9 15

3 6 15

4 3 15

5 0 15

Pepsi

X

15

5

Price Change Suppose Pepsi goes on sale, and now costs only $2 a 12-pack.

12-Packs of Pepsi

All other goods (X)

Total money spent.

0 15 15

1 12 15

2 9 15

3 6 15

4 3 15

5 0 15

Pepsi

X

15

5

12-Packs of Pepsi

All other goods (X)

Total money spent.

0 15 15

1 13 15

2 11 15

3 9 15

4 7 15

5 5 15

6 3 15

7 1 15

7.5

Changes in Price Price increases slide the intercept toward the origin.

Price decreases slide the intercept away from the origin.

Note that the intercept for a good whose price is not changing remains the same.

Pepsi

X

𝑃=$ 3.00𝑃=$ 2.90𝑃=$ 2.80𝑃=$ 2.70𝑃=$ 2.60𝑃=$ 2.50𝑃=$ 2.40𝑃=$ 2.30𝑃=$ 2.20𝑃=$ 2.10𝑃=$ 2.00

Changes in the Price Ratio Changes to income do not change the price ratio.

Changes to prices do change the price ratio.

Pepsi

X

𝐼=$1𝐼=$2𝐼=$3𝐼=$ 4𝐼=$5𝐼=$6𝐼=$7𝐼=$8𝐼=$9𝐼=$10𝐼=$11𝐼=$12𝐼=$13𝐼=$14𝐼=$15𝐼=$16𝐼=$17𝐼=$18𝐼=$19𝐼=$20

𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$3.00$1.00

=3.0

Changes in the Price Ratio Changes to income do not change the price ratio.

Changes to prices do change the price ratio.

Pepsi

X

𝑃=$ 3.00𝑃=$ 2.90𝑃=$ 2.80𝑃=$ 2.70𝑃=$ 2.60𝑃=$ 2.50𝑃=$ 2.40𝑃=$ 2.30𝑃=$ 2.20𝑃=$ 2.10𝑃=$ 2.00

𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$3.00$1.00

=3.0𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$2.90$1.00

=2.9𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$2.80$1.00

=2.8𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$2.70$1.00

=2.7𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$2.60$1.00

=2.6𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$2.50$1.00

=2.5𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$2.40$1.00

=2.4𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$2.30$1.00

=2.3𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$2.20$1.00

=2.2𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$2.10$1.00

=2.1𝑃𝑟𝑖𝑐𝑒𝑅𝑎𝑡𝑖𝑜=$2.00$1.00

=2.0

Budget Constraint Basics Budget Constraints visualize every affordable bundle of goods. We are constrained by prices and our income. We can only choose what we can afford.

As income rises, budget constraints move away from the origin. However, the slope of the budget constraint remains the same.

As prices rise, budget constraints tilt inwards, finding a new intercept at the maximum number of that good we can afford.

Price changes change the slope of the budget constraint.

The slope of the budget constraint represents the marginal cost of purchasing another unit of a good.

The Consumer’s Choice

Back to the Beginning Our goal is to maximize our utility. Unfortunately, we are constrained by prices and income.

Utility increases as our indifference curve moves away from the origin.

We can only afford consumption baskets on or below our budget constraint.

So where do we choose?

Sweet Spot Utility:

B.C.:

Pepsi

X

20

10

At this level of utility, we have an array of affordable options. At this level of utility, we have only one affordable option. At this level of utility, we no affordable options.

P*

X*

The Greatest Good Utility:

B.C.:

The goal of the consumer is to maximize utility.

We seek the highest indifference curve that still has at least one affordable basket of goods.

Pepsi

X

20

10P*

X*

By the Numbers

This chart shows affordable consumption bundles.X P Cost Utility

0 10 20 0

2 9 20 18

4 8 20 32

6 7 20 42

8 6 20 48

10 5 20 50

12 4 20 48

14 3 20 42

16 2 20 32

18 1 20 18

20 0 20 0

Utility: B.C.:

← We can afford 10 Pepsis if we buy 0 of the composite good, but our utility function doesn’t like this.

← As we get a mix of the goods our utility rises.

← But it is this particular bundle that we like the most.

X P Utility

ΔU

10 5 50 -

11 5 55 5

X P Utility

ΔU

10 5 50 -

10 6 60 10MRS: A measure of a consumer’s willingness to trade one good for another.

Price Ratio: The monetary trade-off between goods.

The Greatest Good Utility:

B.C.:

The goal of the consumer is to maximize utility.

We seek the highest indifference curve that still has at least one affordable basket of goods.

Pepsi

X

20

10P*

X*

5

10

5

10

Graphical Analysis It is where the slopes of our two lines are equal at the highest affordable utility that the consumers choice is made.

At this point marginal benefit (MRS) is equal to marginal cost (PR).

Pepsi

X

20

10

Slope = 1/2

Slope = 1/2

Alternative Logic Imagine that you are starting with $10, and you are deciding how much of it you want to spend on candy, and how much of it you want to spend on Star Wars action figures.

Candy Utility ΔU

1 6 6

2 11 5

3 15 4

4 18 3

5 20 2

6 21 1

7 21 0

8 20 -1

9 18 -2

10 15 -3

SWAF Utility ΔU

1 10 10

2 19 9

3 27 8

4 34 7

5 40 6

6 45 5

7 49 4

8 52 3

9 54 2

10 55 1

For simplicity, let’s pretend that both candy and Star Wars action figures cost $1 each.

How should we spend our first dollar?

How should we spend our second dollar?

How should we spend our third dollar?How should we spend our fourth dollar?

How should we spend our fifth dollar?How should we spend our sixth dollar?How should we spend our money?

Marginal Utility Per Dollar We can imagine people spending their money one dollar at a time. They will spend each dollar on the thing that gives them the most

additional, or marginal utility.

And so at the end of their spending spree, the following should be true:

Breaking it Down

MUC: The utility gained per unit of candy.PC: The price of candy.MUC/PC: The utility gained per dollar spent on candy.

MUS: The utility gained per action figure.PS: The price of action figures.MUS/PS: The utility gained per dollar spent on action figures.

𝑀𝑈𝐶

𝑃𝐶|𝐶=3

= 41

𝑀𝑈 𝑆

𝑃𝑆|𝑆=7

=41

The Answer to All of the Questions

𝑀𝑈𝐶

𝑃𝐶

𝑀𝑈 𝑆

𝑃𝑆¿𝑀𝑅𝑆𝐶𝑆 𝑃𝑅Marginal BenefitMarginal Cost

A User’s Guide to Consumer Theory This framework of indifference curves and budget constraints offers us some relatively simple tools for prediction.

We can examine how people will respond to all kinds of changes in their environment, from price changes to complex public policy.

It finds the utilitarian consequences of various actions.

This framework also provides with the raw materials we need to understand demand.

Next Time on MicroeconomicsWe’ll take a closer look at the math behind consumer theory.

Then we’ll start using consumer theory to answer some questions.