Problems from last session 1.A cost function for a bus that runs between the city and a college is estimated by TC = 100P – 64P 2 + 4P 3, P indicates the.

Problems from last session1. A cost function for a bus that runs between the city and a college is

estimated by

TC = 100P – 64P2 + 4P3, P indicates the number of passengers per day. Find the number of passengers per day that minimizes the average cost.

2. A total revenue function is given by TR = 9Q – Q2

a. Find the TR, AR and MR for Q = 0 to 6 by 1.

b. Draw the TR, AR and MR

3. The following demand function is given for a 165 litre freezer:

P = 5000 – 2Q.

a. Find the marginal revenue function

b. Find the price and quantity at which the MR = 0 and

c. Find Q and P at which TR is maximised.

Law of Demand• There is an inverse relationship

between the price of a good and the quantity of the good demanded per time period.

• Substitution Effect

• Income Effect

Components of Demand:The Substitution Effect

• Assuming that real income is constant:– If the relative price of a good rises, then

consumers will try to substitute away from the good. Less will be purchased.

– If the relative price of a good falls, then consumers will try to substitute away from other goods. More will be purchased.

• The substitution effect is consistent with the law of demand.

Components of Demand:The Income Effect

• The real value of income is inversely related to the prices of goods.

• A change in the real value of income:– will have a direct effect on quantity

demanded if a good is normal.– will have an inverse effect on quantity

demanded if a good is inferior.

• The income effect is consistent with the law of demand only if a good is normal.

Market Demand Curve

• Horizontal summation of demand curves of individual consumers

• Exceptions to the summation rules– Bandwagon Effect

• collective demand causes individual demand

– Snob (Veblen) Effect• conspicuous consumption• a product that is expensive, elite, or in short

supply is more desirable

Horizontal Summation: From Individual to Market Demand

Market Demand FunctionQDX = f(PX, N, I, PY, T)

quantity demanded of commodity X

price per unit of commodity X

number of consumers on the market

consumer income

price of related (substitute or complementary) commodity

consumer tastes

QDX =

PX =

N =

I =

PY =

T =

Demand Curve Faced by a Firm Depends on Market Structure

• Market demand curve

• Imperfect competition– Firm’s demand curve has a negative slope– Monopoly - same as market demand– Oligopoly– Monopolistic Competition

• Perfect Competition– Firm is a price taker– Firm’s demand curve is horizontal

Demand Curve Faced by a Firm Depends on the Type of Product

• Durable Goods– Provide a stream of services over time– Demand is volatile

• Nondurable Goods and Services

• Producers’ Goods– Used in the production of other goods– Demand is derived from demand for final

goods or services

Linear Demand Function

QX = a0 + a1PX + a2N + a3I + a4PY + a5T

PX

QX

Intercept:a0 + a2N + a3I + a4PY + a5T

Slope:QX/PX = a1

Linear Demand Function Example Part 1

Demand Function for Good X

QX = 160 - 10PX + 2N + 0.5I + 2PY + T

Demand Curve for Good X

Given N = 58, I = 36, PY = 12, T = 112

Q = 430 - 10P

Linear Demand Function Example Part 2

Inverse Demand Curve

P = 43 – 0.1Q

Total and Marginal Revenue Functions

TR = 43Q – 0.1Q2

MR = 43 – 0.2Q

Price Elasticity of Demand

/

/P

Q Q Q PE

P P P Q

Linear Function

Point Definition

1P

PE a

Q

Price Elasticity of Demand

Arc Definition 2 1 2 1

2 1 2 1P

Q Q P PE

P P Q Q

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Calculating elasticities

• Point estimate: (demand function is known); calculated at a specific point of demand.

• Arc elasticity: uses average values of Q and P as reference points (if only a table is known)

Q

P

P

Q

2/)(

2/)(

)(

)(

2/)(

2/)(

21

21

12

12

21

21

QQ

PP

PP

QQ

QQ

PP

P

Q

23

24

Price elasticity of demand and gross revenues

• h < -1 ==> an inverse relationship between price changes and gross revenues. Elastic

• h > -1 ==> a direct relationship between price changes and gross revenues. Inelastic

• h = -1 ==> no change in gross revenues as price changes. Unit elastic

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The Relationship between Elasticity and Total Revenue

IF DEMAND IS

P Q elastic if TR (relative Q> relative P)

P Q inelastic if TR (relative Q< relative P)

P Q elastic if TR (relative Q> relative P)

P Q inelastic if TR(relative Q< relative P)

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Total revenue, marginal revenue and price elasticity

Suppose P = a - bQ, (linear demand function)

then TR = aQ - bQ2

MR = dTR/dQ = a - 2bQ

Since h = (dQ/dP) . (P/Q)

QbQa

b

)(1

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Quantity

Price

Quantity

Dollars

a

a/ba/2b

TotalRevenue

Demandand MR

Total revenue, marginal revenue and price elasticity

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Marginal Revenue, priceand price elasticity

• If product is price elastic (<-1, marginal revenue must be positive)

1

1

1

?....)(.....)(

P

dQ

dP

P

QP

dQ

dPQPMR

whyQPPnotedQ

PQdMR

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Determinants of price elasticity of demand

• Elasticity is greater (in absolute values, i.e more elastic) when:

there are more substitutes for the product.the product is a more important part of a

consumer’s budget.the time period under consideration is

greater.

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Price Elasticity versus Marginal Return

• Price elasticity means … how strongly do consumers react (by buying less) if you raise your price

– Price elasticity is defined as the reaction of quantity on price

• Marginal return is defined as the reaction of money on quantities sold– How do revenues increase if you sell one more unit– MR = Marginal Revenue = Marginal Return

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Price setting: a simple rule

• Do not set price so low that demand is price-inelastic (>-1):

– Marg. Revenue is negative, i.e. by raising price, total revenue will increase and (!) costs will decrease.

==> optimal price depends upon MC and price elasticity==> The higher (the absolute value of) price elasticity, the lower the optimal price

priceoptimalMCP

rulepricingPMRMC

..../11

1

...)1

1(

Marginal Revenue and Price Elasticity of Demand

11

P

MR PE

Marginal Revenue and Price Elasticity of Demand

PX

QX

MRX

1PE

1PE

1PE

Marginal Revenue, Total Revenue, and Price Elasticity

TR

QX

1PE MR<0MR>0

1PE

1PE MR=0

Determinants of Price Elasticity of Demand

Demand for a commodity will be more elastic if:

• It has many close substitutes

• It is narrowly defined

• More time is available to adjust to a price change

Determinants of Price Elasticity of Demand

Demand for a commodity will be less elastic if:

• It has few substitutes

• It is broadly defined

• Less time is available to adjust to a price change

Income Elasticity of Demand

Linear Function

Point Definition/

/I

Q Q Q IE

I I I Q

3I

IE a

Q

Income Elasticity of Demand

Arc Definition 2 1 2 1

2 1 2 1I

Q Q I IE

I I Q Q

Normal Good Inferior Good

0IE 0IE

Income elasticity

• The percentage change in quantity demanded resulting from a 1 percent change in consumer income (I)

I

Q I

I Q

40

Categories of Income Elasticity

Income elasticity > 1: superior goods Income elasticity > 0, and <1: normal goods Income elasticity < 0: inferior goods

Superior

Normal

Inferior

Q

Y

Example: Using Elasticities inManagerial Decision Making

A firm with the demand function defined below expects a 5% increase in income (M) during the coming year. If the firm cannot change its rate of production, what price should it charge?

• Demand: Q = – 3P + 100M– P = Current Real Price = 1,000– M = Current Income = 40

Solution

• Elasticities– Q = Current rate of production = 1,000– P = Price = - 3(1,000/1,000) = - 3– I = Income = 100(40/1,000) = 4

• Price– %ΔQ = - 3%ΔP + 4%ΔI– 0 = -3%ΔP+ (4)(5) so %ΔP = 20/3 = 6.67%– P = (1 + 0.0667)(1,000) = 1,066.67

Cross-Price Elasticity of Demand

Linear Function

Point Definition/

/X X X Y

XYY Y Y X

Q Q Q PE

P P P Q

4Y

XYX

PE a

Q

Cross-Price Elasticity of Demand

Arc Definition

Substitutes Complements

2 1 2 1

2 1 2 1

X X Y YXY

Y Y X X

Q Q P PE

P P Q Q

0XYE 0XYE

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Cross price elasticity• The percentage change in quantity demanded of

good X resulting from a 1 percent change in the price of good Y

• How does demand for your product react to other companies’ price hikes?

• How does demand for your products 2-n react to price changes of your product 1?

,X Y

X YY X

Q P

P Q

Other Factors Related to Demand Theory

• International Convergence of Tastes– Globalization of Markets– Influence of International Preferences on

Market Demand

• Growth of Electronic Commerce– Cost of Sales– Supply Chains and Logistics– Customer Relationship Management

Suppose that business travelers and vacationers have the following demand schedule for airline tickets from

Paro to Bangkok :

Price Qd (BT) Qd (V)

150 2100 1000

200 2000 800

250 1900 600

300 1800 400

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1.As the price of tickets rises from 200 to 250, what is the price elasticity of demand for business travelers and vacationers?

2. Why might vacationers have a different elasticity than business travelers?

49

Suppose your demand schedule for cd’s is as follows:

Price Qd (Income = 10,000) Qd (Income = 12,000)

8 40 50

10 32 45

12 24 30

14 16 20

16 8 12

a. Calculate the price elasticity of demand as the price of cd’s increases from 8 to 10 for two cases

1. if your income is 10,0002. if your income is 12,000

b. Calculate your income elasticity of demand as your income increases from 10,000 to 12,00 for two cases

1. If the price is 122. If the price is 16

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2. Assume that last year the average income of Thimphu residents (and the average of Druk Pizza customers) rose by 8%. During the same period, the quantity demanded of Druk’s pizza’s rose by 3%. There was no appreciable change in the taste’s of consumers, input prices, substitutes, complements etc. What is the income elasticity of demand for Druk’s pizzas.

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1. Shambala hotel in Thimphu charges 5.25 for a plate of momo’s. The owner is considering raising the price. He does some market research and discovers that the elasticity of demand for his momo’s is 0.71. is this demand considered elastic or inelastic? Will raising the price increase or decrease his revenue, ceteris paribus> be sure to define both elasticity of demand and revenue in your answer.

2. The Seasons Pizza, which is next to Shambala hotel, just raised its price for a slice of pizza. Is seasons pizza a substitute for Shambala’s momo’s? Is the cross price elasticity between momo’s and pizza positive or negative. Will the rise in price of pizza increase or decrease shambala hotels revenue?

3. Suppose the demand for a commodity is given by

Qx = 34 – 0.8 P2x + 0.3 Py + 0.04I

Where

Qx is the demand for good “x”

PX is the price of good “x”

PY is the price of good “Y”

` I is income

1. What is the price elasticity of demand when PX = 10, Py = 20 and I = 5000.

2. What is the cross price elasticity for X with respect to good Y. Are these goods substitutes or complements?

3. What is the income elasticity of demand for this good? Is the good inferior or normal?