Demand Analysis

Chapter 5

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Chapter 5 KEY CONCEPTS

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Measuring Market Demand Demand Sensitivity Analysis: Elasticity Price Elasticity of Demand Price Elasticity and Marginal Revenue Price Elasticity and Optimal Pricing Policy Cross-price Elasticity of Demand Income Elasticity

market demand curve elasticity endogenous variables exogenous variables point elasticity arc elasticity price elasticity of demand elastic demand unitary elasticity inelastic demand

Measuring Market Demand

optimal price formula substitutes complements cross-price elasticity income elasticity normal goods inferior goods. counter-cyclical noncyclical normal goods cyclical normal goods

Graphing the Market Demand Curve

Market demand is total demand.

Evaluating Market Demand Demand differs among market segments. Add segment demand to get market demand.

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Price Elasticity of Demand

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Any elasticity is simply the percentage change in one thing divided by the percentage change in something else

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Price Elasticity of Demand

Arc Price Elasticity

Any elasticity is simply the percentage change in one thing divided by the percentage change in something else

Q1 − Q2 Q1 + Q2 %ΔQuantity 2 e= = P1 − P 2 %Δ Pr ice P1 + P 2 2

Price P2 P1

The price elasticity of demand is: %age change in Quantity %age change in Price

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Quantity Demanded

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Arc Price Elasticity of Demand -Example Price Quantity P 90 40 70 120 70 50 200 30 280 50 10 360 Elasticity between $50 and $70:

200 − 120 + 120 Ep = 200 50 − 70 = −1.5 50 + 70

Arc Price Elasticity of Demand -Example Price Quantity P 90 40 70 120 70 50 200 30 280 50 10 360 Elasticity between $50 and $70:

Point 2 Point 1

120

200

200 − 120 + 120 Ep = 200 50 − 70 = −1.5 50 + 70

Q

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Point 2 Point 1

120

200

Q

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Arc Price Elasticity of Demand -Example Price Quantity P 90 40 70 120 70 50 200 30 280 50 10 360 Elasticity between $50 and $70:

200 − 120 + 120 Ep = 200 50 − 70 = −1.5 50 + 70 11

Q1

Q2

Point Price Elasticity of Demand dQ %ΔQuantity Q ⎛ dQ ⎞ ⎛⎜ P ⎞ e= = dP = ⎝ ⎠ %Δ Price dP ⎝ Q ⎠ P

Price Point 2 Point 1

120

200

P

A

Q Q

Quantity Demanded

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Point Price Elasticity Calculation e=

∂Q ∂P P Q

Example of Point Price Elasticity

P

∂Q P • ∂P Q

Q = 400 - 4P A

P is the derivative of demand

is the price and quantity combination at a particular point on the demand curve.

Q

Q

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Example of Point Price Elasticity

Example of Point Price Elasticity

Q = 400 - 4P

Q = 400 - 4P

What is elasticity at price of 10 and quantity of 360?

What is elasticity at price of 10 and quantity of 360?

∂Q P • = (-4)(10/360) = -.11 ∂P Q

e=

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Price Elasticities For A Variety of Products Note: all are negative! Product Productor orservice service

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Elasticity Elasticity of ofdemand demand

Product Productor orservice service

Price Elasticity and Revenue

Elasticity Elasticity of ofdemand demand

Housing Housing Electricity Electricity(household) (household)

.01 .01 .13 .13

Milk Milk Household Householdappliances appliances

.63 .63 .63 .63

Bread Bread Telephone Telephoneservice service

.15 .15 .26 .26

Movies Movies Beer Beer

.87 .87 .90 .90

Medical Medicalcare care Eggs Eggs

.31 .31 .32 .32

Shoes Shoes Motor Motorvehicles vehicles

.91 .91 1.14 1.14

Legal Legalservices services Automobile Automobilerepair repair

.37 .37 .40 .40

China, China,glassware, glassware,etc. etc. Restaurant Restaurantmeals meals

1.54 1.54 2.27 2.27

Clothing Clothing

.49 .49

Lamb Lamband andmutton mutton

2.65 2.65

• The relationship between price elasticity of demand and revenue is of particular interest. • Why?

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Price Elasticity and Revenue

Price Elasticity and Revenue

TR = P * Q

• The relationship between price elasticity of demand and revenue is of particular interest.

and

Q = 400 - 4P

MR = dTR/dQ

• Why? Because many situations we observe in the real world can be explained if you have knowledge of how total revenue changes with the price elasticity of demand.

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Price Elasticity and Revenue

Price Elasticity and Revenue

TR = P * Q

TR = P * Q

and

Q = 400 - 4P

and

Q = 400 - 4P

MR = dTR/dQ solve demand for P:

MR = dTR/dQ solve demand for P:

Q = 400 - 4P 4P = 400 - Q P = 100 - .25Q

Q = 400 - 4P 4P = 400 - Q P = 100 - .25Q TR = P * Q TR = (100 - .25Q) * Q = 100Q - .25Q*Q

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Elasticity and Revenue TR = 100Q - .25Q*Q MR = dTR/dQ = 100 - .5Q Graphing these results gives:

Figure Figure5.5 5.5 Elasticity and Revenue Relationship 24

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At price = $90 e = -9.0

At price = $70 e = -2.33

Figure Figure5.5 5.5

Figure Figure5.5 5.5

Elasticity and Revenue Relationship

Elasticity and Revenue Relationship

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At price = $50 e = -1.00

At price = $30 e = -0.43

Figure Figure5.5 5.5

Figure Figure5.5 5.5

Elasticity and Revenue Relationship

Elasticity and Revenue Relationship

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At price = $10 e = -0.11

Elastic Inelastic Figure Figure5.5 5.5

Figure Figure5.5 5.5

Elasticity and Revenue Relationship

Elasticity and Revenue Relationship

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Thus:

Thus:

• If demand is price elastic:

• If demand is price elastic: decrease price --> increase tot. rev. increase price --> decrease tot. rev.

• If demand is price inelastic:

• If demand is price inelastic:

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Thus:

Thus:

• If demand is price elastic: decrease price --> increase tot. rev. increase price --> decrease tot. rev.

• If demand is price elastic: decrease price --> increase tot. rev. increase price --> decrease tot. rev.

• If demand is price inelastic: decrease price --> decrease tot. rev. increase price --> increase tot. rev.

• If demand is price inelastic: decrease price --> decrease tot. rev. increase price --> increase tot. rev.

Note: Price and Revenue do NOT always move in the same direction 34

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Question?

Question?

• Should a firm always produce at the point of unitary elasticity? After all, this is the point of highest revenue.

• Should a firm always produce at the point of unitary elasticity? After all, this is the point of highest revenue.

• Real world examples ...

• Real world examples ... – The Mineral Spring

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Question?

What Affects Price Elasticity?

• Should a firm always produce at the point of unitary elasticity? After all, this is the point of highest revenue.

• Number of Substitutes

• Real world examples ... – The Mineral Spring – The Football Stadium

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What Affects Price Elasticity?

What Affects Price Elasticity?

• Number of Substitutes

• Number of Substitutes

• Price as Fraction of Income

• Price as Fraction of Income • Time Period

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Price Elasticity An Example of Its Use

Price Elasticity

price elasticity of smokers by age: 12-17 years 20-25 years 26-35 years 36-74 years

Bus ridership is a service with a price elasticity (in Connecticut) ranging from -1.82 to -3.45.

-1.40 -0.89 -0.47 -0.45

Could revenues be increased by raising fares?

Would a tax on tobacco affect young or old smokers the most? Source: The Margin (Dec. 1987) 42

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Price Elasticity Yet Another Example

Price Elasticity Yet Another Example

price elasticities for air tickets: First Class -0.45 Regular Economy -1.30 Excursion -1.83

Gasoline

1929 - 41

1948 - 73

-0.06

-0.26

Will all passengers react in the same manner to a fare change?

Knowing this, will raising the tax on gasoline help to conserve energy? Who will bear the burden of this tax, the rich or the poor?

Source: Business Economics (Sept. 1980)

Source: Review of Business and Economic Research (Winter 75-76)

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Coupons An Example of Elasticity

Coupons An Example of Elasticity

• Why would firms offer coupons rather than simply lowering the price of their product?

• Why would firms offer coupons rather than simply lowering the price of their product? • The answer lies in the difference between individuals who use coupons and those who do not use coupons.

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Coupons An Example of Elasticity

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Why would firms offer coupons rather than simply lowering the price of their product?

The answer lies in the difference between individuals who use coupons and those who do not use coupons.

Coupon users and nonusers have different price elasticities.

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Coupons An Example of Elasticity • Issuing coupons is a form of third-degree price discrimination.

See Seepage page145 145 52

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Coupons An Example of Elasticity

Coupons An Example of Elasticity

• Issuing coupons is a form of third-degree price discrimination.

Issuing coupons is a form of thirdthird-degree price discrimination.

• It requires that:

It requires that:

But, Marginal Revenue is related to elasticity:

See Seepage page145 145 54

See Seepage page145 145 55

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Income Elasticity Some Numbers

Income Elasticity of Demand

Alcohol 1.54 Alcohol 1.54 Housing, Housing,owner owneroccupied occupied 1.49 1.49 Furniture 1.48 Furniture 1.48 Dental 1.42 Dentalservices services 1.42 Restaurant 1.40 Restaurantmeals meals 1.40 Shoes 1.10 Shoes 1.10 Medical 0.92 Medicalinsurance insurance 0.92 Gasoline 0.48 Gasolineand andoil oil 0.48 Butter 0.42 Butter 0.42 Coffee 0.00 Coffee 0.00 Margarine -0.20 Margarine -0.20 Flour -0.36 Flour -0.36

% change in Quantity % change in Income

source: source:Houthakker Houthakkerand andTaylor Taylor 56

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Cross Price Elasticity Some Numbers

Cross Price Elasticity of Demand %change in Quantity of One Good %change in Price of Another Good

Good Good X X

Good Good Y Y

Cross-E Cross-E

Butter Butter Fuel Fuel Oil Oil Pork Pork Electricity Electricity Entertainment Entertainment Cereals Cereals

Margarine Margarine Nat. Nat. Gas Gas Beef Beef Nat. Nat. Gas Gas Food Food Fresh Fresh Fish Fish

+0.81 +0.81 +0.20 +0.20 +0.28 +0.28 +0.20 +0.20 -0.72 -0.72 -0.87 -0.87

Source: Source: Demand Demand Analysis, Analysis, Taylor Taylorand and Halvorsen Halvorsen 58

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Derived Demand

Cross-Price Elasticity Relationships

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If Ec > 0, goods are Substitutes

If Ec < 0, goods are Complements

If Ec = 0, goods are Independent

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Chapter Chapter 66 62

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