Chapter 5 Some Applications of Consumer Demand, and Welfare Analysis

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Chapter 5 Some Applications of Consumer Demand, and Welfare Analysis

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Chapter 5 Some Applications of Consumer Demand, and Welfare Analysis. Price Sensitivity of Demand. Elasticity of demand Percentage change in demand F rom a given percentage change in price. Price-Elasticity Demand Curves. Elastic demand, | ξ |>1 1% change in price - PowerPoint PPT Presentation

Transcript of Chapter 5 Some Applications of Consumer Demand, and Welfare Analysis

Page 1: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

Chapter 5

Some Applications of Consumer Demand, and Welfare Analysis

Page 2: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

Price Sensitivity of Demand Elasticity of demand

Percentage change in demandFrom a given percentage change in price

2

%%

.

qqq

p pp

q pp q

Page 3: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

Price-Elasticity Demand Curves

Elastic demand, |ξ|>11% change in price

○ >1% change in quantity demanded Inelastic demand, |ξ|<1

1% change in price○ <1% change in quantity demanded

Unit elastic demand, |ξ|=11% change in price

○ =1% change in quantity demanded

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Page 4: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

Elasticity along a linear demand curve

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Quantity 0

Price

A

Pmax

q= a-b.p

μ

|ξ|<1

|ξ|>1

P1 |ξ|=1

q pp q

Page 5: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

Price-Elasticity Demand Curves

Perfectly inelastic demand curvePerfectly vertical demand curveZero quantity response to a price change

Perfectly elastic demand curveHorizontal demand curvePrice > p

○ Quantity = 0Price = p

○ Any quantity

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Perfectly elastic & perfectly inelastic demand curves

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Perfectly inelastic demand curve.With zero elasticity, the quantity demanded is constant as prices change.

Quantity 0

Price

D

(a)

Perfectly elastic demand curve. With infinite elasticity, the quantity demanded would be infinite for any price below p and zero for any price above p.

Quantity 0

Price

D

(b)

Page 7: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

Properties of Demand Functions

1. Price and income multiplication by the same factor leaves demand unaffected “No money illusion property”

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Page 8: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

1. No Money Illusion Property

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Multiplying all prices by the same factor shifts the budget line from BB’ to B’”B”. Multiplying prices and the agent’s income by the same factor has no effect on the budget line.

Good 1 (x 1)0

Good 2 (x

2)

ef

B

B’

B”

B’”

Page 9: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

2. Ordinal utility property

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Regardless of the utility numbers assigned to the three indifference curves, the agent maximizes utility by choosing point e. Thus demand is unaffected

Good 1 (x 1)0

Good 2 (x

2)

B’

B

90(3)100(5)

120(8)e

Page 10: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

From Individual to Market Demand

Market demand curveAggregate of individual demand curvesHorizontally add up individual demand curves

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Page 11: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

Market demand from individual demand

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(a)

Person i

Quantity5 13

P1

P2

Price

(b)

Person j

Quantity10 20

Price

(c)

Person k

Quantity12 30

Price

(d)

Aggregate demand

Quantity27 63

Price

Di

DjDk

The market demand curve D is the horizontal summation of the individual demand curves Di , Dj , and Dk .

D

Page 12: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

Welfare Measures The welfare effects of price increase can be

assessed using Demand curve:

○ Loss in consumer surplus Consumer choice model:

○ Price compensating variation

Page 13: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

1. Consumer Surplus

Consumer surplusNet gain to consumers measured as the

difference between the willingness to pay and the amount actually paid

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Page 14: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

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Quantity of cocaine demanded

0

Price

70

10

33.3

100

CS

1. Consumer Surplus

Consumer surplus. The area under the demand curve and above the price measures the agent’s total willingness to pay for the quantity of the good she is consuming minus the amount she must pay.

Page 15: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

Measures of Consumer Gain/ Loss

Loss of consumer surplusDifference between

○ consumer surplus for price p○ consumer surplus for price p+∆p

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Page 16: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

Change in consumer surplus

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When the price increases, the change in the area under the demand curve and above the price measures the welfare loss caused by the price change.

Good 1 (x 1) 0

Price

p

a

p+∆p

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2. Price-compensating variation in income Price-compensating variation in income measures

the compensation needed due to an increase in price To understand the price-compensating variation in

income we first introduce the expenditure function Expenditure function

Minimum income/expenditure amount (E) To achieve a predetermined utility (u)At given prices (p1,p2)

E=E(p1,p2,u)

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Page 18: Chapter 5 Some Applications of Consumer Demand, and  Welfare Analysis

The Expenditure Function The problem

The Lagrangian

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uxxu

xpxpMinxx

),( 21

2211},{ 21

s.t.

)),((),,( 22121 xxuuxxuxxL 121 pp

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Derivation of an Expenditure function

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Suppose p1=$0.5 and P2=$1, What is the minimum level of income needed to bring the consumer to a utility level of u*?

Good 1 (x 1)0

Good 2 (x

2)

I1(u*)f

e

B110

15

7

20 B2 B3

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Measures of Consumer Gain/ Loss

Price-compensating variation in incomeAdditional income given to consumerAfter price changeSame utility (before price change)

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Price-compensating variation in income

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ZB is the amount of income that must be given to the agent after the price increase in order to restore him to I1, the indifference curve he was on before the price change

Good 1 (x 1)0

Good 2

I1

I2

f

ed

B”

Z

B’

B

p

Price-compensating variation (in income)

Suppose p1=$1 and P2=$1. If P2 increases to $2, How much extra income is needed to compensate the consumer?

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Price-Compensating Variations andExpenditure Functions

Prices: p1, p2

Utility level: u*Expenditure: E=E(p1,p2,u*)

Increase in p1 to p1+ϵExpenditure: E’=E(p1+ϵ,p2,u*)

Price-compensating variation = E’-E== E(p1+ϵ,p2,u*) - E(p1,p2,u*)

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