Chapter Five Applying Consumer Theory. © 2007 Pearson Addison-Wesley. All rights reserved.5–2 Applying Consumer Theory In this chapter, we examine five

Chapter Five

Applying Consumer Theory

© 2007 Pearson Addison-Wesley. All rights reserved. 5–2

Applying Consumer Theory

• In this chapter, we examine five main topics.– Deriving demand curves– How changes in income shift demand

curves– Effects of a price change– Cost-of-living adjustments– Deriving labor supply curves


Deriving Demand Curves

• An individual chooses an optimal bundle of goods by picking the point on the highest indifference curve that touches the budget line (Chapter 4). When a price changes, the budget constraint the consumer faces shifts, so the consumer choose a new optimal bundle.


• By varying one price and holding other prices and income constant, we can determine how the quantity demanded changes as the price changes, which is the information we need to draw the demand curve.



• We derive a demand curve using the information about tastes from indifference curves.

• These indifference curves are convex to the origin: Mimi views beer and wine as imperfect substitutes (Chapter 4). We can construct Mimi’s demand curve for beer by holding her budget, her tastes, and the price of wine constant at their initial levels and varying the price of beer.



Figure 5.1 Deriving an Individual’s Demand Curve 4.3

5.2

12.0

2.8

12.0

6.0

4.0

26.70 44.5 58.9

L1 (pb = $12) L2 (pb = $6) L3 (pb = $4)

26.70 44.5 58.9

e3

e2

e1

E3

E2

E1

I 1

I 2

I 3

Beer, Gallons per year


D1, Demand for beer

Price-consumption curve

(a) Indifference Curves and Budget Constraints

(b) Demand Curve



• Price-consumption curve, is the line through the equilibrium bundles, such as , , and , that Mimi would consume at each price of beer, when the price of wine and Mimi’s budget are held constant.

1e 2e 3e


How Changes in Income Shift Demand Curves

• Effects of a rise in income– We illustrate the relationship between the

quantity demanded and income by examining how Mimi’s behavior changes when her income rises, while the prices of beer and wine remain constant.

© 2007 Pearson Addison-Wesley. All rights reserved.

Figure 5.2 Effect of a Budget Increase on an Individual’s Demand Curve

Income-consumptioncurve

Engel curve for beer

0

2.8

4.8

7.1

49.138.226.7 Beer, Gallons per year

0

12

0



I 2I 3

I 1


(b) Demand Curves

(c) Engel Curve

e2

e3

E3

E1

E2

Y1 = $419

Y2 = $628

Y3 = $837

L3

L2

L1

e1

D 1D 2D 3

E1*

E2*

E3*


• The income-consumption curve through bundles , , and in panel a shows how Mimi’s consumption of beer and wine increases as her income rises. As Mimi’s income goes up, her consumption of both wine and beer increases.

How Changes in Income Shift Demand Curve

1e 2e 3e


• Engel curve– the relationship between the quantity

demanded of a single good and income, holding prices constant

How Changes in Income Shift Demand Curve


Page 112 Solved Problem 5.1

Y2/p*

Y1/p*

Y1 = pq1

Y2 = pq2

q1 = Y1/p q

2 = Y2/pe

2e1

E2

E1

p

1

q, Cans of Cragmontper week

q1

q2q, Cans of Cragmont

per week


(b) Engel Curve

Cragmont Engel curve

L1

L2

I1

I2


Consumer Theory and Income Elasticities

• Income elasticities tell us how much the quantity demanded changes as income increases. We can use income elasticities to summarize the shape of the Engel curve, the shape of the income-consumption curve, or the movement of the demand curves when income increases.


Income Elasticities

• We defined the income elasticities of demand in Chapter 3 as

where is the Greek letter xi

percentage change in quantity demanded /

percentage change in income /

Q Q

Y Y


Consumer Theory And Income Elasticities

• normal good– a commodity of which as much or more is

demanded as income rises

• inferior good– a commodity of which less is demanded as

income rises

0

0


Income-Consumption Curves and Income Elasticities

• The shape of the income-consumption curve for two goods tells us the sign of the income elasticities: whether the income elasticities for those goods are positive or negative.


Some Goods Must Be Normal

• It is impossible for all goods to be inferior.

• If both goods were inferior, Peter would buy less of both goods as his income rises-which makes no sense.


Figure 5.3 Income-Consumption Curves and Income Elasticities

Food, Pounds per year

Food normal,housing normal

Food inferior,housing normal

Food normal,housing inferior

b

c

e

a

L1

L2

I

ICC2

ICC1

ICC3


Income Elasticities May Vary with Income

• A good may be normal at some income levels and inferior at others.

© 2007 Pearson Addison-Wesley. All rights reserved.

Figure 5.4 A Good That Is Both Inferior and Normal

Y2

Y1

Y1

Y2

Y3

Y3

L1

L2

L3

e2

e3

e1

E2

E3

E1

I 1

I2

I3

Hamburger per year

Income-consumption curve

Hamburger per year


(b) Engel Curve

Engel curve


Effects of a Price Change

• An increase in a price of a good, holding other prices and income constant, has two effects on an individual’s demand. One is the substitution effect: If utility is held constant, as the price of the good increases, consumers substitute other, now relatively cheaper goods for that one.


• The other is the income effect: An increase in price reduces a consumer’s buying power, effectively reducing the consumer’s income and causing the consumer to buy less of at least some goods.

Effects of a Price Change


Income and Substitution Effects with a Normal Good

• The substitution effect is the change in the quantity of a good that a consumer demands when the good’s price changes, holding other prices and the consumer’s utility constant

• The income effect is the change in the quantity of a good a consumer demands because of a change in income, holding prices constant.


Income and Substitution Effects with a Normal Good• The total effect from the price change is

the sum of the substitution and income effects, as the arrows show. Mimi’s total effect (in gallons of beer per year) from a drop in the price of beer is

Total effect= substitution effect + income effect

32.2=3.9+28.3


• Because indifference curves are convex to the origin, the substitution effect is unambiguous: More of a good is consumed when its price falls. A consumer always substitutes a less expensive good for a more expensive one, holding utility constant.




• The direction of the income effect depends on the income elasticity. Because beer is a normal good for Mimi, her income effect is positive. Thus both Mimi’s substitution effect and her income effect go in the same direction.


Figure 5.5 Substitution and Income Effects with Normal Goods

12.0

5.5

0 58.926.730.6Substitutioneffect

Total effect

Income effect


I 2

I 1

L*

L2

L1

e2

e1

e*


Income and Substitution Effects with an Inferior Good

• If a good is inferior, the income effect goes in the opposite direction from the substitution effect. For most inferior goods, the income effect is smaller than the substitution effect. As a result, the total effect moves in the same direction as the substitution effect, but the total effect is smaller.


• A good is called a Giffen good if a decrease in its price causes the quantity demanded to fall.

• The Law of Demand was an empirical regularity, not a theoretical necessity. Although it’s theoretically possible for a demand curve to slope upward, economists have found few, if any, real-world examples of Giffen goods.

Income and Substitution Effects with an Inferior Good


Figure 5.6 Giffen Good

Movies, Tickets per year

L1

L*

Total effect

Income effect

Substitution effect

L2

e1

e2

e*

I 1

I 2


Cost-of-Living Adjustments

• By knowing both the substitution and effects, we can answer questions that we could not if we knew only the total effect.


Inflation Indexes

• The price of most goods rise over time. We call the increase in the overall price level inflation.


Real Versus Nominal Prices

• The actual price of a good is called the nominal price. The price adjusted for inflation is the real price.


Calculating Inflation Indexes

• The CPI for the first year is the amount of income it takes to buy the market basket actually purchased that year:

(5.1)

The cost of buying the first year’s bundle in the second year is

(5.2)

1 11 1 1 C FY p C p F

2 22 1 1 C FY p C p F


• To calculate the rate of inflation, we determine how much more income it would take to buy the first year’s bundle in the second year, which is the ratio of Equation 5.1 to Equation 5.2:

2 21 12

1 11 1 1

C F

C F

p C p FY

Y p C p F




• The CPI is a weighted average of the price increase for each good, and , where the weights are each good’s budget share in the base year, and .C

2 1/F Fp p

2 1/C Cp p

F


CPI adjustment

• CPI adjustment to income does not keep an individual on his original indifference curve.

• Indeed, this person is better off in the second year than in the first. The CPI adjustment overcompensates for the change in inflation in the sense that his utility increases.


Figure 5.7 The Consumer Price Index

C2

C1

e2

e1

I 1

L1

e*

L* L2

I2

F, Units of food per year

Y2*/p 2

FY

1/p1F

Y1/p1

C

Y */p2C

F2

F1

Y2/p2

F

Y2/p2

C


True Cost-of-Living Adjustment

• How big an increase in Klaas’s salary would leave him exactly as well off in the second years as in the first? We can answer this question applying the same technique we use to identity the substitution and income effects.


Table 5.1 Cost-of-Living Adjustments


Deriving Labor Supply Curves

• Labor-Leisure Choice– People choose between working to earn

money to buy goods and services and consuming leisure: all time spent not working. The number of hours worked per day, H, equals 24 minus the hours of leisure or nonwork, N, in a day:

H=24 － N.

– Using consumer theory, we can determine the demand curve for leisure once we know the price of leisure.


• Labor-Leisure Choice– We use an example to show how the

number of hours of leisure and work depends on the wage, unearned income (such as inheritances and gifts from parents), and tastes.

U ＝ U(Y, N).



• Labor-Leisure Choice– Her total income, Y, is her earned income

plus her unearned income, Y*:

Y ＝ wH ＋ Y*.

– The slope of her budget constraint is －w1, because each extra hour of leisure she consumes costs her w1 goods.

– Her supply curve for hours worked is the mirror image of the demand curve for leisure: For every extra hour of leisure that Jackie consumes, she works on hour less.



Income and Substitution Effects

• An increase in the wage causes both income and substitution effects, which alter an individual’s demand for leisure and supply of hours worked.

• The substitution effect, the movement from to e*, must be negative: A compensated wage increase causes Jackie to consume fewer hours of leisure, N*, and work more hours, H*.

1e


Income and Substitution Effects

• The income effect is the movement from e* to .

• When leisure is a normal good, the substitution and income effects work in opposite direction, so whether leisure demand increases or not depends on which effect is larger.

• If leisure is an inferior good, both the substitution effect and the income effect work in the same direction, and hours of leisure definitely fall.

2e


Figure 5.8 Demand for Leisure

Time constraint

H2 = 12 H1 = 824 0

N2 = 12 N1 = 160 24H, Work hours per day

N, Leisure hours per day

H2 = 12 H1 = 8

N2 = 12 N1 = 160H, Work hours per day


Demand for leisure

I 2

I1 1

–w2

L1

L2

(a) Indifference Curves and Constraints

(b) Demand Curve

–w11

e2Y2

Y1

w1

w2

e1

E2

E1


Figure 5.9 Supply Curve of Labor

(a) Leisure Demand

Demand for leisure

w1

w2

16120N, Leisure hours per day

E1

E2

(b) Labor Supply

Supply of work hours

w1

w2

8 120H, Work hours per day

e2

e1


Figure 5.10 Income and Substitution Effects of a Wage Change

Time constraint

H2

H* H124 0

N2

N* N10 24

Substitution effect

Income effect

Total effect

H, Work hours per day


I 2

I 1

L2

L*

L1

e2

e1

e*


Page 133 Solved Problem 5.3

(a) Leisure Normal

Time constraint

H2

H3

H124 0


L2

I 2

I1

L1

Y *

e2

e1

(b) Leisure Inferior

Time constraint

H124 0


L2

I1

L1

Y *

e1

I 3

e3


Application (Page 134) Leisure-Income Choices of Textile Workers

55 25

45 75

42.4

57.6

29.5

70.5

42.9

57.1H, Work hours per week

N, Leisure hours per week

I 2I 1

L2

L*

L191.18

200

88.69

0

e1

e2e*


Shape of the Labor Supply Curve

• Whether the labor supply curve slopes upward, bends backward, or has sections with both properties depends on the income elasticity of leisure.

• Do labor supply curves slope upward or backward? Economic theory alone cannot answer this question: Both forward-sloping and backward-bending supply curves are theoretically possible. Empirical research is necessary to resolve this question.


Figure 5.11 Labor Supply Curve That Slopes Upward and Then Bends Backward

(a) Labor-Leisure Choice

Time constraint

H2

H3H

124 0H, Work hours per day

E1

E3

E2

L2

I 2

I3

I1

L3

L1

e2

e1

e3

(b) Supply Curve of Labor

Supply curve of labor

H2

H3

H1 240H, Work hours per day


Income Tax Rates and Labor Supply

• Why do we care about the shape of labor supply curves? One reason is that we can tell from the shape of the labor supply whether an increase in the income tax rate － a percent of earnings－ will cause a substantial reduction in the hours of work.


• Taxes on earnings are an unattractive way of collecting money for the government if supply curves are upward sloping because the taxes cause people to work fewer hours, reducing the amount of goods society produces and raising less tax revenue than if the supply curve were vertical or backward bending.



• On the other hand, if supply curves are backward bending, a small increase in the tax rate increases tax revenue and boots total production (but reduces leisure).




• The effect of a tax rate of ＝ 0.28 is to reduce the effective wage from w to

(1 － )w ＝ 0.72w.


Figure 5.12 Relationship of Tax Revenue to Tax Rates

600

800

400

200

500 * = 79 100

, Marginal tax rate, %

Tax revenue


Cross Chapter Analysis Page 145

Q2

Q3

Q10 Q, Hours of day care per day

I 2

I 3

I 1

LPSLLSLo

e2

e1

Y2

Yo

e3


台灣工資 ( 價格 ) 勞動供給彈性

年度 1979 1986 1990 1993 1997 2000 2001 2003

供給彈性 0.048 0.064 0.111 0.026 0.148 0.115 0.158 0.080

台灣婦女工資 (價格 )供給彈性

資料來源 : 莊慧玲、林世昌 (2006) ，清華大學經濟系，「台灣婦女勞動供給實證研究之發展」，經濟論文叢刊

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Chapter Five Applying Consumer Theory. © 2007 Pearson Addison-Wesley. All rights reserved.5–2 Applying Consumer Theory In this chapter, we examine five