chapter 5 applying consumer theory. 5 - 2 copyright © 2012 pearson education. all rights reserved....

Chapter 5

Applying Consumer theory

5 - 2 Copyright © 2012 Pearson Education. All rights reserved.

Topics

• Deriving Demand Curves.

• How Changes in Income Shift Demand Curves.

• Effects of a Price Change.

• Cost-of-Living Adjustments.

• Deriving Labor Supply Curves.


Figure 5.1 Derivingan Individual’s Demand Curve

26.70

Initial Values

Pb = price of beer = $12

PW = price of wine = $35Y = Income = $419.

W = YPW

- Pb PW

b

Budget Line, L

12.0

2.8

12.0

26.70

p b, $

per

uni

t

e1

E1

I1

Beer (b), Gallons per year

Win

e, (

W) ,

Gal

lons

per

year

(b) Demand Curve Initial optimal bundle of beer and wine


L1 (pb = $12)

(a) Indifference Curves and Budget Constraints



New Values



W = YPW

- Pb PW

b

Budget Line, L

Price of beer goes down!

4.3

12.0

2.8

12.0

6.0

26.70

p b, $

per

uni

t

L2 (pb = $6)

26.70 44.5

e2

e1

I1

I2


Win

e, (

W) ,

Gal

lons

per

year

(b) Demand Curve


L1 (pb = $12)

E1

44.5

E2




New Values



W = YPW

- Pb PW

b

Budget Line, L

Price of beer goes down again!

4.3

5.2

12.0

2.8

12.0

6.0

4.0

26.70 44.5 58.9

p b, $

per

uni

t

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

26.70 44.5 58.9

e

e1

I1

I2

I3


D1, Demand for Beer

Price-consumption curve

Win

e, (

W) ,

Gal

lons

per

year


(b) Demand Curve


L1 (pb = $12)

E1

2

E2

e3

E3


Price-Consumption Curve

• A line through optimal bundles at each price of one good (beer) when the price of the other good (wine) and the budget are held constant.

• The demand curve corresponds to the price-consumption curve.


Solved Problem 5.1

• In Figure 5.1, how does Mimi’s utility at E1 on D1 compare to that at E2?

• Answer: Use the relationship between the points in

panels a and b of Figure 5.1 to determine how Mimi’s utility varies across these points on the demand curve.


Solved Problem 5.2

• Mahdu views Coke, q, and Pepsi as perfect substitutes: He is indifferent as to which one he drinks. The price of a 12-ounce can of Coke is p, the price of a 12-ounce can of Pepsi is p* and his weekly cola budget is Y. Derive Mahdu’s demand curve for Coke using the method illustrated in Figure 5.1.


Solved Problem 5.2 (cont.)


Effects of a Rise in Income

• Engel curve - the relationship between the quantity demanded of a single good and income, holding prices constant.

• Income-consumption curve shows how consumption of both goods changes when income changes, while prices are held constant.


Y1

Figure 5.2 Effect of a Budget Increase on an

Individual’s Demand Curve

Initial Values



W = YPW

- PW

b

Budget Line, L

Pb

Win

e, G

allo

ns p

erye

ar

0

2.8

26.7 Beer, Gallons per year

0

12

0



I1

Pri

ce o

f be

e r,

$ pe

r un

it

Y,

Bud

get

E1

= $419

L1

e1

D1

E1*Income goes up!

$628


Initial Values



W = YPW

- PW

b

Budget Line, L

Pb

Income goes up!

$628

Win

e, G

allo

ns p

erye

ar

0

2.8

4.8

38.226.7 Beer, Gallons per year

0

12

0



I2I1

Pri

ce o

f be

e r,

$ pe

r un

it

Y,

Bud

get

e2

E1

Y1 = $419

Y2 = $628

L2

L1

e1

D1D2

E1*

E2

E2*




Y

Y

Y

Initial Values



W = YPW

- PW

b

Budget Line, L

Pb

Income goes up again!W

ine,

Gal

lons

per

year

Income-consumption curve

Engel curve for beer

0

2.8

4.8

7.1

49.138.226.7 Beer, Gallons per year

0

12

0



I2I3

I1

Pri

ce o

f be

e r,

$ pe

r un

it

Y,

Bud

get

e2

E1

1 = $419

2 = $628

3 = $837

L3

L2

L1

e1

D1D2D3

E1*

E2

E2*

E3

E3*

e3




Solved Problem 5.3

• Mahdu views Coke and Pepsi as perfect substitutes. The price of a 12-ounce can of Coke, p, is less than the price of a 12-ounce can of Pepsi, p*. What does Mahdu’s Engel curve for Coke look like? How much does his weekly cola budget have to rise for Mahdu to buy one more can of Coke per week?


Solved Problem 5.3


Consumer Theory and Income Elasticities

• Formally,

where Y stands for income.

• Example If a 1% increase in income results in a 3% decrease in

quantity demanded, the income elasticity of demand is = -3%/1% = -3.

Q

Y

Y

Q

YY

QQ

Y

Q

%

%


Consumer Theory and Income Elasticities (cont.)

• Normal good - a commodity of which as much or more is demanded as income rises. Positive income elasticity.

• Inferior good - a commodity of which less is demanded as income rises. Negative income elasticity.


Figure 5.3 Income-Consumption Curves and Income Elasticities

• As income rises the budget constraint shifts to the right. The income

elasticities depend on….

• …where on the new budget constraint the new optimal consumption bundle will be

Hou

sing

, Squ

are

feet

per

year

Food, Pounds peryear

Food normal,housing normal

Food inferior,housing normal

Food normal,housing inferior

b

c

e

a

L1

L2

I

ICC2

ICC1

ICC3


Figure 5.4 A Good That Is Both Inferior

and Normal

• When Gail was poor and her income increased.. …she bought more

hamburger

• But as she became wealthier and her income rose… ….she bought less

hamburger and more steak.

Y2

Y1

Y1

Y2

Y3

Y3

L1

Y,

Inco

me

L2

L3

e2

e3

e1

E2

E3

E1

I1

I 2

I3

Hamburger peryear

Income-consumption curve

Hamburger peryear

yA

ll o

the

r g

oo

ds

pe

re

ar


(b) Engel Curve

Engel curve


Effects of a Price Change

• Substitution effect - 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.

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


Figure 5.5 Substitution and Income Effects with Normal Goods

1CP1

CPC =

Y1 - F

Budget Line, L1

1FP

Budget Line, L2 (increase in salary)

2CP2

CPC =

Y2 - F 2

FP

11FC PP


Figure 5.6 Giffen Good

When the price of movie tickets decreases the budget constraint rotates out…

allowing the consumer to increase her utility.

Nevertheless, the total effect is negative. WHY?

Bas

ketb

all,

Tic

kets

per

year

Movies, Tickets per year

L1

Total effect

L2

e1

e2

I1

I2


• Even though the substitution effect is positive…. …the income effect is larger

and negative (since this is an inferior good).

Bas

k etb

all,

Tic

kets

per

year

Movies, Tickets per year

L1

L*

Income effect

Substitution effect

L2

e1

e2

e*

I1

I2

Total effect

Figure 5.6 Giffen Good


Inflation Indexes

• Inflation - the increase in the overall price level over time. nominal price - the actual price of a good. real price - the price adjusted for inflation.

• How do we adjust for inflation to calculate the real price?


Inflation Indexes (cont.)

• Consumer Price Index (CPI) – measure the cost of a standard bundle of goods for use in comparing prices over time.

We can use the CPI to calculate the real price of a hamburger over time.

In terms of 2008 dollars, the real price of a hamburger in 1955 was:

18.1158.26

1.211 burger a of price

2005for CPI

2008for CPI


Effects of Inflation Adjustments

• Scenario: Klaas signed a long-term contract when he was hired. According to the COLA clause in his contract, his employer increases his salary each year by the same percentage as that by which the CPI increases. If the CPI this year is 5% higher than the CPI last year, Klaas’s salary rises automatically by 5% over last year’s.

• Question: what is the difference between using the CPI to adjust the long-term contract and using a true cost-of-living adjustment, which holds utility constant?


Figure 5.7 The Consumer Price Index

C2

C1C,

Un

its o

f cl

oth

ing

pe

ye

ar

e2

e1

I1

L1 L2

I2

F, Units offood peryear

Y1/p1F2F1

Y1/p1C

Y2 /p2C

FY2/p2

F

The firm ensures that Klaas can buy the same bundle of goods in the second year that he chose in the first year…

But since Klaas is better off, the CPI adjustmentovercompensates for the change in inflation

1cP1

CPC =

Y1 - F

Budget Line, L1

1FP


2cP2

CPC =

Y2 - F 2

FP

11FC PP


True Cost-of-Living Adjustment

• True cost-of-living index - an inflation index that holds utility constant over time.

• Question: how big an increase in Klaas’s salary would leave him exactly as well off in the second year as in the first?


True Cost-of-Living Adjustment

C2

C1C,

Un

its o

f cl

oth

ing

pe

r ye

ar

e2

e1

I1

L1

e*

L* L2

I2

F, Units of food per year

Y1/p1F2F1

Y1/p1C

Y2 /p2C

Y*/p2C

F Y2/p2F2 FY /p2*

1cP1

CPC =

Y1 - F

Budget Line, L1

1FP


2cP2

CPC =

Y2 - F 2

FP

11FC PP


Table 5.1 Cost-of-Living Adjustments


CPI Substitution Bias

• Income adjustments based on CPI suffer from an upward bias.

• The CPI-based adjustment suffers from substitution bias – it ignores that consumers may substitute toward the relatively inexpensive good when prices change disproportionately.


Labor-Leisure Choice

• 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.

The price of leisure is forgone earnings.• The higher your wage, the more an hour of leisure

costs you.


Labor-Leisure Choice: Example

• Jackie spends her total income, Y, on various goods. The price of these goods is $1 per unit.

• Her utility, U, depends on how many goods and how much leisure she consumes:

U = U(Y, N).

• Jackie’s earned income equal:

wH.

• And her total income, Y, is her earned income plus her unearned income, Y*:

Y = wH + Y*.


Figure 5.8 Demand for Leisure

Budget Line, L1

Y = w1H

Y = w1(24 − N).

Each extra hour of leisure she consumes costs her w1 goods.

Y, G

oods

per

day Time constraint

H1 = 824 0N1 = 160 24

H,Work hours per day

N, Leisure hours per day

H1 = 8

N1 = 160H, Work hours per dayN, Leisure hours per day

I1

L1

w, W

age

per

hour

(b) Demand Curve

–w1 1Y1

w1

e1

E1

(a) Indifference Curves and Constraints


Figure 5.8 Demand for Leisure

Budget Line, L1

Y = w1H

Y = w1(24 − N).

Budget Line, L2

Y = w2H

Y = w2(24 − N).

w2 > w1

Y, G

oods

per

day Time constraint

H2 = 12 H1 = 824 0N2 = 12 N1 = 160 24

H,Work hours per dayN, Leisure hours per day

H2 = 12N2 = 120

H, Work hours per dayN, Leisure hours per day

Demand for leisure

I2

I11

–w2

L1

L2

w, W

age

per

hour

–w1 1

e2Y2

Y1

w1

w2

e1

E2

(b) Demand Curve

E1

H1 = 8

N1 = 16

(a) Indifference Curves and Constraints


Figure 5.9 Supply Curve of Labor


Figure 5.10 Income and Substitution Effects of a Wage Change

Since income effect is positive, leisure is a normal good.Y

, G

oo

ds

pe

r d

ay Time constraint

H2H * H124 0

N2N * N10 24

Substitution effect

Income effect

Total effect

H, Work hours per day

N, Leisure hours per d ay

I2

I1

L2

L*

L1

e2

e1

e*


Solved Problem 5.5

• Enrico receives a no-strings-attached scholarship that pays him an extra Y* per day. How does this scholarship affect the number of hours he wants to work? Does his utility increase?


Solved Problem 5.5 (cont.)


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

Y, G

oods

per

day

(a) Labor-Leisure Choice

Time const raint

H2 H3H124 0

H, Work hours per day

E1

E3

E2

L2

I2

I3

I1

L3

L1

e2

e1

e3

w, W

age

per

hour

(b) Supply Curve of Labor

Supply curve of labor

H2H3H1 240

, Work hours per day

At low wages, an increase in the wage causes the worker to work more….

H

but at high wages, an increase in the wage causes the worker to work less….


Figure 5.12 The Relationship of U.S. Tax Revenue and the Marginal Tax Rate


Figure 5.13 Per-Unit Versus Lump-Sum Child Care Subsidies

chapter 5 applying consumer theory. 5 - 2 copyright © 2012 pearson education. all rights reserved....

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