These three graphs illustrate the preferences of Bob, Carol

These three graphs illustrate the preferences of Bob, Carol

Subject: Economics    / General Economics
Question

1. [10 points] These three graphs illustrate the preferences of Bob, Carol, and Ted for apples and peaches. Each consumer has $30 of income. Apples are $2 each. Peaches are $3 each.

a. Suppose the price of peaches falls to $2. Draw a new budget line for each consumer and find the new optimal bundle of apples and peaches each would buy. How does the new quantity of peaches compare with the original quantity? Indicate the change in the first column of the table below (e.g. denote an increase of 1 by +1).

Total Effect of Price Change Substitution Effect of Price Change Income Effect of Price Change

Bob

Carol

Ted

b. For each consumer, determine the substitution effect of the price change by drawing a hypothetical budget line with the same slope as your new budget lien, but just tangent to the consumer’s original indifference curve. How much of a change in peach consumption does the substitution effect account for? Indicate that change in the second column of the table.

c. Now determine the income effect. Compare each consumer’s peach consumption in (b) to his or her final peach consumption in (a). Indicate the difference in column 3 of the table. (Check that the sum of the substitution and income effect equals the total effect.)

d. Do Bob, Carol, and Ted consider peaches normal, inferior, or not responsive to a change in income?

Bob ___________________; Carol ___________________; Ted ___________________;

e. Suppose Bob decides that apples and peaches are perfect compliments. Now, what are the income and substitution effects for Bob?

2. This table contains prices and the demands of a consumer whose behavior was observed in 5 different price-income situations.

Situation p1 p2 x1 x2

A 2 2 10 70

B 2 4 70 20

C 2 2 20 30

D 6 2 10 30

E 2 4 20 20

a. Sketch each of his budget lines and label the point chosen in each case by the letters A, B, C, D, and E. (10 points)

b. Is the consumer’s behavior consistent with WARP? Explain.

c. Shade all of the points that you are certain are worse than bundle C.

d. Suppose that you are told that the consumer has convex and monotonic preferences and that he obeys SARP. Shade the points that are at least as good as bundle C.

3. The U.S. Bureau of Labor Statistics periodically gathers data on household budgets to compile the consumer price index. The tables below report total current consumption expenditures and expenditures on certain major categories of goods for five different income groups in the United States for 2011. Group A is the lowest income quintile (lowest 20%) and Group E is the highest income quintile (highest 20%).

Table 1: Expenditures by Category for Various Income Groups in 2011

Income Group

A

B

C

D

E

Alcoholic Beverages 170 265 324 528 994

Apparel and Services 850 1140 1453 1988 3266

Cash Contribution 687 931 1311 1910 3766

Education 807 474 562 827 2585

Entertainment 981 1622 2121 3107 5027

Food away from home 1099 1608 2125 3103 5163

Food at home 2448 3051 3496 4364 5828

Health care 1489 2611 3319 3994 5149

Housing 8771 12136 14944 18840 29321

Personal care 270 408 549 742 1202

Personal insurance and pensions 422 1693 3505 6431 15068

Tobacco 316 359 409 403 266

Gifts 429 541 635 1124 2458

Transportation 3256 5142 7592 10205 15264

Average Before-tax Income 9805 27117 46190 74019 161292

Average Annual Expenditures 22001 32092 42403 57460 94551

a. Complete Tables 2a and 2b. Use either Before-tax Income or Average Annual Expenditures as the denominator, as directed. (Consider cutting and pasting into Excel).

b. Which goods are normal goods with respect to before-tax income? With respect to average annual expenditures? (See index in Varian to locate definitions of types of goods in textbook.)

c. Which goods are luxury goods with respect to before-tax income? With respect to Average annual expenditures? At which changes in income/expenditure level?

d. Which of these goods satisfy your textbook’s definition of necessity goods? Inferior goods? At what changes in income/expenditure levels?

e. If there are differences in answers to 3b to 3d by definition of income (i.e., Total annual Expenditures vs Before-tax income), why might these differences exist?

Table 2a: Percent Allocation of Before-tax Income

Income Group

A

B

C

D

E

Alcoholic Beverages

Apparel and Services

Cash Contribution

Education

Entertainment

Food away from home

Food at home

Health care

Housing

Personal care

Personal taxes

Tobacco

Gifts

Transportation

Before-tax Income

100%

100%

100%

100%

100%

Table 2b: Percent Allocation of Annual Average Expenditures

Income Group

A

B

C

D

E

Alcoholic Beverages

Apparel and Services

Cash Contribution

Education

Entertainment

Food away from home

Food at home

Health care

Housing

Personal care

Personal taxes

Tobacco

Gifts

Transportation

Total Expenditures

100%

100%

100%

100%

100%

4. Dudley has a utility function U(C,R) = C – (12-R)2, where R is leisure and C is consumption per day. He has 16 hours per day to divide between work and leisure. If Dudley has a nonlabor income of $20 per day and is paid a wage of $6 per hour, how many hours of leisure will he choose per day? Show your work.

5. Mandy has an income of $800 in period 1 and will have an income of $500 in period 2. Her utility function is U(c1, c2) = c0.801 c0.202, where c1 is her consumption in period 1 and c2 is her consumption in period 2. The interest rate is .25. She unexpectedly won a prize that made her period 2 income $1,000 (period 1 income remained $800). By how much would her period 1 consumption increase or decrease? Show your work.