# Science

2-1. How many hours will a person allocate to leisure activities if her indifference curves between

consumption and goods are concave to the origin?

2-2. What is the effect of a rise in the price of market goods on a worker’s reservation wage,

probability of entering the labor force, and hours of work?

2-3. Sally can work up to 3,120 hours each year (a busy social life and sleep take up the remaining

time). She earns a fixed hourly wage of $25. Sally owes a 10 percent payroll tax on the first $40,000

of income. Above $40,000 of income, there is no payroll tax. Sally also faces a progressive income

tax rate. There is no income tax on the first $10,000 of income. From $10,000 up to $60,000, the

marginal income tax rate is 25 percent. Above $60,000, the marginal income tax rate is 50 percent.

Graph Sally’s budget line.

2-4. Tom earns $15 per hour for up to 40 hours of work each week. He is paid $30 per hour for

every hour in excess of 40. Tom faces a 20 percent tax rate and pays $4 per hour in child care

expenses for each hour he works. Tom receives $80 in child support payments each week. There are

168 hour in the week. Graph Tom’s weekly budget line.

2-5. What happens to a worker’s desired hours of work if employers pay an overtime premium

equal to “time and a half”(that is, 1.5 times the straight-time wage) for any hours worked in excess

of 40 hours? What would happen to hours of work if the overtime premium were raised to double

the straight-time wage?

2-6. A person owns a small farm near a large city and must decide whether to work on that small

farm or take a job in the city. Her utility depends on her income per day, Y, and the number of

hours allocated to leisure activities, L. Daily income from farm work is:

20 2f f f Y = h − h ,

where hf is hours of work on the farm; and daily income from the city job is:

YC = 14hC,

where hC is hours of work in the city.

(a) If she can work on the farm or in the city, but not both, which sector would she choose?

(b) If she can work both on the farm and in the city, how would she allocate her time?

2-7. Cindy gains utility from consumption C and leisure L. The most leisure she can consume in any

given week is 168 hours. Her utility function is U(C,L) = C × L. This functional form implies that

Cindy’s marginal rate of substitution is C / L. Cindy receives $630 each week from her greatgrandmother

– regardless of how much Cindy works. What is Cindy’s reservation wage?

2-8. The utility function of a worker is represented by U(C, L) = C × L, so that the marginal utility

of leisure is C and the marginal utility of consumption is L. Suppose this person currently has a

weekly income of $600 and chooses to enjoy 70 hours of leisure per week. How many additional

dollars of income would it take to entice the worker to work 10 more hours?

2-9. You can either take a bus or drive your car to work. A bus pass costs $5 per week, whereas

driving your car to work costs $60 weekly (parking, tolls, gas, etc.). You spend half-an-hour less on

a one-way trip in your car than on a bus. How would you prefer to travel to work if your wage rate

is $10 per hour? Will you change your preferred mode of transportation if your wage rate rises to

$20 per hour? Assume you work five days a week and time spent riding on a bus or driving a car

does not directly enter your utility.

2-10. Shelly’s preferences for consumption and leisure can be expressed as

U(C,L) = ( C – 200 ) × ( L – 80 ).

This utility function implies that Shelly’s marginal utility of leisure is C – 200 and her marginal

utility of consumption is L – 80. There are 168 hours in the week available to split between work

and leisure. Shelly earns $5 per hour after taxes. She also receives $320 worth of welfare benefits

each week regardless of how much she works.

(a) Graph Shelly’s budget line.

(b) What is Shelly’s marginal rate of substitution when L = 100 and she is on her budget line?

(c) What is Shelly’s reservation wage?

(d) Find Shelly’s optimal amount of consumption and leisure.

2-10. Among single, college-educated women aged 22 – 25, average annual hours worked is 2,160

and the average wage is $22.50. If the average wage increases to $25 per hour, average annual

hours worked increases to 2,340. What is the elasticity of labor supply for this group of workers?

2-11. Mike’s utility for consumption and leisure is U(C,L) = C × L so that his marginal rate of

substitution between leisure and consumption is C/L. There are 168 hours in the week and he earns

$10 per hour.

(a) What is Mike’s optimal amount of consumption and leisure?

(b) If the government starts a welfare policy that pays B to all non-workers and pays $0 to all

workers, at what value of B will Mike opt out of the labor force in order to go on welfare?

2-12. Explain why a lump sum government transfer can entice some workers to stop working (and

entices no one to start working) while the earned income tax credit can entice some people who

otherwise would not work to start working (and entices no one to stop working).

**2-13. In 1999, 4,860 TANF recipients were asked how many hours they worked in the previous**

**week. In 2000, 4,392 of these recipients were again subject to the same TANF rules and were again**

**asked their hours of work during the previous week. The remaining 468 individuals were randomly**

**assigned to a “Negative Income Tax” (NIT) experiment which gave out financial incentives for**

**welfare recipients to work and were subject to its rules. Like the other group, they were asked**

**about their hours of work during the previous week. The data from the experiment are contained in**

**the table below.**

**Total**

**Number Of**

**Recipients**

**Number of**

**Recipients Who**

**Worked At Some**

**Time in the Survey**

**Week**

**Total Hours Of**

**Work By All**

**Recipients in the**

**Survey Week**

**1999 2000 1999 2000**

**TANF 4,392 1,217 1,568 15,578 20,698**

**NIT 468 131 213 1,638 2,535**

**Total 4,860 1,348 1,781 17,216 23,233**

**(a) What effect did the NIT experiment have on the employment rate of public assistance**

**recipients? Develop a standard difference-in-differences table to support your answer.**

** **

**(b) What effect did the NIT experiment have on the weekly hours worked of public assistance**

**recipients who worked positive hours during the survey week? Develop a standard difference-indifferences**

**table to support your answer.**

** **