Problem 2-1

The table below reports the unemployment rate, labor force participation rate, and (working-age) population for the United States in January 2008, 2011, and 2016. Using the data, answer the following questions.

1. What was the size of the labor force at the start of each year?
2. How many people were officially unemployed at the start of each year?
3. What about these numbers may cause some concern even though the unemployment rate to start 2016 was a notch below the unemployment rate in 2008 as the economy was entering the Great Recession?

Problem 2-3

Tom earns $15 per hour for up to 40 hours of work each week and $30 per hour for every hour in excess of 40. Tom also faces a 20 percent tax rate, pays $4 per hour in child care expenses for each hour he works, and receives $80 in child support payments each week. There are 110 (non-sleeping) hours in the week. Graph Tom’s weekly budget line.

Problem 2-4

Cindy gains utility from consumption \(C\) and leisure \(L\). The most leisure she can consume in any given week is 110 hours. Her utility function is \(U(C, L) = C \times L\). This functional form implies that Cindy’s marginal rate of substitution is \(C / L\). Cindy receives $660 each week from her great-grandmother–regardless of how much Cindy works. What is Cindy’s reservation wage?

Problem 2-6

Shelly’s preferences for consumption and leisure can be expressed as \[U(C, L) = (C – 100) \times (L – 40)\] This utility function implies that Shelly’s marginal utility of leisure is \(C – 100\) and her marginal utility of consumption is \(L – 40\). There are 110 hours in the week available to split between work and leisure. Shelly earns $10 per hour after taxes. She also receives $320 worth of assistance benefits each week regardless of how much she works.

1. Graph Shelly’s budget line.
2. What is Shelly’s marginal rate of substitution when \(L = 100\) and she is on her budget line?
3. What is Shelly’s reservation wage?
4. Find Shelly’s optimal amount of consumption and leisure.

Problem 2-7

Explain why receiving a cash grant from the government 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).

Problem 2-8

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.

‘Working Recipients’ = Number of Recipients Who Worked At Some Time in the Survey Week; ‘Hours Worked’ = Total Hours Of Work By All Recipients in the Survey Week

1. 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.
2. 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-in-differences table to support your answer.

Problem 2-9

Consider two workers with identical preferences, Phil and Bill. Both workers have the same life cycle wage path in that they face the same wage at every age, and they know what their future wages will be. Leisure and consumption are both normal goods.

1. Compare the life cycle path of hours of work between the two workers if Bill receives a one-time, unexpected inheritance at the age of 35.
2. Compare the life cycle path of hours of work between the two workers if Bill had always known he would receive (and, in fact, does receive) a one-time inheritance at the age of 35.

Problem 2-11

A worker plans to retire at the age of 65, at which time he will start collecting his retirement benefits. Then there is a sudden change in the forecast of inflation when the worker is 63 years old. In particular, inflation is now predicted to be higher than it had been expected so that the average price level of market goods and wages is now expected to be higher. What effect does this announcement have on the person’s preferred retirement age:

1. if retirement benefits are fully adjusted for inflation?
2. if retirement benefits are not fully adjusted for inflation?

Problem 2-13

Over the last 100 years, real household income and standards of living have increased substantially in the United States. At the same time, the total fertility rate, the average number of children born to a woman during her lifetime, has fallen in the United States from about three children per woman in the early twentieth century to about two children per woman in the early twenty-first century. Does this suggest that children are inferior goods?

Problem 2-14

Consider a person who can work up to 80 hours each week at a pre-tax wage of $20 per hour but faces a constant 20% payroll tax. Under these conditions, the worker maximizes her utility by choosing to work 50 hours each week. The government proposes a negative income tax whereby everyone is given $300 each week and anyone can supplement her income further by working. To pay for the negative income tax, the payroll tax rate will be increased to 50%.

1. On a single graph, draw the worker’s original budget line and her budget line under the negative income tax.
2. Show that the worker will choose to work fewer hours if the negative income tax is adopted.
3. Will the worker’s utility be greater under the negative income tax?