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Econ 481- Problem Set 2 Labor Supply

Econ 481 Spring 2017 Problem Set 2: Labor Supply  Please show your work, writing key equations in letters before solving them. Please clearly label axes, slopes, and kink points on all graphs. 1. (All numbers in thousands) In December 2016, the civilian non-institutional population was 254,742. The number of employed workers was 152,111. The number of unemployed workers was 7,529. The number not in the labor force is 95,102. a. What was the labor force participation rate? b. What was the employment rate? c. What was the unemployment rate? d. Why might the unemployment rate might underestimate the severity of an economic downturn? 2. Josephine earns $20 per hour. She faces a uniform 15 percent tax rate on all earned income and pays $8 per hour in child-care expenses for each hour that she works. She receives $80 in child support payments (her only non-labor income) each week. There are 168 hours in the week. a. What is Josephine’s gross hourly wage? b. What is Josephine’s net-of-tax wage? c. What is Josephine’s take home hourly pay? d. Graph Josephine’s weekly budget line, labeling axes, intercepts and slopes. e. Now suppose that Josephine is offered an overtime wage of $30 per hour for every hour that she works above 40 hours per week (all other parameters stay the same). Show how this changes the budget constraint. 3. Consider an individual with the following utility function: U(C,L) = C1/2L1/2, where C is quantity of consumption and L is hours of leisure in a week. Total time available to allocate between leisure and consumption is 112 hours per week. The individual has non-labor income of $200 per week and an hourly wage of $10. a. What is the marginal rate of substitution of leisure for consumption? b. Write down the equation for this individual’s budget constraint. Graph it. c. Solve for this individual’s optimal level of consumption, leisure, and hours of work d. What is her reservation wage? 4. Let’s compare the incentives generated by two different types of public programs. The Aid to Families with Dependent Children (AFDC – welfare before reform) provides an income subsidy, G, at 0 hours of work, that is taxed away at a rate t when an individual chooses to work. The Earned Income Tax Credit (EITC), on the other hand, consists of a subsidy (at rate s) for individuals working low hours, up to a max credit (C) at a certain level of income, and then is phased out (at a rate t) above a certain income cutoff. a. Draw what an AFDC budget constraint looks like, including a standard budget constraint for comparison. Why does the AFDC discourage work? (Explain, using the concept of income and substitution effects in your answer) b. Draw what an EITC budget constraint looks like, including a standard budget constraint for comparison. How does the EITC solve the work disincentive problem created by the AFDC? (Again, refer to income and substitution effects in your answer) c. The effects of the EITC on labor supply are not positive for all individuals. On a graph, illustrate a case in which the EITC reduces the number of hours worked by an individual. Explain using income and substitution effects. 5. Suppose you want to estimate the following labor supply equation: Annual Work Hours = ? + ?*(Average Hourly Wage) + ? You gather data on US workers aged 22 to 55 from the Current Population Survey. You define the Average Hourly Wage as self-reported total annual labor income divided by self-reported total annual work hours. a. Describe in words how to interpret the coefficient ? (ignore any concerns about causality for now) b. Give two separate reasons why you might be concerned that ? is not a good estimate of the causal effect of a change in the hourly wage a worker faces on the number of hours that they work

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