Question 1:
a) Define the income and substitution effects of a wage change on hours of labor supply.
b) Given a particular wage, w, explain and show graphically an individual's optimal choice of leisure (and labor supply). What equation holds at the optimal choice; in terms of the marginal rate of substitution (MRS), the marginal utilities for leisure (MUl) and consumption (MUc), and the wage (normalizing the price of consumption to one)?
c) Explain and show graphically the derivation of this individual's labor supply curve - i.e., the relationship between wages and the individual's desired hours of work.
d) Explain and show graphically the income and substitution effects of a wage increase on hours of work for the case in which an individual is on the backward-bending segment of the labor supply curve. Which effect dominates and what happens to overall hours supplied in this case?
Question 2:
Peggy is a single mother who currently does not work and has a two year-old child named Bud. Peggy's concerned parents give her $30/day (non-labor income) to support her and Bud. Peggy has just interviewed for a job as a cashier at Kroger's grocery store. They are willing to hire her at a wage of $8/hour. If Peggy takes the job, she will have to pay $20/day for childcare while she is at work. This question concerns Peggy's decision on whether to take the job.
a) What is a reservation wage? Suppose that Peggy is unwilling to take the cashier's job at the current offered wage of $8/hour. What does this imply about her reservation wage?
b) Suppose that Peggy can work at most 16 hours in a day and that if Peggy works even one hour she has to pay the $20 in childcare for Bud. Draw Peggy's effective budget constraint and her indifference curve through her chosen point of not working which is consistent with what her preferences must be given that she chooses not to work at the current offered wage.
c) For the indifference curve you have drawn, show graphically Peggy's reservation wage. Would she be more likely or less likely to take the job if her indifference curve was steeper than the one you have drawn? What does a steeper indifference curve imply about Peggy's relative marginal utility of leisure? Suppose Kroger's grocery store decides to offer free child care but does not change the wage they offered Peggy. Draw Peggy's new budget constraint. Show graphically whether she is more or less likely to take the job now?
d) Suppose Marge, Peggy's friend, was willing to work for Kroger's grocery store at $7/hour. What might this imply about the shape of Marge's indifference curves (i.e., her tastes) relative to Peggy's? Is this necessarily the case? Explain.
Question 3:
Two types of programs that have been used historically to lift families out of poverty are: i) income maintenance programs such as Welfare (i.e., AFDC and TANF); and ii) the Earned Income Tax Credit (EITC). Compare and contrast these programs in the following way:
a) Show graphically how they change an individual's budget constraint?
b) How do they affect an individual's incentive to work? Show graphically their income and substitution effects?
c) How do the magnitudes of the incentive effects depend on individuals' preferences for leisure? In your explanation draw some indifference curves to fit your discussion.
d) What are the programs' tradeoffs between maintaining work incentives versus providing income insurance against negative shocks to the family (e.g., high fixed costs of working, inability to find a job during an economic downturn).
Question 4: Similar to welfare programs, taxes may affect labor supply since taxes alter the effective wage (i.e., the after-tax wage actually received). For example, an individual earning $10/hour who faces a tax rate of 20- percent has an effective wage of $10/hour = (1-0.20).$10. Let's think about how taxes affect an individual's budget constraint assuming that he/she has no non-labor income. Suppose Max earns a wage of $10/hour (i.e., before-tax wage) and he faces the following tax schedule: Income Tax Rate $0 - $20,000 0.10 $20,000 - $40,000 0.15 Over $40,000 0.20 a) Draw Max's budget constraint. What are the slopes of his budget constraint in each tax bracket? How much leisure is consumed at each kink in the budget constraint (i.e., if Max's optimal choice was at a kink, how much leisure would he have)? How does this budget constraint compare to the budget constraint that would exist if there were no taxes?
b) Policy makers often argue that decreasing tax rates would increase work incentives, sometimes even enough to increase tax revenues. According to neoclassical labor supply theory, is this necessarily true? Explain. How does your answer depend on the income and substitution effects?
c) Write down the standard regression equation to estimate the labor supply elasticity. Which regression coefficient is associated with an estimate of the labor supply elasticity? What have researchers estimated the labor supply elasticity to be for men? How can estimates of the labor supply elasticity help to crudely predict the effect of taxes on labor supply? (Incorporate the effect of a 15-percent decrease in taxes on labor supply in your answer.)