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ECON 412

Labor Economics and Labor Markets

Homework 1

Fall 2022

Problem 1

Consider Figure 1, which shows the budget lines for a worker who can work at most T = 4000 hours per year, at a wage rate of w = 5 dollars per hour.  The  lower budget line corresponds to the situation without any policy intervention. The upper budget line shows how the feasible set shifts due to a government program.  [See also Borjas Chapter 2.12 for a similar application on the Earned  Income Tax Credit.]  Under this program, the individual gets a wage subsidy of 0.50 dollars per hour worked, up to a maximum of 2000 hours worked (or 1000 dollars in subsidy).  After that, if the individual works more than 2000 hours, the subsidy is taxed away at a rate of 0.50 dollars per hour.   This yields the “kinked”budget line depicted in Figure 1, where Leisure is on the horizontal axis and Consumption is on the vertical axis.  Both are expressed in hours or dollars per year.

Figure 1:  Budget lines with and without policy

 

Answer the following questions, and explain in detail. When relevant, you can assume that leisure is a normal good.

1.1.

Consider someone who would choose to work for 3000 hours (i.e., consume 1000 hours of leisure) in the absence of the program. After the program is introduced, this individual would

A) definitely consume more leisure.

B) definitely consume less leisure.

C) consume less leisure, but only if the substitution effect dominates the income effect.

D) consume more leisure, but only if the substitution effect dominates the income effect.

1.2.

Suppose someone who would choose to work for 1000 hours (i.e, consume 3000 hours of leisure) before the program was introduced. After the program is intro- duced, this individual would

A) definitely consume more leisure.

B) definitely consume less leisure.

C) consume less leisure, but only if the substitution effect dominates the income effect.

D) consume more leisure, but only if the substitution effect dominates the income effect.

1.3.

Consider an individual who, in the absence of the program, optimally chooses not to work (i.e.  they consume L = 4000 hours of leisure and C = 0 dollars of consumption). After the program is introduced, this individual

A) would definitely start working.

B) would definitely choose not to work.

C) might start working, but only if her reservation wage lies between 5 dollars and 5.5 dollars per hour.

D) might start working, but only if her reservation wage lies exceeds 5 .5 dollars per hour.

1.4.

Now assume you are the policy maker in charge of this government program. You would like to approve and implement the program only if (1) it would increase labor force participation (i.e. if it increases the amount of people who work at least some number of hours) and (2) if it would not reduce the hours of work among people who were already working before the program was introduced.  Based on your answers to the previous questions, how does the program affect (1) labor force participation and (2) work hours among working people? Are the aggregate effects ambiguous? What are the pros and cons of this policy in terms of (dis)incentivizing work?

Problem 2

Consider a single parent who has a weekly time endowment of T = 60 hours, has an hourly wage offer of 10 dollars, and receives a weekly government transfer of 200 dollars per week (irrespective of hours worked).

2.1.

Write down the budget constraint and the time constraint, and draw the budget set for this individual. Make a graph of the optimal allocation and the indifference curve at the optimum, assuming the parent chooses to work 20 hours per week. Carefully label the axes and all relevant points. You may assume the individual’s utility function is well-behaved” (i.e., continuous, increasing and concave in both consumption and leisure).

2.2

Now consider a new scenario such that if this parent chooses to work any positive amount of hours, then they will need to pay for daycare, which charges a flat rate of 100 dollars per week (irrespective of how many hours the child spends at daycare).  If the parent does not work at all and stays home full-time, then daycare is not needed. Make a graph of the new budget line, carefully labeling all relevant points (in particular, the new endowment point). How do you think the optimal choice of labor supply would change in the presence of childcare costs? (Hint:  the answer will typically depend on whether the person has high or low “tastes for work”, i.e., flat or steep indifference curves)

2.3

How would the scenario from Question 2.2 affect aggregate labor supply along the intensive margin (i.e. the amount of hours worked among parents who choose to work) and along the extensive margin (i.e. the fraction of parents who choose to work at all)?  Explain the change in labor/leisure in terms of income and/or substitution effects. Add a graph.

Problem 3

Two of your friends, Ann and Bob, read a newspaper article in which it is mentioned that, on average, Americans work longer hours than Europeans, and therefore enjoy less leisure. Ann claims this makes sense because Europeans face a higher labor income tax rate, which lowers the relative price of leisure.  Bob, however, claims it is probably because Europeans have lower tastes for work (or higher tastes for leisure) than Americans. Using the insights from the basic labor- leisure model we saw in class, can you prove either of your friends wrong, or can they both be right? Explain.

Problem 4

4.1.

Cindy gets utility from consumption (C) and leisure (L), and has a weekly time budget of T = 100 hours. Her utility function is U(C, L) = C * L. Regardless of how much Cindy works, she receives $400 each week from her great-grandmother. What is Cindy’s reservation wage?

4.2

What is Cindy’s optimal labor supply (h) and consumption (C) if she gets a wage offer of 8 dollars per hour?  What is her resulting utility level?  Show your work.

4.3

What is her optimal labor supply and consumption if her wage offer drops to 2 dollars per hour? What is her utility level? Show your work.

4.4

Intuitively, how do you think Cindy’s reservation wage change if her great- grandmother suddenly decides to cut her allowance down to 200 dollars per week? Calculate the new reservation wage and briefly discuss.