412 Homework 2 PDF

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California State University, Fullerton Economics 412

A. Gill Spring 2021 Homework Set #2

1.

(3 points) Cesar 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. Cesar faces a 20 percent tax rate on hourly earnings and must pay $5 per hour in child-care expenses for each hour that he works. Cesar receives $80 in dividends each week. There are 168 hours in the week. Carefully show Cesar’s weekly budget constraint on a diagram.

2.

Robert’s preferences for consumption (C) and leisure (L) indicate that his utility function for consumption and leisure is: U = (C – 330) X (L – 60) Assume that there are 110 hours in the week available to split between work and leisure. Robert earns $13 per hour and receives $540 per week in income from his parents. ( 1 point each) a. What is Robert’s marginal utility of consumption when L= 75? b. What is Robert’s reservation wage? c. Will Robert work? Why or why not? d. What is Roberts’s marginal rate of substitution when L = 70 and he is on his budget constraint? e. Explain why the combination of leisure and consumption you derived in part (d) is not an optimal combination for Robert. f. Produce a diagram to illustrate your answer to part (e). g. Derive the values of Robert’s optimal consumption of leisure and consumption. h. Suppose Robert wins the lottery and will receive a payment of $1,000 per week for life, giving him $1540 in non-work income. Will he work? Show why or why not.

3.

(3 points) William receives $100 in dividends each week. He earns an hourly wage of $20 per hour. Assume that there are 168 hours available to William each week. William decides to work 42 hours per week at his current wage. When his wage increase to $25 per hour, William elects to work 37 hours per week. Use a diagram to show William’s initial combination of work hours and consumption, his new combination of work hours and consumption after the wage increase, and carefully decompose the change in work hours into substation and income effects. (Note: for the income and substitution effects I am just looking for a sketch of the diagram. So, for example, you will not be able to show me the exact sizes of the income and substitution effects because I did not give you a utility function).

4.

Suppose that Shelly receives an hourly wage (W) and non-labor income V. ( 1 point each) a. Given her current circumstances, she works exactly 40 hours per week. Show this situation on a diagram. b. Now suppose that her employer institutes an overtime wage policy that pays Shelly 1.5 times her hourly wage. Use a diagram to show that Shelly will unambiguously increase her hours of work as a result of the overtime pay. c. Suppose that Shelly’s coworker, Tim, was working 50 hours per week when he received the same wage as Shelly (W). Use a diagram to show that Tim could reduce his hours of work from 50 hours if he was offered the same overtime pay received by Shelly (1.5 times his hourly wage). d. Why do Shelly’s hours of work unambiguously increase, while Tim’s hours of work could increase or, as shown, decrease?

5.

(2 points) Consider a woman who receives $100 per week in dividends. If she works, she receives $10 per hour in salary, but she also must pay $50 per week in “fixed” child-care expenses. Show that given her current situation, this woman decides not to work. Explain. Would a subsidy to cover child-care expenses increase the probability that this woman will want to work? Show and explain....