Chapter 22

Suppose there are 8,000 hours in a year (actually there are 8,760 ) and that an individual has a potential market wage of $\mathrm{\$}5$ per hour. a. What is the individual's full income? If he or she chooses to devote 75 percent of this in come to leisure, how many hours will be worked? b. Suppose a rich uncle dies and leaves the individual an annual income of $\mathrm{\$}4,000$ per year. If he or she continues to devote 75 percent of full income to leisure, how many hours will be worked? c. How would your answer to part (b) change if the market wage were $\mathrm{\$}10$ per hour instead of $\mathrm{\$}5$ per hour? d. Graph the individual's supply of labor curve implied by parts (b) and (c).

Using the concept of the opportunity cost of time, discuss the following: a. Which persons might you expect to pay the higher fares to fly the faster Concorde to Europe? b. Which individuals do you expect would be more likely to stand in long lines and even camp out overnight to purchase tickets to a sporting event? c. Are greens fees a larger fraction of the total cost of a golf game for a prospering physi cian or a peanut vendor? d. How would the degree of traffic congestion affect which individuals drive to work and which take mass transit?

A welfare program for low-income people offers a family a basic grant of $\mathrm{\$}6,000$ per year. This grant is reduced by $\mathrm{\$}.75$ for each $\mathrm{\$}1$ of other income the family has. a. How much in welfare benefits does the family receive if it has no other income? If the head of the family earns $\mathrm{\$}2,000$ per year? How about $\mathrm{\$}4,000$ per year? b. At what level of earnings does the welfare grant become zero? c. Assume the head of this family can earn $\mathrm{\$}4$ per hour and that the family has no other in come. What is the annual budget constraint for this family if it does not participate in the welfare program? That is, how are consumption (C) and hours of leisure $(H)$ related? What is the budget constraint if the family opts to participate in the welfare program? (Remember, the welfare grant can only be positive.) e. Graph your results from parts (c) and (d) $f$ Suppose the government changes the rules of the welfare program to permit families to keep 50 percent of what they earn. How would this change your answer to parts and (e)? $\mathrm{g}$ Using your results from part (f), can you predict whether the head of this family will work more or less under the new rules described in part (f)?

Following in the spirit of the labor market game described in Example $22.4,$ suppose the firm's total revenue function is given by \[ T R=10 L-L^{2} \] and the union's utility is simply a function of the total wage bill \[ U\{w, L)=w L \] a. What is the Nash equilibrium wage contract in the two-stage game described in Example $22.4?$ b. Show that the alternative wage contract $w^{\prime }=L^{\prime }=4$ is Pareto superior to the contract identified in part (a). c. Under what conditions would the contract described in part (b) be sustainable as a subgame perfect equilibrium?