Economics 450 - Assignment 5
Q1. Suppose a union and an employer start to negotiate on January 1, 2009 over wages to be paid for the year 2009. There will be 50 paid weeks in the year (the rest being unpaid vacation time). No work will be done until they reach an agreement.
The employer's net revenue, after paying all costs other than wages, is $500 per worker per week. The workers can earn $240 per week if they leave this employer and go to work elsewhere (with no possibility of coming back).
While negotiations continue workers can collect $130 per week in unemployment benefits (this is a straight subsidy that does not have to be repaid). The employer has retained an expert negotiator who charges $200 per week per worker.
The negotiations proceed as follows. At the beginning of each week the employer's and the union's negotiators meet, and one side proposes a wage for the rest of the year. If this proposal is accepted work begins immediately. If not, the workers collect unemployment benefits for the week, the employer's negotiator is paid for the week, and nothing happens for the rest of the week; next week there is a new meeting and a new proposal.
At the first meeting a coin is tossed to determine which side makes the proposal for that week. In subsequent meetings they take turns: first one side makes a proposal, then the following week the other side makes a proposal, and so on.
How long will these negotiations take? What wage agreement will be reached?
Q2. A local brewery has a monopoly on beer sales in a small town. The demand curve for beer is
P = 1200 - .16 B,
where B is the number of six-packs of beer sold per hour, and P is the price of a six-pack, in cents. There are 2000 workers, who are represented by a union. Each worker produces one six-pack of beer per hour. Workers who are not employed at the brewery can work elsewhere at a wage of $3.20 per hour.
The union's objective is to maximize the total income of its members. Suppose the union can choose both the wage and the number of people hired, and the employer's only choice is whether to accept the union's offer or go out of business. What wage and employment level should the union set?
Q3. Suppose 100 men and 100 women graduate from high school. After high school, each can work in a low-skill job and earn $200,000 over his or her lifetime, or each can pay $50,000 and go to college. College graduates are given a test. If someone passes the test, he or she is hired for a high-skill job paying lifetime earnings of $300,000. Any college graduate who fails the test, however, is relegated to a low-skill job. Academic performance in high school gives each person some idea of how he or she will do on the test if they go to college. In particular, each person's GPA, call it x, is an "ability score" ranging from 0.01 to 1.00. With probability x, the person will pass the test if he or she attends college. Upon graduating high school, there is one man with x = .01, one with x = .02, and so on up to x = 1.00. Likewise, there is one woman with x = .01, one with x = .02, and so on up to x = 1.00.
a. Persons attend college only if the expected lifetime payoff from attending college is higher than that of not attending college. Which men and which women will attend college? What is the expected pass rate of men who take the test? What is the expected pass rate of women who take the test?
b. Suppose policymakers feel not enough women are attending college, so they take actions that reduce the cost of college for women to $10,000. Which women will now attend college? What is the expected pass rate of women who take the test?