unions and worker productivity

1.
In the context of a supply-demand diagram of the low-skill labour market, a minimum wage above the competitive equilibrium will reduce employment relative to the competitive equilibrium. Show that the total revenue earned by labour may nonetheless increase. Given such an increase, show that, if all workers have the same chance of losing their job the expected value of a worker's wage will rise.

2.
A manufacturer of pantyhose sells all its output in a competitive market. Each pair sells for $5. The labour market in which the manufacturer purchases its labour is not competitive, however, and is described by the labour-supply curve:
W = 5 + 0.2 L
where W = hourly wage rate and L = number of workers.
a.
How many workers will the firm hire in order to maximize profits if each worker produces 3 pairs of pantyhose per hour? What wage will the firm pay?
b.
If a union organizes the workers and rigidly insists on a wage of $12.50 per hour, what effect will this have? Explain.

3.
A minimum wage will influence different labour markets in different ways. In four separate graphs illustrate and briefly explain the following cases:
a.
a competitive market in which the minimum wage causes a 50 percent employment reduction;
b.
a competitive market not influenced by the minimum wage;
c.
a monopoly market where the minimum wage increases employment; and
d.
a monopoly market where the minimum wage decreases employment.
(Hint: Under the monopoly model of minimum wages, the effective marginal expenditure curve has a horizontal range at the level of the minimum wage and then jumps to rejoin the original marginal expenditure curve.)

4.
Suppose an individual is trying to decide whether to go to graduate school. If she spends two years in graduate school obtaining her degree, paying$10,000 each year (includes tuition, room and board, books, food,...), she will get a job that will pay $50,000 per year for the rest of her working life. If she does not go to school, she will go into the work force immediately. She will then make $20,000 per year for the next three years, $30,000 for the following three years, and $50,000 per year every year after that. If the interest rate is 10 percent, is graduate school a good financial investment?
Use your NPV calculations to support your decision, stating any assumptions you make explicitly if needed.