1. A firm faces a constant per unit price of $600 for its output. The firm hires E workers from a union at a daily wage, W, to produce output, q, where q = 4E.

Given the production function, the marginal product of labor is 2/(E). There are 400 workers in the union. Any union worker who does not work for the firm can find a non-union job paying $100 per day.

a) What is the firm's labor demand function?

b) Suppose the union's goal is to ensure that all 400 workers have a job at the unionized firm. What wage should it set

c) What are the firm's daily profits at that outcome if its only costs are the wages paid to non-union workers?

d) What is the union relative wage advantage as a proportion of the non-union wage?

e) Suppose the union's goal is to maximize total income of its members, recognizing that members who do not get a job at the closed-shop firm can always go work in the non-union sector. If the union gets to choose the wage the closed-shop firm pays and the firm then chooses the number of workers given that wage, what wage should the union set at the closed-shop firm? (Set up the maximization problem even if you don't know the math needed to solve it. If you do know the math, also find how many workers the unionized firm will want to hire at the union wage.)