Consider a labor market with a monopolistic firm that has a labor demand curve of MRPL=16-.5L, where L is thousands of hours of work. Suppose that workers at the firm are organized into a union that has a union objective function of U=WL, where W is the hourly wage.
Find an expression for the union’s marginal rate of substitution of hours of employment for wages. (Hint: recall that the MRS is the ratio of the marginal utility of L to the marginal utility of W.)
Suppose that when negotiating a contract, the union can set wages but cannot affect the amount of labor utilized by the firm. What wage will maximize the union’s objective function?
Now suppose that the union is able to bargain over both wages and the level of employment. Will their optimal contract exhibit the same wage as in part b? Explain why or why not.