B. * Suppose that each firm in the industry has the same technology described by the production function f1,2 5 A, a with a , 1, and suppose that there is some recurring fixed cost to operating in this industry.

a. Derive the labor demand curve for each firm.

b. Suppose that the competitive wage for workers of the skill level in this industry is w*. Define the optimization problem that the labor union must solve if it wants to arrive at its optimal membership size and the optimal wage according to the objective defined in A(d). (It may be more straightforward to set this up as a maximization problem with w rather than , as the choice variable.)

c. Solve for the union wage w U

that emerges if the union is able to use its market power to dictate the wage. What happens to employment in the firm?