Federal anti-trust laws prohibit many forms of collusion in price setting between firms. Labor unions, however, are exempt from anti-trust laws and are allowed to use market power to raise wages for their members.
A: Consider a competitive industry in which workers have organized into a union that is now renegotiating the wages of its members with all the firms in the industry.
(a) To keep the exercise reasonably simple, suppose that each firm produces output by relying solely on labor input. How does each firm’s labor demand curve emerge from its desire to maximize profit? Illustrate a single firm’s labor demand curve (with the number of workers on the horizontal axis).
(b) On a graph next to the one you just drew, illustrate the labor demand and supply curves for the industry as a whole prior to unionization.
(c) Label the competitive wage w∗ and use it to indicate in your first graph how many workers an individual firm hired before unionization.
(d) Suppose that the union that is negotiating with the firm in your graph is exercising its market power with an aim to ward maximizing the overall gain for its members. Suppose further that the union is sufficiently strong to be able to dictate an outcome. Explain how the union would go about choosing the wage in this firm and the size of its membership that will be employed by this firm. (Hint: The union here is assumed to have monopoly power—and the marginal cost of a member is that member’s competitive wage w∗.)
(e) If all firms in the industry are becoming unionized, what impact will this have on employment in this industry? Illustrate this in your market graph.
(f) Suppose that those workers not chosen to be part of the union migrate to a non-unionized industry. What will be the impact on wages in the non-unionized sector?
B: Suppose that each firm in the industry has the same technology described by the production function f (ℓ) = Aℓα with α < 1, and suppose that there is some 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 ℓ as the choice variable.)
(c) Solve for the union wage wU that emerges if the union is able to use its market power to dictate the wage. What happens to employment in the firm?
(d) Can you verify your answer by instead finding MR and MC from the perspective of the union —and then setting these equal to one another?
(e) Given the fixed cost to operating in the industry, would you expect the number of firms in the industry to go up or down?