A Single Buyer in the Labor Market: The text treated extensively the case where market power is concentrated on the supply side — but it could equally well be concentrated on the demand side. When a buyer has such market power, he is called a monopsonist. Suppose, for instance, the labor market in a modest-sized town is dominated by a single employer (like a large factory or a major university). In such a setting, the dominant employer has the power to influence the wage just like a typical monopolist has the power to influence output prices.
A: Suppose that there is a single employer for some type of labor, and to simplify the analysis, suppose that the employer only uses labor in production. Assume throughout that the firm has to pay the same wage to all workers.
(a) Begin by drawing linear labor demand and supply curves (assuming upward sloping labor supply). Indicate the wage w∗ that would be set if this were a competitive market and the efficient amount of labor ℓ∗ that would be employed.
(b) Explain how we can interpret the labor demand curve as a marginal revenue curve for the firm.
(c) How much does the first unit of labor cost? Where would you find the cost of hiring a second unit of labor if the firm could pay the second unit of labor more than the first?
(d) We are assuming that the firm has to pay all its workers the same wage —i.e. it cannot wage discriminate. Does that imply that the marginal cost of hiring the second unit of labor is greater or less than it was in part (c)?
e) How does the monopsony power of this firm in the labor market create a divergence between labor supply and the firm’s marginal cost of labor — just as the monopoly power of a firm causes a divergence between the output demand curve and the firm’s marginal revenue curve?
(f) Profit is maximized where MR =MC. Illustrate in your graph where marginal revenue crosses marginal cost. Will the firm hire more or fewer workers than a competitive market would (if it had the same demand for labor as the monopsonist here)?
(g) After a monopolist decides how much to produce, he prices the output at the highest possible level at which all the product can be sold. Similarly, after a monopsonist decides how much to buy, he will pay the lowest possible price that will permit him to buy this quantity. Can you illustrate in your graph the wage wM that our dominant firm will pay workers?
(h) Suppose the government sets a minimum wage of w∗ (as defined in (a)). Will this be efficiency enhancing?
(i) We gave the example of a modest-sized town with a dominant employer as a motivation for thinking about monoposonist firms in the labor market. As it becomes easier to move across cities, do you think it is more or less likely that the monopsony behavior we have identified is of significance in the real world?
(j) Labor unions allow workers to create market power on the supply side of the labor market. Is there a potential efficiency case for the existence of labor unions in the presence of monopsony power by firms in the labor market? Would increased mobility of workers across cities strengthen or weaken this efficiency argument?
B: Suppose that the firm’s production function is given by f (ℓ) = Aℓα (with α < 1) and the labor supply curve is given by ws (ℓ) = βℓ.
(a) What is the efficient labor employment level ℓ∗? (Hint: You should first calculate the marginal revenue product curve.)
(b) At what wage w∗ would this efficient labor supply occur?
(c) Define the firm’s profit maximization problem — keeping in mind that the wage the firm must pay depends on ℓ.
(d) Take the first order condition of the profit maximization problem. Can you interpret this in terms of marginal revenue and marginal cost?
(e) How much labor ℓM does the monopsonist firm hire—and how does it compare to ℓ∗?
(f) What wage wM does the firm pay—and how does it compare to w∗?
(g) Consider the more general case of a monopsonist firmwith production function f (ℓ) facing a labor supply curve of w(ℓ). Derive the MR =MC condition (which is the same as the condition that the marginal revenue product equals MC) from the profit maximization problem.
(h) Can you write the MC side of the equation in terms of the wage elasticity of labor supply?
(i) True or False: As the wage elasticity of labor supply increases, the monopsonist’s decision approaches what we would expect under perfect competition.