2 Labor Demand with Monopoly Product Markets 1. Augment the competitive market firm's optimization problem to allow the price of the product to decrease with the quantity of output produced, so p = p(q) and p(q) < 0. Write the firm's profit function and optimization problem. 2. Derive the condition: MRq = p(1+ where n is the elasticity of product demand the firm faces in the labor market. 3. Interpret the condition. Explain how it nests the perfectly competitive case. 4. How does the firm's production differ from the competitive case? How does this impact its demand for labor? Consider the production function and product demand functions: q = f(L) = L/2 q(p) = 100 - 2p 5. How much will the firm produce in a competitive market? How much will the firm produce if it is a monopoly? 1 6. How many workers will the firm employ in a competitive market in which it must produce until price equals marginal cost? 7. How many workers will the firm employ if it is a monopoly? How does this compare to the previous answer? 8. What is the difference in MPL between the competitive and monopoly case? Explain. 3 Monopsony 1. Interpret the first order condition in the monopsony model: pf'(L) (w' (L)L + w(L)) = 0 Specifically, discuss the role of each of the terms on the lefthand side of the equation in explaining how the firm's profit changes when it increases the number of workers it hires. 2. Suppose a monopsonist produces output exclusively by hiring workers. Each unit of output sells for $10, and the firm pays workers $8 to produce each unit of output. How large is the markup and implied elasticity of labor supply to the firm?