2. Assume that firm M (the manufacturer) sells an input (a lawn mower) to firm R (the retailer). Now R sells the lawn mower to the public. R does not incur any cost associated with providing its retail service (that is, its retail cost is zero). Let X represent the number of lawn mowers. Assume also that both M and R are monopolists, and P is the lawn mower price charged to the public with the (inverse) demand P=100 X. Let PW denote the wholesale price R pays to M per lawn mower.

A. Find the derived demand for lawn mowers facing M (i.e., the demand function for M as a function of PW). Hint: Find the marginal revenue equals marginal cost condition for R, where Rs marginal cost is the price PW. Solving for X gives the derived demand.

B. If Ms MC is constant and 20, find the equilibrium prices and quantity, PW, P, X and the profits of the two firms.

C. Assume now that M and R form a single vertically integrated firm, M-R. Find the equilibrium values of P and X and the profit of M-R.

D. Compare the unintegrated case in part b with the integrated case in part c. Is it true that both the firms and the public would prefer the case in part c? Explain.

3. Assume the same facts as in problem 2, except that monopolist R is now replaced with competitive industry R.

A. Find the derived demand for lawn mowers facing M (i.e., the demand function for M as a function of PW). Hint: Make use of the fact perfect competition equilibrium is defined by demand equals supply, where supply is simply a horizontal line P = MC for the retail sector which is simply PW because we assume that there is no additional retail cost. Solving for X gives the derived demand.

B. Find the equilibrium prices and quantity, PW, P, X and the profits of the two firms.

C. Assume that M vertically integrates forward into the competitive industry R, thereby extending its monopoly to cover both manufacturing and retailing. Find the equilibrium values of P and X and the profit of the combined firm M-R.

D. Compare the unintegrated case in part b with the integrated case in part c. Is it profitable to monopolize forward? What is the intuitive explanation for your result?