Question

(Monopoly) Any firm in the market for tiddlywinks has constant marginal cost,

M C = 30, and no fixed costs. The market’s demand curve is given by

D(p) = 4000 − 40p.

A) (Perfect Competition) If there is perfect competition, what are the equilibrium price and total quantity sold in the market, p^∗ and Q^∗? Does a firm in the market earn any (nonzero) profits?

B) Now consider a monopolist. What is the monopolist’s marginal revenue function, M R(Q)?

C) What is the profit maximizing quantity for the monopolist, Q^m, and the resulting price, p^m? At this price and quantity, what is the monop- olist’s profit?

D) Draw a graph depicting the monopoly outcome for this market and label the deadweight loss resulting from the monopoly, DW L. What is the dollar value of DW L? Is this large or small, relative to the competitive equilibrium’s total surplus, T S^∗? Briefly explain.

E) What is the elasticity of demand, ε^∗, at the competitive equi- librium price and quantity? What is the elasticity of demand, ε^m, at the monopoly outcome?

Answer 1

A. Under perfect competition the industry will produce where P= marginal cost. Thus in this case we would have P=100-Q/40. Thus in equilibrium we have 100-Q/40=30. Thus we have Q*=2800. The price will be P=30 which is the same as the marginal cost.

B. The marginal revenue function is the first derivative of the total revenue function. Thus in this we have total revenue as TR=100Q-Q^2/40. Thus the marginal revenue as 100-Q/20. This is the marginal revenue function.

C. Here we have the profit function as Profit=100Q-Q^2/40-30Q. Thus we have the FOC as 100-Q/20-30. This we set equal to 0 and so we have the optimal quantity as Q=1400. We have the price as P=65. This the monopoly optimal. The profit is given by Profit = 100*(1400)-(1400)^2/40-(30*1400).

E. At the competitive price and quantity we have the elasticity as 0 as the demand curve will be horizontal in a competitive setup. In case of the monopoly situation we will have the elasticity as ed=-40.30/2800=-3/7.