Question

A monopolist can produce at a constant average (and marginal) cost of AC MC 5 It faces a market demand curve of Q-71-P Calculate the profit-maximizing price and quantity for this monopolist. Also calculate its profits. The monopoly would produce units of output at a price of (Enter numeric responses using real numbers rounded to two decimal places.) In turn, the monopoly would earn profit of $ Suppose a second firm enters the market. Let Q1 be the output of the first firm and Q2 be the output of the second. Market demand is now given by Q1+Q2 71-P Assuming that this second firm has the same costs as the first, write the profits of each firm as a function of Q1 and Q2 The profit functions for Firm 1 (111 ) and for Firm 2 (Π2) are ○ A. Π,-Ps Q1-501 and 112-Ps Q2-502

Answer 1

Under monopoly, equilibrium is attained where MR = MC.

By equating MR and MC, we get equilibrium quantity. From that, we get equilibrium price.

Under monopoly, equilibrium is attained where MR = MC. By equating MR and MC, we get equilibrium quantity. From that, we get equilibrium price. MC = 5Q = 71 - P P = 71 - Q TR = PQ = (71 - Q) Q = 71Q - Q^2 MR = 71 - 2Q Equilibrium: - MR = MC 71 - 2Q = 5 2Q = 66 Q = 33 P = 71 - 33 = 38 Profit = TR - TC = PQ - MC times Q = 38 times 33 - 5 times 33 = 33 (38 - 5) = 33 times 33 = 1089 Q_1 + Q_2 = 71 - P P = 71 - Q_1 - Q_2 = 71 - (Q_1 + Q_2) Firm 1 Profit = TR - TC pi_1 = PQ_1 - MC times Q_1 pi_1 = PQ_1 - 5Q_1 pi_1 = [71 - (Q_1 + Q_2)] Q_1 - 5Q_1 Firm 2 pi_2 = PQ_2 - MC times Q_2 pi_2 = PQ_2 - 5Q_2 pi_2 = [71 - (Q_1 + Q_2)] Q_2 - 5Q_2 Answer is (E)