(1) Suppose that the demand for a good is given by Qa -500-2P and the cost funct
ID: 1151974 • Letter: #
Question
(1) Suppose that the demand for a good is given by Qa -500-2P and the cost function for a firm is C(0)-0. (a) If the firm is in a prefect competitive market, compute the equilibrium price P, and quantity Qe (b) Compute the consumer surplus. (c) Now suppose the firm becomes a monopolist. Compute the profit maximizing price Pm and quantity Om (d) Compute the monopolist profit (e) Compute the consumer surplus and the welfare loss in the monopoly situation. After selling in the first market, there are still some consumers in the market who are willing to buy at a lower price. Now consider the market for these consumers as the second market. (f) Derive the inverse demand function P2 (0) for the second market. (g) Compute the profit maximizing price and quantity for the second market. (h) Compute the second market profit. (i) Compute the consumer surplus and the new welfare loss in the second market. G) Combining both the first and second markets, what is the firm's total output? What are the firm's total consumer surplus and total profit? (k) Based on the results from above, if the monopolist decides to introduce a third market for those consumers who are willing to buy at an even lower price, will the firm making any profit from the third market? What will be the inverse demand function for this third market? How will the overall consumer surplus and welfare loss change? (Hint: no calculation is needed in here, but explain your answer).Explanation / Answer
Qd = 500 - 2P
2P = 500 - Qd
P = 250 - 0.5Qd
Marginal cost (MC) = dC(Q)/dQ = 1
(a) In perfect competitive equilibrium, Price = MC.
250 - 0.5Qd = 1
0.5Qd = 249
Qd (= Qc) = 498
Price (Pc) = MC = 1
(b) From demand funciton, when Qd = 0, P = 250 (Reservation price)
Consumer surplus (CS) = Area between demand curve and market price = (1/2) x (250 - 1) x 498 = 249 x 249
= 62,001
(c) A monopolist maximizes profit by equating Marginal revenue (MR) with MC.
Total revenue (TR) = P x Qd = 250Qd - 0.5Qd2
MR = dTR/dQd = 250 - Qd
Equating with MC,
250 - Qd = 1
Qd = 249
P = 250 - (0.5 x 249) = 250 - 124.5 = 125.5
(d) Monopoly Profit = Qm x (Pm - MC) = 249 x (125.5 - 1) = 249 x 124.5 = 31,000.5
(e) With monopoly,
CS = (1/2) x (250 - 125.5) x 249 = (1/2) x 124.5 x 249 = 15,500.25
Deadweight loss = (1/2) x (Pm - Pc) x (Qc - Qm) = (1/2) x (125.5 - 1) x (498 - 249) = (1/2) x 124.5 x 249 = 15,500.25
NOTE: As per Chegg Answering Policy, first 5 parts are answered.
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