You are given the following information: Q = 240 - P C(qi ) = 50qi 2)Find the qu
ID: 1208600 • Letter: Y
Question
You are given the following information:
Q = 240 - P
C(qi ) = 50qi
2)Find the quantity and price in a perfectly competitive setting. (Set P=AC=MC)
Solve for the Perfectly competitive Price and Supply
Calculate the producer, consumer and total surpluses.
3)Find the following if the market is controlled by a monopolist:
Quantity supplied by the firm.
Market Price
Profits earned by the firm.
Deadweight loss under the monopoly.
4)Find the following if the market is controlled by two firms who make their production decision simultaneously (Cournot):
Quantities supplied by each firm.
Market Price
Profits earned by each firm.
Deadweight loss under the duopoly.
5)Find the following if the market is controlled by two firms who make their production decision sequentially (Stackelberg):
Quantities supplied by each firm.
Market Price
Profits earned by each firm.
Deadweight loss under the duopoly.
6)Explain (in words and with graphs) how market efficiency is different among the different market settings. Use total surplus as your gauge.
Explanation / Answer
Q = 240 - P
So, P = 240 - Q
C = 50q
(2) In perfect competition, P = MC
MC = dC / dq = 50
Equating with price,
240 - Q = 50
Q = 240 - 50 = 190
P = MC = 50
Consumer surplus (CS) is the area between demand curve & price.
From demand curve, when Q = 0, P = 240 (Reservation price)
CS = (1/2) x (240 - 50) x 190 = (1/2) x 190 x 190 = 18,050
Producer surplus (PS) is area between supply curve (MC) and price. Here, since P = MC, producer surplus is zero.
Total surplus (TS) = CS + PS = 18,050
(3) A monopolist maximizes profit by equating MR with MC.
Total revenue, TR = P x Q = 240Q - Q2
Marginal revenue, MR = dTR / dQ = 240 - 2Q
Equating with MC,
240 - 2Q = 50
2Q = 190
Q = 95
P = 240 - 95 = 145
Profit = TR - C = (P x Q) - 50Q = (145 x 95) - (50 x 95) = 13,775 - 4,750 = 9,025
Deadweight loss = (1/2) x Difference in price x Difference in quantity
= (1/2) x (145 - 50) x (190 - 95) = (1/2) x 95 x 95 = 4,512.50
Note: First 2 questions are answered.
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