Part 1: Suppose that the market demand curve is P-100-Q and the market supply cu
ID: 1103876 • Letter: P
Question
Part 1: Suppose that the market demand curve is P-100-Q and the market supply curve is P-Q. 1. What is the competitive market equilibrium (CME) price and quantity? 2. What is the maximum amount of total surplus in this market? 3. What is consumer surplus, producer surplus, and total surplus at the CME? 4. If this market were dominated by a monopoly, what would be the resulting price and quantity? Hint: the monopoly's marginal cost curve is the supply curve. You need to derive the marginal revenue curve to find the monopoly solution. 5. What is consumer surplus, producer surplus, and total surplus under the monopoly? 6. What is the deadweight loss associated with a lack of competition? 7. If the government sets a price ceiling on the monopoly at $40, what will the monopoly choose for ? does it compare to what you found in 5? 8. What is total surplus, consumer surplus, and producer surplus when the monopoly faces this price ceiling? How 9. If the government wants to eliminate deadweight loss associated with the monopoly using a price ceiling, where should the government set the price ceiling?Explanation / Answer
(1) In competitive equilibrium, demand price equals supply price.
100 - Q = Q
2Q = 100
Q = 50
P = 100 - 50 = 50
(2) Total surplus is maximum when there is CME.
From demand function, when Q = 0, P = 100 (Maximum price)
From supply function, when Q = 0, P = 0 (Minimum price)
Total surplus (TS) = (1/2) x (100 - 0) x 50 = (1/2) x 50 x 50 = 2,500
(3)
Consumer surplus (CS) = Area between demand curve and market price = (1/2) x (100 - 50) x 50 = 25 x 50 = 1,250
Producer surplus (PS) = Area between supply curve and market price = (12) x (50 - 0) x 50 = 25 x 50 = 1,250
TS = CS + PS = 1,250 + 1,250 = 2,500
(4) Monopolist will equate Marginal revenue (MR) with Marginal cost (MC = Q in this case).
Total revenue (TR) = P x Q = 100Q - Q2
MR = dTR / dQ = 100 - 2Q
Equating MR & MC,
100 - 2Q = Q
3Q = 100
Q = 33.33
P = 100 - 33.33 = 66.67
NOTE: First 4 questions are answered.
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