Problem 5 Monopoly Suppose that in order to protect industry profits from recent
ID: 1159041 • Letter: P
Question
Problem 5 Monopoly Suppose that in order to protect industry profits from recent cost increases,a in the giant cookie market merged to found 1 giant giant cookie manufacturer, ll firms t function c(v) 96- 2y+6y2. Consumer demand remains Qu 492 4p. 1. Find the market inverse demand for giant cookies 2. Find the quantity supplied by a profit maximizing monopolist, the market price, and the monopolists profit 3. Find the consumer surplus, producer surplus, and deadweight loss created by the monopoly 4. The cookie monopoly argues that the deadweight loss created by their monopoly is justified because the merger resulted in decreased production cost. Is this argument justified when comparing consumer surplus, producer surplus, and total welfare to the perfectly competitive market in the previous problem? Who benefits and who loses from the merger? 5. Suppose the government institutes a price cap at p 70 in an attempt to move closer to the competitive equilibrium. Find the quantity produced, market price, consumer surplus, producer surplus, and deadweight loss. Who gains and who loses from regulation? Is the regulation welfare improving? 6. Calculate the elasticity of demand at the monopoly's optimal y 7. Explain why the giant cookie monopoly has little market power.Explanation / Answer
(1) Qd = 492 - 4p
4p = 492 - Qd
p = 123 - 0.25Qd [Inverse demand]
(2) Profit is maximized when Marginal revenue (MR) equals Marginal cost (MC), and since there is a single firm in market, Qd = y so that p = 123 - 0.25y.
Total revenue (TR) = p x y = 123y - 0.25y2
MR = dTR/dy = 123 - 0.5y
MC = dc(y)/dy = - 2 + 12y
Equating with MR,
123 - 0.5y = - 2 + 12y
12.5y = 125
y = 10
p = 123 - (0.25 x 10) = 123 - 2.5 = 120.5
TR = p x y = 120.5 x 10 = 1205
TC = c(y) = 96 - (2 x 10) + (6 x 10 x 10) = 96 - 20 + 600 = 676
Profit = TR - TC = 1205 - 676 = 529
(b)
From demand function, when Qd = 0, p = 123 (Reservation price)
Consumer surplus = Area between demand curve and market price = (1/2) x (123 - 120.5) x 10 = 5 x 2.5 = 12.5
When y = 10, MR = 123 - (0.5 x 10) = 123 - 5 = 118
Producer surplus = Area between supply (MC) curve and market price = (1/2) x (120.5 + 118) x 10 = 5 x 238.5
= 1192.5
In efficient outcome, p = MC.
123 - 0.25y = - 2 + 12y
12.25y = 125
y = 10.20
p = MC = - 2 + (12 x 10.2) = - 2 + 122.4 = 120.4
Deadweight loss = (1/2) x Difference in price x Difference in output = (1/2) x (120.5 - 120.4) x (10.20 - 10)
= (1/2) x 0.1 x 0.2 = 0.01
(4) The argument is not justified and is logically incorrect. The deadweight loss is not due to a fall in MC, but due to the fact that the monopoly has resulted in a loss in consumer surplus that is higher than the gain in producer surplus, because unlike in efficient outcome, monopoly price is higher than MC. As a result, consumers lose and producers gain from the merger.
NOTE: As per Chegg Answering Policy, first 4 questions are answered.