Suppose the table below shows the demand curve facing a monopolist who produces
ID: 1129386 • Letter: S
Question
Suppose the table below shows the demand curve facing a monopolist who produces at a constant marginal cost of $8 per unit
a. What is the firm’s demand curve and marginal revenue curve? b. What are the firm’s profit-maximizing output, price and profit? c. What would be the equilibrium price and quantity if this were a perfectly competitive industry?
Given your answers in problem 3 above, d. What would be the consumer surplus, producer surplus, and deadweight loss for the monopoly? E. What would be the consumer surplus, producer surplus, and deadweight loss for the perfectly competitive industry?
price quantity price Quantity 40 0 20 10 366 2 16 12 32 4 12 14 28 6 8 16 24 8 4 18Explanation / Answer
a.To obtain MR vurve, we have to derive the inverse demand curve first. The intercept of the inverse demand curve on price axis is 40. The slope of the inverse demand curve is the change in price divided by the change in quantity. Therefore the slope is : -2, and the demand curve is :
P = 40 - 2Q
TR = P*Q = (40-2Q) * Q = 40Q-2Q2
MR = 40-4Q
b. the firm's profit maximizing output will occur, where MR=MC. Now here MC= $8. So the profit maximizing quantity
40-4Q = 8
Q = 8
Profit maximising price can be determined by substituting profit maximising quantity into demand equation
P=40-2(8) = $24
Therefore Total revenue(TR) = P*Q= 24 * 8 = $192
The profit of the firm = TR-TC. Total cost is equal to average cost times the level of output produced. SInce MC is constant, average variable cost is equal to marginal cost. So, TC = 8Q = 8*8 = $64. the proft is:
TR - TC = 192-64 = $128
C. In a competitive market,P=MC at equilibrium. Therefore
P= MC
40-2Q = 8
Q=16
Therefore, P = 40-2(16)= $8
d. The social gain obtain from deadweight loss. The deadweight loss = (24-8)*(16-8)*(2)= 16*8*2 = 256
Consumer Surplus = 128+256 = 384. The monoply's profit reduced to zero.
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