Question

The following table shows the demand curve facing a monopolist who produces at a constant marginal cost of $10:

Price	Quantity
18	0
16	4
14	8
12	12
10	16
8	20
6	24
4	28
2	32
0	36

a) Calculate the firm’s marginal revenue curve.

b) What are the firm’s profit-maximizing output and price? What is its profit?

c) What would the equilibrium price and quantity be in a competitive industry?

d) What would the social gain be if this monopolist were forced to produce and price at the competitive equilibrium? Who would gain and lose as a result? Illustrate the difference between the competitive and monopolistic outcomes in a graph.

Answer 1

a) From the given table, demand curve has a vertical intercept of 18 and a horizontal intercept of 36.

Then, the equation of the demand curve can be given as : (P-18)/(0-18) = (Q-0)/(36-0)

or, (P-18)/-18 = Q/36

or, -2P+36=Q

or, 2P = 36-Q

or, P = 18 - (Q/2) is the demand curve

Now, total revenue TR = P*Q = 18Q - (Q²/2)

Then, marginal revenue MR = dTR/dQ = 18-Q is the firm's marginal revenue curve.

b) For profit maximizing , MR=MC

or, 18-Q = 10

or, Q = 8 units is the equilibrium quantity level

and P = 18-(Q/2) = 18-(8/2) = $14 is the equilibrium price level.

c) In a competitive industry, P=MC

or, 18 - (Q/2) = 10

or, Q = 16 units is the equilibrium quantity in a competitive industry

and P = 18-(Q/2) = 18-(16/2) = $10 is the equilibrium price level in a competitive industry.

d) Incase of monopoly, Profit = TR-TC = (P*Q)-(MC*Q) = ($14*8)-($10*8) = $32

Incase of competitive market, Profit = TR-TC = (P*Q)-(MC*Q) = ($10*16)-($10*16) = $0

Thus, firms will lose if it comes from monopoly to competitive industry.

However, consumers in competitive industry will gain as the consumers will get higher quantity (8 units to 16 units) at lower price ($14 per unit to $10 per unit). Thus, consumers gains while producers loses.

We have shown the equilibrium conditions in the diagram below: