Question

1. Consider a monopolist whose total cost function is TC = Q³ – 30Q² + 301Q, whose inverse demand function is P = 1501 – 30Q where Q is output and P is the price.
   1. If the firm were to act as a single price monopolist, how much will it produce? What price it will charge? How large will be its profit? Calculate the firm’s Lerner Index of monopoly power.
   2. Now suppose this firm can practice perfect price discrimination. How much does it produce? If the firm produces Q = 25, what is the lowest price it charges for any unit, and what are its profits?

Answer 1

a) If the firm were to work as single price monopolist , using the demand function , it would set the price such that profit is maximised. Profit is maximised at the level of output where marginal cost equals marginal revenue.

b) In case of perfect price discrimination, the monopolist extracts all of the consumer surplus that it would have gained otherwise. Total revenue of such monopolist would be PQ + the shaded area PP'E as shown in fig 1 , ( area of PP'E = (1/2)*PP'*P'E )

At Q = 25, P = 1501-30*25 = 751 . This is the least price the discriminatory monopolist would charge.

Total revenue = 751*25 + 0.5*(1501-751)*25 = 28,150

Total cost a Q= 25 = (25)^{3 _-} 30*(25)² + 301*25 = 4,400

Profit =

Total Revenue - total cost = 23,750

Fig 1 : Perfect discrimination