Question

Suppose there is a meat market that is serviced by a monopolist. Consumer preferences are summarized by P=-55q+997. The monopolist has the following marginal cost function MC(q)=150+39q. The optimal quantity that the monopolist will supply the market is q=847/149 and the monopolist will set the price as p=101968/149.

Now suppose the market is supplied by perfectly competitive firms with the same aggregate cost structure as the monopolist. The optimal quantity the perfect competitive industry will output is q=847/94 and the prevailing price is p=47133/94.

Questions:

a) What is the monopolist producer surplus? (Answer is 2407, how did they get that?

b) What is the producer surplus under perfect competition? (Answer is 27978951/17672, how did they get that?)

c) What is the dead weight loss from monopoly? (Answer is 520, how did they get that?)

Answer 1

a) PS = 0.5*(Monopoly price - minimum marginal cost + monopoly price - marginal cost at monopoly quantity)*monopoly quantity

= 0.5*(101968/149 - 150 + 101968/149 - (150 + 39*847/149))*(847/149)

= 2407

b) PS = 0.5*(competitive price - minimum marginal cost)*competitive quantity

= 0.5*(47133/94 - 150)*847/94

= 1583.236 (This is the value of 27978951/17672)

c) DWL = 0.5*(monopoly price - marginal cost at monopoly quantity)*(competitive quantity - monopoly quantity)

= 0.5*(101968/149 - (150 + 39*847/149))*(847/94 - 847/149)

= 520

(The functions are all linear and so the formulas are derived for linear functions)