BUS 33230: The Economics of Companies Problem Set 6 1. We have already shown in class the following results for a Coumot oligopoly with N companies, all having constant marginal cost 0, xed cost f, and facing an inverse demand curve p = a bQ, where Q is total quantity: a. . (llC Quantlty ofa rm. q (N+1)b . a N Market price. p m +2mc . _ i N _ 2 Consumer surplus. CS 2b (NH): (a C) 1: Freeentry equilibrium N: N9 = 1 q / bf Total surplus in the market, gross of any entry costs, equals consumer surplus plus producer surplus. Explain why producer surplus is not equal to zero, even if the market is in a free-entry equilibrium (which has a number of companies N that makes the zero-prot condition hold). Find an expression for total surplus and then use it to solve for the socially optimal N(N+2) (N+1)2 number of companies in the market. (Hint: the derivative of 2 ) S (N+1)3' with respect to N i How does the socially optimal number of companies compare to the free-entry number? If the freeentry equilibrium number of companies is 7, how many would be the optimal number? Why is there this difference