Suppose two firms compete in prices in a market with demand Q =2 - p, and both firms have a cost function C(q) = 1/2 q² . Firms have to serve all the demand they get at the prices announced by the two firms.

(a) Suppose both firms announce the same price, p = 3/4 . Compute the profits that each will obtain, and the mark-up they charge.

(b) Prove that you have just found an equilibrium. That is, if they expect the rival to charge that price, thy maximize profits by also charging that price.