Suppose there is a perfectly competitive market where each firm has the same marginal cost, c = 4 and the market demand is given by Q(P ) = 120 - 3P . There are no fixed costs. One of these firms, firm A, has the option to make an investment, I 0 and become the dominant firm with probability q(I) = I/(1+I), in which case the rest of the firms form the competitive fringe with a supply Qf s = 20 + 2P . With probability 1 - q(I), firm A continues to be a competitive firm. Investment I has a cost given by C(I) = ln(1 + I).

(a) Find the profit maximizing investment level I for firm A.

(b) Calculate the expected Lerner index for firm A at I you found above