Question

Consider a homogeneous product industry with inverse demand function p-35 -Q a) Assume that the industry is initially monopolized by an incumbent firm (firm I) which has the exclusive right to use the state-of-the-art technology summarized by the total cost function C-10q. Find the initial monopoly equilibrium (price, quantity, industry profit, consumer surplus and total surplus) and the associated degrees of concentration (Herfindahl index) and market power (Lerner index) b) Assume now that a new firm (firm N) discovers and patents a more efficient technology, summarized by the total cost function C-8q. The new technology can be used only by the new firm, which enters the market and compete in prices with the previous monopolist (according to the Bertrand model with asymmetric costs). Find the resulting Bertrand equilibrium (price, quantity, industry profit, consumer surplus and total surplus) and the associated degrees of concentration (Herfindahl index) and market power (Lerner index)

Answer 1

(a) P = 35 - Q, Monopoly Eq^n: - TC = 10q, MC = 10, at Eq^m MR = MC, So 35 - 2Q = 10, So 25/2 = Q = 12.5 Thus P = 35 - 12.5 = 22.5 Thus P^M = 22.5, Q^M = 12.5, pi = (P - MC) Q = (12.5)^2 = 156.25 = pi CS = 1/2 [12.5] times (12.5) = 78.125 Total surplus = CS + pi = 234.375 Now from, TC = 8q, MC_N = 8, MC_I = 10, Now Bertrand Model, at eq^n P_I = P_N = 10, since form N is a lower cost firm, so P_N has to be Min 8, P_I can�t charge below $10 = which equals its MC If P_I, P_N > 10, then price war will start, so firm N can at Max charge = 10 [since if P_I > 10, then P_N can be little smaller than 10, P_N = P_I - epsilon, lim_epsilon rightarrow 0,