3. There are two rms in a market competing by choosing prices every period. Firm 1 has marginal cost zero, while rm 2 has marginal cost c > 0. The demand function is given by Q=20fp. (a) Show that in the Bertrand equilibrium rm 1 will have a prot (20 c) c and rm 2 will have zero prot. (b) Suppose rms are attempting to collude using the following scheme. In the collusive phase they set p1 = 302 = 10 and split the market in half. If any rm deviates, they both revert to the Bertrand equilibrium forever. The interest rate is 10%. i. Suppose c = 2. Will collusion be possible? (Evaluate the incentives of both. ms.) ii. Suppose instead that c = 5. Will collusion be possible now? (c) How would your answer to part 3(b)ii change if under the collusive agreement rm 1 gets 80% of the market share and rm 2 gets 20%