Question 3 In addition to imposing tariffs on firms, governments can also subsidize firms in order to increase output and profits. Suppose that in a Cournot oligopoly, the government has an amount of s dollars that it can divide between two firms as a subsidy. Specifically, if a is some percentage, then the government gives a percent of the cost- reducing subsidy to firm 1, and (1 - o) percent to firm 2, so that the total subsidy received by each firm is as and (1 - a)s, respectively. Suppose then that the demand curve is given by P = 50 - Q1 -Q2 and that MR1 = 50 -201 - Q2, MC1 = 10 -as MR1 = 50 - Q1 - 202, MC2 = 10 - (1 -Q)s Also, total costs for each firm are given by TC (Q1) = (10 - as) Q1, TC2(Q2) = (10 - (1 -a)s) Q2 1. Solve for each firm's best response function, as well as the Nash equilibrium. 2. Suppose that we are in the special case where the subsidy is split evenly between the two firms, so that o = ;, and that s = 20. Graph each firm's best response function, and solve the Nash equilibrium, and determine each firm's profit. 3. Now suppose that a = 1 (and that s = 20 still). Once again, graph and solve for the Nash equilibrium, and determine each firm's profit. Does the change in profits that you found in this equilibrium compared to what you found in part 2 above make sense given the change in the allocation of the subsidy? Why? 4. One government policy may be to set a subsidy so that both firms increase their level of output in equilibrium. Examining your solution for Nash equilibrium Qi and Q2 from part 1 above, what values of a will guarantee that if s increases, both Qi and Q2 will also increase