Question 3 In addition to imposing tnris on rms, governments can also subsidize rms in order to increase output and prots. Suppose that in a Cournot oligopoly, the government has an amount of 5 dollars that it can divide between two firms as a subsidy. Specically, if a is some percentage. then the government gives cr percent of the cost.- redueing subsidy to rm ll and (1 a) percent to rm 2, so that the total subsidy received by each rm is as and (1 eds. respectively. Suppose then that the demand curve is given by P9wo-o and that. MR] = 502Q1Qz, M01 = 10"\"0'3 MR1 =50Q12Q2, MC: =10-(1)8 Also, total costs for each rm are given by T01(Q1) = (10 013) Q1, TC;(Q:) = (10 (1 (1)8) Q: 1. Solve for each rm's best response function, as well as the Nash equilibrium. 2. Suppose that we are in the special case where the subsidy is split evenlyr between the two rms, so that a = %, and that s = 20. Graph each rm's best response function, and solve the Nash equilibrium, and determine each rm's prot. 3. Now suppose that a = 1 (and that s = 20 still). Once again. graph and solve for the Nash equilibrium, and determine each rm's prot. Does the change in prots 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 rms increase their level of output in equilibrium. Examining your solution for Nash equilibrium Q; and Q; from part 1 above, what values of a will guarantee that if 5 increases, both Q; and Q; will also increase