Two chemical firms belonging to different countries compete "a la Cournot" selling their identical product in the world market. Inverse market demand is p= 1 − Q Firm 1 produces with constant marginal cost C1 while firm 2 produces at the different constant marginal cost C2 a. Compute and draw the best response functions assuming that C2 >C1. Give the value of the intercepts. b. Check that the production of firm 1 at the Cournot-Nash equilibrium is q1 = (1−c1)/3 + (c2-c1)/3 Write (without any calculation) the production of firm 2. c. (3 pts) Using the formulas obtained at b give the Cournot-Nash equilibrium productions if both firm attain the same cost, that is c1 = c2 = c d. (5 pts) Suppose now that c1 is greater than c2 because the country where firm 1 operates imposes a tax per unit of output that the other firm doesn't bear. Assume specifically that c1 = c + t and c2 = c Using again the formulas in b compute the equilibrium productions. e. Represent the equilibrium of c and d in a diagram. Use this diagram and a demand diagram to explain intuitively the effects of the tax on firm's relative market shares, total production and market price. f. Comment briefly what this example tells about the role of "fiscal harmonization" (similar taxes in two countries).