Consider an industry with Firm 1 and Firm 2 engaging in quantity competition. The two face the inverse market demand function as P = 800 - where the two supply together Q = 9₁ +92 units to the market. Suppose each firm bears the same cost production as C(q) = 100 + 200q when producing q units. Moreover, suppose the government imposes a specific tax of $100 per unit only on Firm 1. a. Derive Firm 1's best response function, 9₁(92), against Firm 2's output level choice, 92 when the two act simultaneously. b. Find the equilibrium output level of Firm 1 at the N.E. equilibrium. c. Find again the equilibrium output level of Firm 1 if it acts as the follower while Firm 2 as the leader. d. Find the difference in social welfare under the Cournot equilibrium in question b and under the Stackelberg equilibrium in question c. Which equilibrium is more efficient?