\f( ) In collusion MR = MC at elvilibrium . TR = PXQ = au - a 2 MR OTR / DQ = a - 24 7 a-2a = ( = > 2 = a* du - att = Q - G - L 2 = 2 ate 2 Profit IN = cut c 2 - C G - C 2 = at 2 2 = 4 ( a-c ) The collusion out come is as Nash mi incentive equilibrium . A firm will violateer if itto has make to produce " greater lucentity , and more profits,5. Consider a sequential version of the Cournot competition in exercise 4 assignment #31. Suppose there are two rms engaged in quantity competition. Firm 1 (the leader) decides how much to produce. After observing the choice made by rm 1, rm 2 (the follower) decides how much to produce. The inverse demand is P = a Q where Q = 11 + (12. Assume that rm's 2' total cost of production is TO(q,-) = cq, where c the constant marginal cost of productimi. (a) Find the best reSporise functiOn fer rm 2 (the follower) using the rst-order condi- tiOn. Check the second-order corlditiOn. (b) Solve the game by backward induction and determine equilibrium quantities, price, and prots. (0) Compare the quantities of rm 1 and rm 2 in this equilibrium, and the total quantity Q in this equilibrium with the total quantity in the Cournot equilibrium in exercise 4 assignment #3. (4) Suppose there are two identical firms engaged in quantity competition (Cournot compe- tition). The inverse demand is P = a - Q where Q = q1 + 92. Assume that firm's i total cost of production is TC(qi) = cqi where c the constant marginal cost of production. (a) Find the best response functions using the first-order conditions. Check the second- order conditions. (b) Compute the Cournot-Nash equilibrium (i.e., quantities, price, and profits). (c) Suppose firms could collude. Solve for the quantities and profits under collusion. (d) Is the collusion outcome a Nash equilibrium. Why or why not