Q1. The Corleone and Chung families are the only providers of good h in the U.S.The market demand for good h is h = 1, 200 - 20p. The costs of production for each ofthem are represented by the cost functions C1(h1) = 10h1 and C2(h2) = 20h2, respectively.Suppose both families must choose their output levels simultaneously.
(a) Derive their reaction functions.
(b) Calculate the Cournot equilibrium in this market. Indicate output levels, market price,and individual profits.
Q2. Consider the Corleone and Chung families from Question 1. Suppose the twofamilies sign an agreement to restrict the amount of good h in the market. By doing this,market price and profits will increase. Suppose the agreement specifies that given the costdifferential, Corleone will receive 3/5 of the total profits and Chung will receive 2/5.
(a) Find the solution to this collusion problem. Indicate individual outputs, market price,total profits, and individual profits.
(b) Does either family have an incentive to break the agreement? Who and why?Hint: Remember that the first order conditions obtained from differentiation gives aninterior solution. If the first order conditions do not yield a solution, try cases inwhich one of the firms produces zero.
Q3. MBI and Pear are the only two producers of computers. MBI started producingcomputers earlier than Pear. MBI's costs of production are given by C1(y1) = y21. Pear'scost function is C2(y2)=5y2. The national demand for computers is y = 106 - 105p.
(a) Calculate the Stackelberg equilibrium in which MBI is the leader in this market.Indicate output levels, market price, and the profits of each firm.
(b) Suppose that both firms enter this market at the same time. Calculate the Cournotequilibrium and compare it to the situation in part (a).