3. The Corleone and the Chung families are the only providers of good h. in the U.S. The market demand for good h is hD = 1,000 20p you may have noticed that this is different from the equation given in Hw (perhaps it is related to Luca E. Conometra, the statistician friend of the families, having had problems passing the \"Mathematical Econometrics\" course). The costs of production for each of the families are represented by the cost functions 0107.1) 2 mm and 02012) = 20%, respectively. (a) Suppose both must choose their output levels simultaneously. Calculate the two reaction functions and the Cournot equilibrium in this market. Indicate individual outputs, market price, and prots of each family. (b) Suppose the two families sign an agreement to restrict the amount of good h in the market. By doing this, market price and prots will increase. Suppose the agreement species that, given the cost differential, Corleone will receive 2/ 3 of the total prots and Chung will receive 1/ 3. Calculate the solution to this collusion problem. Indicate output produced by each family, market price, total prots of the cartel, and prots for each family. (c) Does either of the families have an incentive to break the agreement? Who and why? Hint for part (b): Remember that the rst order conditions obtained from differentiation give the solution when it is interior. If using them the solution is not found, you should try solutions in which some rm produces zero