Consider a market with two firms A and B producing a good. Their cost functions are CA(QA) = Q + aQA + F and CB (QB) = Q3 +bQB + FB, respectively. Where FA and FB are fixed costs. The demand function for the good is P(Q)= a - BQ, where Q = QA + QB. (4+4+4 Marks) a. Write the profit maximization problem of the two producers. Assume that each producer treats the other producer's output decisions as given and write the first order conditions for the optimization problem for both producers. Use Cramer's rule to find the optimal quantities chosen by both producers. b. Write the total differential of the first order conditions treating QA and QB as endogenous variables and a, b, a, as exogenous variables. Express the sytem of equations in the matrix form Ax = b. c. Use Cramer's rule to find the impact of a change in the marginal cost of firm A on output decisions of firms A and B, respectively and discuss their sign.