1. Consider two firms producing an identical product in a market where the demand is described by p = 1; 200 2Y. The corresponding cost functions are c_{1} (y_{1}) = y^{2}_{1} and c_{2} (y_{2}) = 3y^{2}_{2}.
(a) State the profit maximization problem of firm 1 and use the first order condition to derive firm 1's reaction function.
(b) State the profit maximization problem of firm 2 and use the first order condition to derive firm 2's reaction function.
(c) Solve the system of reaction functions to identify how much each firm is producing; what is the market quantity, the market price, and the corresponding individual and collective profits.
(d) Assuming that the firms can coordinate their actions, what are the individual quantities produced the market quantity, the market price, and the resulting joint profits?
(e) How will the firms distribute the joint profits (Hint: find the minimum amount that each firm is willing to accept and the maximum amount available for each firm under the cartel agreement ). Is this form of cooperation sustainable? Explain.