(a) Compute the optimal cartel solution and the resulting profit of an individual firm.

QUESTION TWO The market's demand function for a product is: p=100 - Q, where Q is the total industry output. There are eleven identical firms in this industry, each of which has a cost function C(q)= 4q + q2. Firms compete in quantity, and the market price adjusts to clear the market. Suppose these firms decide to form a cartel. Initially, all firms join the cartel. (a) Compute the optimal cartel solution and the resulting profit of an individual firm. Next, the firms attempt to achieve the cartel solution for the current period. One firm, however, considers cheating on its cartel output by producing its profit-maximizing output. Assume that the remaining ten members will produce the cartel output. (b) Find the optimal quantity the cheating firm will produce and how much profit it makes from cheating. Next, suppose that instead, these firms will be in the same business indefinitely, that is, no one knows how long the game will last and will treat it as an infinitely repeated game. The firms all have the same discount rate 820. (c) Describe briefly the idea of a trigger strategy. Suppose that all the firms use trigger strategy, when does a firm not want to cheat? Show your work and explain. Hint: use the Cournot output of each firm as the punishment