1. Consider the following specification: The only two firms in the good Q-market have different cost functions, specifically: C, (Q,) = 40; and C2(Q2) = 8Q2. Market demand for the product is given by: P = 760 - 10Q, where Q is the total output. (No other firms produce the product.) Show the problems you solve in part for partial credit in case you make any mistakes. (a) (12 pts.) Find the cartel optimum. Assuming no side payments, what is the profit level of each firm? (b) (13 pts.) Show that cartel member 2 has an incentive to cheat on the agreement. To do this, assume that cartel member I will not cheat and that the market-clearing price will prevail. What is the implied profits for each if cartel member 2 cheats and cartel member 1 does not? Compare these to the profits in part a. (Who makes more or less, and how do total profits compare?)