Collusion Consider a market with two firms, 1 and 2, that manufacture a homogenous product. The inverse demand for the product is: P(Q) = 1200 - 2Q where Q is total output. Production costs for each of the two firms is identical and given by C(qi) = 100q; where qi is firm i's output. Thus, Q = q1 + 92. (a) Write out the profit function of firm 1. (b) Assume firms play the static Cournot equilibrium. Compute the best response function for each firm. (c) Compute the Nash equilibrium level of output, price, and profits. Now assume the two firms form a cartel that produces the monopoly output for this market. The firms agree to share the cartel output and profit equally.(d) What aggregate output will the cartel agree upon? What will be the market price and profit of each firm? (e) Show why this cartel is not stable if the firms interact only once. What is each firm's optimal deviation if the other firm chooses the cartel quantity? Now suppose that the cartel is expected to exist indefinitely and firms discount future profits at rate o where 0