1. (10 points) Two firms compete in one market. Their cost functions are C1(y1) and C2(y2) respectively, with increasing marginal cost. Products are homogeneous, so the total market supply is Y = y1 + 32. The downward sloping market (inverse) demand function is P = P(Y). (a) If these two firms compete following Cournot competition, write down their optimization problem and the associated first order conditions (no need to solve it). (b) If these two firms collude to monopoly the market, write done joint optimization problem and the associated first order conditions (no need to solve it). Do they produce more or less than Cournot result? Explain clearly why. (c) Design one economics-based approach to detect collusion. Explain the key idea of the approach and outline the main data needed to implement it