Q#1

Suppose that the vitamin C industry in Germany consists of only two firms : Bayer and Merck. Bayer's cost function is: Ca(qs) = qs. Merck's cost function is: Car(qur) = 4qM. Assume that the inverse demand function is p(q) = 10-q. 1. Assume first that Bayer and Merck compete & la Cournot. Write down the profit maximization problem of the each firm. Find the reaction functions of each firm. 2. Find the Cournot equilibrium outputs and price. What are the profits of each firm? 3. Explain why it could make sense for Bayer and Merck to enter in a collusive agreement in which Merck does not produce and Bayer compensates Merck for not producing? What is the maximum amount of money that Bayer would be willing to pay Merck to stay out of the market? 4. Quantify the loss in consumer welfare from such collusive agreement. 5. Assume now that the two firms compete a la Bertrand. Find the Bertrand equilibrium outputs and price. Explain.The following utility functions represent preferences of a consumer over goods z, and r, (and zy). Prices of these goods are denoted p, and pa (and p3). Consumer has income m. Find the demand functions for all goods in each case. 1. u(21, 12, x3) = \\ min(21, x2) + 73 2. u(x], 17) = max(1 , 12)