1. Suppose there are two snowboard manufacturers, Burton and K2. Consider the following demand functions for the two companies' snowboards: Burton K2 9B = 900 - 2pB + PK qk = 900 - 2pK + PB pe and pa are the prices set by Burton and K2, respectively. qs and qu are the quantities sold by Burton and K2, respectively. For simplicity, assume that the marginal cost of producing snowboard is zero. (a) Each company sets its price to maximize profits (Bertrand competition). Derive the best response functions of Burton and K2. [10 marks] (b) Find the Bertrand equilibrium prices, quantities and profits. [5 marks] Now assume that these firms compete in quantities (Cournot): each company sets its quantity to maximize profits. We can rewrite the above demand functions as: Burton K2 PB = 900 - 198 - 39K PK = 900 - 59K - 39B (c) Derive the new best response functions of Burton and K2. Compare with the best-responses obtained in part (a). [10 marks] (d) Find the Cournot equilibrium prices, quantities and profits. [5 marks] (e) In view of your answers in parts (b) and (d), discuss firms' ability to raise their price above marginal costs in each model. Comment on the efficiency (in terms of total welfare) of the Cournot and Bertrand models. [10 marks] (f) Consider now a more general system of inverse demand functions. Burton K2 PB = 900 - BAB - 79K PK = 900 - BqK - 748 where 8 > 0 and y E [0, B]. We have seen that y/82 expresses the degree of product dif- ferentiation. Explain in words (you do not need to derive the mathematical expressions for equilibrium prices and quantities) how the level of product differentiation affects the difference in prices between the Cournot and Bertrand equilibria. [10 marks]