Oligopoly, Pricing Strategies Question

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Answer the following questions about oligopolies and pricing strategies. Note: Please round all numbers to 2 decimal places. a) Firm A and Firm B both sell identical (i.e., homogenous) products. Firm A's marginal cost of production is $20, while Firm B's marginal cost is $22. Identify (i) the equilibrium prices, and (ii) the market shares, if both firms simultaneously choose their prices in a non-cooperative game (Bertrand competition). Assume that with equal prices, the two firms evenly split demand. (4 points) b) Now consider two other firms: Firm 1 and Firm 2. Both firms sell differentiated (i.e., heterogeneous) products. Their demand functions are given by q1 = 240 - 2P, + P2 and q2 = 240 -2P2 + P1 where Pi and P2 are the prices charged by Firm 1 and Firm 2, respectively, and q1 and q2 are the quantities demanded. Each firm has fixed costs equal to $1,000 and marginal costs equal to $10.Identify (i) the equilibrium prices, (ii) the equilibrium quantities, and (iii) the profits, if both firms simultaneously choose their prices in a non-cooperative game (Bertrand competition). (7 points) c) Consider again Firm 1 and Firm 2 from part (b). Now suppose that Firm 1 and Firm 2 form a cartel (i.e., they collude over prices). Identify the cartel price, the quantity that each firm in the cartel will then produce, and the profit of each firm in the cartel. (5 points) d) Consider again Firm 1 and Firm 2 from parts (b) and (c). Instead of forming a cartel (as in part (c)), each of the two firms now wants to use a first degree price discrimination scheme. Briefly explain how using a first degree price discrimination scheme, compared to forming a cartel, changes (i) the quantity produced by each firm, (ii) the profit of each firm, (iii) consumer surplus, and (iv) total welfare. Note: No math is required to answer this question. (4 points)