Question for Competitive Analysis:

2. Collusion with asymmetric firms. Consider a market with total demand of Q = 100 - P . Two firms simultaneously set prices in each period and consumers purchase from the firm with the lowest price; if both firms set the same price, then consumers are equally distributed between the two firms. Firm H has constant marginal cost CH = 25, firm L has lower constant marginal cost of CL = 20. Firms interact over an indefinite number of periods and the discount factor for each firm is given by o. Assume that firms can only set prices in integer amounts: i.e. 26, 25, 24 but not 24.5, etc. (a) If firm L was the only firm in the market, what is profit maximizing price? What is the associated profits for firm L? (b) What is the Nash equilibrium of the one-shot game (that is, if firms were to set prices only once). What are the profits of each firm in this equilibrium? Suppose that firms engage in a collusive agreement, where they set price equal to firm L's profit maximizing price from part (a) in each period splitting the profits evenly. If either firm ever deviates from the collusive agreement they both revert to the one-shot equilibrium derived in part (b) indefinitely (grim-trigger strategy). (c) For what values of o is this agreement stable? (Hint: A collusive agreement is stable on if both firms are willing to stay in the agree- ment.) (d) Now suppose that the firms decide to split the profits in the collusive agreement such that the low cost firm gets share s of the profits and the high cost firm gets 1 - SI of the profits. In order to make the agreement stable for smaller values of o relative to part (c), should s, be more or less than 1/2? Explain