= 2 100-C 2 3. (Limit Pricing). Suppose an Entrant with marginal cost c = 20 is considering entering a market to challenge an Incumbent monopolist. The monopolist is either a High Cost firm (MC = 40) or a Low Cost firm (MC 10). Market demand is Q 100 P. A High cost monopolist would set pm = 70 and produce Qm 30. A Low cost firm monopolist would set pm 55 and QM = 45. The Incumbent's profits as a function of marginal cost are +(c) = ( in period 1 and also in period 2 if no entry occurs. In period 2, the Entrant observes the Incumbent's period 1 price and chooses to Enter or not. If it Enters, the two firms compete as Bertrand price competitors, choosing prices simultaneously. a. Suppose the Entrant must pay a sunk cost K = 200 if it enters. Suppose the Entrant can observe the type (cost function) of the Incumbent before entry. Find the Entrant's profit (including K) if it enters against a High cost firm and against a Low cost firm. Could a High cost Incumbent deter entry by setting Pm 55 in period 1? b. Suppose instead that the Entrant cannot observe the Incumbent's type. Assume also that the Incumbent cannot reveal its type in any way that is believable by the Entrant. All the Entrant knows is that the probability that the firm is Low cost is p. If the Incumbent is a High cost firm, find a condition (which will depend on p) under which it might Limit price by setting its price P1 = 55 in period 1 to mimic a low cost firm. = 2 100-C 2 3. (Limit Pricing). Suppose an Entrant with marginal cost c = 20 is considering entering a market to challenge an Incumbent monopolist. The monopolist is either a High Cost firm (MC = 40) or a Low Cost firm (MC 10). Market demand is Q 100 P. A High cost monopolist would set pm = 70 and produce Qm 30. A Low cost firm monopolist would set pm 55 and QM = 45. The Incumbent's profits as a function of marginal cost are +(c) = ( in period 1 and also in period 2 if no entry occurs. In period 2, the Entrant observes the Incumbent's period 1 price and chooses to Enter or not. If it Enters, the two firms compete as Bertrand price competitors, choosing prices simultaneously. a. Suppose the Entrant must pay a sunk cost K = 200 if it enters. Suppose the Entrant can observe the type (cost function) of the Incumbent before entry. Find the Entrant's profit (including K) if it enters against a High cost firm and against a Low cost firm. Could a High cost Incumbent deter entry by setting Pm 55 in period 1? b. Suppose instead that the Entrant cannot observe the Incumbent's type. Assume also that the Incumbent cannot reveal its type in any way that is believable by the Entrant. All the Entrant knows is that the probability that the firm is Low cost is p. If the Incumbent is a High cost firm, find a condition (which will depend on p) under which it might Limit price by setting its price P1 = 55 in period 1 to mimic a low cost firm