Econ170SQ4FALL07

Econ170SQ4FALL07 - Economics 170 UCLA E. McDevitt SQ #4...

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Economics 170 UCLA E. McDevitt SQ #4 Imperfect Information and Limit Pricing 1. Assume a two periods. There is an incumbent firm and a potential entrant. The incumbent firm is the only firm in period one. The potential entrant can observe the price of the incumbent in period one and can then choose between enter or not enter in period two. The potential entrant cannot observe the incumbent’s cost function, but knows that the incumbent is either a low-cost producer with probability α or a high-cost producer with probability 1- α . The market demand curve is P = 16- Q. Marginal cost is $4 if the incumbent is a high-cost producer (MC is also equal to 4 for the potential entrant). Marginal cost is zero for the incumbent if the incumbent is a low-cost producer. There is a fixed entry cost $10. 1.a. Assume the incumbent is a high-cost producer. Find monopoly quantity, price and profit. (Call this price “high price”). If potential entrant does not enter in period two, then the incumbent receives this profit if period one and period two. However, if the PE enters in period two, then the incumbent gets monopoly profit in period one and Cournot profit in period two. The PE receives Cournot profit minus F in period two if it enters. Find Cournot quantities, price and profits. b. Assume the incumbent is a low-cost producer. Find monopoly quantity, price and profit. (Call this price “low price”). If potential entrant does not enter in period two, then the incumbent receives this profit if period one and period two. However, if the PE enters in period two, then the incumbent gets monopoly profit in period one and Cournot profit in period two. The PE receives Cournot profit minus F in period two if it enters. Find Cournot quantities, price and profits. c. Return to the assumption that the incumbent is a high-cost producer. However, now it charges “low price” (which you determined in part b). What is the incumbent’s profit in period one given that it charges low price? In this scenario, if the PE does not enter in period two then the incumbent will simply charge the monopoly price consistent with being a high cost producer (which you determined in part a). If the PE does enter in period two, then the incumbent and potential entrant play Cournot (profits already determined in part a). d. Show the game in extensive form (tree diagram) with Nature being the first player. Nature “chooses” between high-cost producer and low-cost producer. If a high-cost producer, incumbent then chooses between low price and high price. If a low-cost producer, incumbent definitely chooses low price. After the incumbent chooses between low price and high price in period one, the PE then chooses between enter or not enter in period two. e. Given low price, what would the PE choose
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Econ170SQ4FALL07 - Economics 170 UCLA E. McDevitt SQ #4...

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