Two Firms, CS Corp. and JL & Associates make identical goods and sell them in th
ID: 1253843 • Letter: T
Question
Two Firms, CS Corp. and JL & Associates make identical goods and sell them in the same market. Market demand is given by Q = 1200 -P . Once a Firm has built capacity, it can produce up to its capacity each period with a marginal cost of MC = 0. Building a unit of capacity costs 240 (for both Firms). Once production occurs, price in the market adjusts to the level at which all production is sold. (In other words, these Firms engage in quantity competition, not price competition.)a. IF CS knew that JL was going to build 100 units of capacity, how much would CS want to build? If CS knew that JL was going to build X units of capacity, how much would CS want to build?
b. IF CS and JL each had to decide how much capacity to build without knowing the other's capacity decision, what would the Cournot equilibrium be?
Explanation / Answer
Part a seems like a question about the Stackelberg model, but initial capacity for one of firms is given and is asking about the 2nd firm's reaction. So I would calculate using the Cournot equation. a) Let CS be firm 1 and JL be firm 2. Q = 1200 - P -> P = 1200 - Q Note that building a unit of capacity costs 240 up to capacity really means MC is 240 for building capacity of each unit. Let Pi = Profit Pi1 = (P-c)q1 = (1200 - q2 - 240)q1 - q1^2 Max Pi -> dPi1/dq1 (First order condition) -> 960 - q2 - 2q1 = 0 q1 = 480 - 0.5q2 Given q2 = 100, q1 = 430. Part 2 of a) q1 = 480 - 0.5q2 b) using the same equation q1 = 480 - 0.5q2 By symmetry: q2 = 480 -0.5q1 Sub q2 into q1 -> q1 = 480 - 0.5(480 - 0.5q1) = 240 + 0.25q1 q1 = 320 We know that q1 they have the same Pi max equation. So we know that q1 = q2 q2 = 320 Cournot eq -> Q = q1 + q2 = 640, P = 1200 - 640 = 560
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