Consider the following oligopolistic market. In the first stage, Firm 1 chooses quantity q₁. Firms 2 and 3 observe Firm 1's choice, and then proceed to simultaneously choose 92 and 93, respectively. - Market demand is given by p(Q) = 100 – Q, and Q = 9₁ +92 +93. Firm 1's costs are c₁ (9₁) = 59₁, firm 2's costs are c₂ (92) = 4q2 and firm 3's costs are C3 (93) = 493. and 93, Starting from the end of the game, you can express Firm 2's best response function in terms of 91 and you can similarly express Firm 3's best response function in terms of q₁ and 92. Using these, answer the following questions. If rounding is needed, write your answers to 3 decimal places. a) If Firm 1 chooses q₁ = 3, what quantity will Firm 2 choose? b) If Firm 1 chooses q₁ = 100, what quantity will Firm 2 choose? c) In the subgame perfect Nash equilibrium of this game, firm 1 produces what quantity? d) In the subgame perfect Nash equilibrium of this game, firm 2 and firm 3 each produce what quantity?

Consider the following oligopolistic market. In the first stage, Firm 1 chooses quantity q₁. Firms 2 and 3 observe Firm 1's choice, and then proceed to simultaneously choose 92 and 93, respectively. - Market demand is given by p(Q) = 100 – Q, and Q = 9₁ +92 +93. Firm 1's costs are c₁ (9₁) = 59₁, firm 2's costs are c₂ (92) = 4q2 and firm 3's costs are C3 (93) = 493. and 93, Starting from the end of the game, you can express Firm 2's best response function in terms of 91 and you can similarly express Firm 3's best response function in terms of q₁ and 92. Using these, answer the following questions. If rounding is needed, write your answers to 3 decimal places. a) If Firm 1 chooses q₁ = 3, what quantity will Firm 2 choose? b) If Firm 1 chooses q₁ = 100, what quantity will Firm 2 choose? c) In the subgame perfect Nash equilibrium of this game, firm 1 produces what quantity? d) In the subgame perfect Nash equilibrium of this game, firm 2 and firm 3 each produce what quantity?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Two firms compete as Stackelberg duopolists in a market with inverse demand given by 132.00 – 20, where pis the per-unit price, q; is the output for Firm i(either Firm 1 or 2), and Q = q1 + q2. Firm 1 is the leader in this market. Both firms face constant marginal costs of $4 per unit. Assume no fixed costs. What is the optimal output for Firm 1? (Round to two decimals if necessary.) What is the optimal output for Firm 2? (Round to two decimals if necessary.)
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