Consider a game in which we add an extra stage to the standard Bertrand model of price competition where firms choose a capacity level. Consider a market with two firms. In the first stage, each firm chooses a production capacity level q₁ at a cost of 0.25 per unit of capacity, where 0 ≤q¡ ≤ 1. In the second stage, the firms observed each other's capacity and respond by competing over prices. Once capacity is decided, the firms can produce up to that capacity with zero marginal cost. Each firm faces a demand of p = 1 Q and choose prices simultaneously in the second stage, and sales are distributed as in the standard Bertrand model. (a) Verify and explain that in the second stage, both firms will set a common price p₁ =p² =p* = 1- q1 – q2. (b) In the first stage, each firm simultaneously and independently chooses its capacity, q₁. Find the equilibrium capacities and price. (Hint: both firms anticipate equilibrium price p* in the second stage) (c) 2 Compare your results in (b) if both firms only compete in choosing q as in the standard Cournot model with the inverse market demand p = 1 - Q and identical marginal cost of 0.25 per unit of output.

Consider a game in which we add an extra stage to the standard Bertrand model of price competition where firms choose a capacity level. Consider a market with two firms. In the first stage, each firm chooses a production capacity level q₁ at a cost of 0.25 per unit of capacity, where 0 ≤q¡ ≤ 1. In the second stage, the firms observed each other's capacity and respond by competing over prices. Once capacity is decided, the firms can produce up to that capacity with zero marginal cost. Each firm faces a demand of p = 1 Q and choose prices simultaneously in the second stage, and sales are distributed as in the standard Bertrand model. (a) Verify and explain that in the second stage, both firms will set a common price p₁ =p² =p* = 1- q1 – q2. (b) In the first stage, each firm simultaneously and independently chooses its capacity, q₁. Find the equilibrium capacities and price. (Hint: both firms anticipate equilibrium price p* in the second stage) (c) 2 Compare your results in (b) if both firms only compete in choosing q as in the standard Cournot model with the inverse market demand p = 1 - Q and identical marginal cost of 0.25 per unit of output.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.5P

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