1. Consider the following Cournot game: . There are n ≥ 1 firms. • Firm i, i = 1, 2, ..., n, chooses an output qi € [0, ∞]. • The market inverse demand is P = a - bq, where a, b>0 and q = Σ₁_19i. =1 • Firm i's cost function is ci(qi) = cqi, where c > 0. (a) Solve the monopoly problem, in which there is only one firm in the market. (b) Find the Nash equilibrium outputs with n firms. Find the price in the equilibrium. (c) Show that the Nash equilibrium of the above game covers cases of market outcomes arranging from monopoly (n = 1) to perfect competition (n →∞).

1. Consider the following Cournot game: . There are n ≥ 1 firms. • Firm i, i = 1, 2, ..., n, chooses an output qi € [0, ∞]. • The market inverse demand is P = a - bq, where a, b>0 and q = Σ₁_19i. =1 • Firm i's cost function is ci(qi) = cqi, where c > 0. (a) Solve the monopoly problem, in which there is only one firm in the market. (b) Find the Nash equilibrium outputs with n firms. Find the price in the equilibrium. (c) Show that the Nash equilibrium of the above game covers cases of market outcomes arranging from monopoly (n = 1) to perfect competition (n →∞).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.4P

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