SCIT1003 Chapter 7: Duopoly Prof. Tsang

Assignment 7.1 The relationship between P & q is not necessary linear. What is the effect of a nonlinear relationship, e.g. P=a exp(-q/b) + c, to Cournot competition, with q=q1+q2? Assume a=130, b=70 & marginal cost c Profit for firm1: p1=[a exp(-(q1+q2)/b)]*q1 Profit for firm2: p2=[a exp(-(q1+q2)/b)]*q2 Find the optimized q for the duopoly & monopoly problem.

Profit of firm1 (unit in 1000s) q2 40 50 60 70 80 90 q1 40 50 60 70 80 90 Nash equilibrium

Assignment 7.2 Repeat Assignment 7.1 with P=a exp(-q*q/b/b) + c, where q=q1+q2 Assume a=130, b=70 & marginal cost c Find the optimized q for the duopoly & monopoly problem.