1. SCIT1003 Chapter 7: Duopoly
Prof. Tsang

15. 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.

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

17. 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.