Question 4(a)The equation Q A = 1/2(12-Q) b ) is the so called reation function

Question

Question 4(a)The equation QA= 1/2(12-Q)b) is the so called reation function of duopolist A in a COurnot model becasue given the value of Qb, Qa gives the best or profit-maximizing level of sales of oligopolist A(reaction functions are derived in the first section of the appendix to this chapter).  Show that this is the case with reference to Figure10-1.(b) What is the reaction function of oligopolist B?

Problem 5 is the question, but had to share question 4 in order to answer question 5.  

Question 5 Starting with the reaction functions of duoplists A and B from Problem 4, find the Cournot solution algebraically.

Explanation / Answer

QA = (12-(12-QA)/2)/2

4 QA = 24 -12 +QA

QA = 4

QB = (12-4)/2 = 4   

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