Starting with the reaction functions of duopolists A and B from Problem 4, find

Question

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

Problem 4 data: "a). The equation Qa = 1/2(12-Qb) is the so-called reaction function of duopolist A in a Cournot model because given the value of Qb'Qa gives the best profit-maximizing level of sales of oligopolist A (reaction functions are derived in the first section of the appendix to this chapter)."

The reaction function of duopolist A is QA = (12-QB)/2 (1)

The reaction function of duopolist B is QB = (12-QA)/2 (2)

Find the Cournot solution by substituting equation (1) into equation (2) and solve for QB then QA.

Explanation / Answer

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

4 QA = 24 -12 +QA

QA = 4

QB = (12-4)/2 = 4

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