Purchase Solution

The Cournet solution for the duopoly

Not what you're looking for?

Ask Custom Question

Given the reaction function of duopolist A, QA = (12-QB)/2 (1) and the reaction function of duopolist B, QB = (12-QA)/2 (2), find the Cournot solution, that is to find QA and QB by substituting (1) into (2).

Purchase this Solution
Solution Summary

The Cournet solution for the duopoly is shown.

Solution Preview

First, lets find the QA and QB of the equilibrium point. The reaction functions are expressed in term of quantity which maximizes the profit of the firm. For example, QA = (12 - QB) / 2 gives the function that maximizes the profit for firm A. Since the idea is to find the equilibrium point, we want to find QA and QB which maximizes both firm A and firm B's profit to the largest extent. To do this, all we need to do is substitute (1) into (2).
QA = (12 - QB) / 2 (1)
QB = (12 - QA) / 2 (2)

QA = (12 - QB)/2
QA = [12 - (12 - QA)/2]/2
2QA = 12 - 6 + QA/2
4QA = 12 + QA
QA = 12/3
QA = 4

Since the two reaction functions are identical, QB would give the same ...

Purchase this Solution
Free BrainMass Quizzes
Pricing Strategies

Discussion about various pricing techniques of profit-seeking firms.

Economics, Basic Concepts, Demand-Supply-Equilibrium

The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.

Economic Issues and Concepts

This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.

Basics of Economics

Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.

Elementary Microeconomics

This quiz reviews the basic concept of supply and demand analysis.

View More Free Quizzes
Related BrainMass Solutions

  • cournot duopoly

    output but more than the monopoly; the duopoly price is more than the competitive price but less than the monopoly; the total profits are more for the duopoly than the competitive profits but less than the monopoly profits.

  • Equilibrium deadweight loss in duopoly

    Thank you for using BrainMass. Equilibrium deadweight loss in Cournot duopoly given demand and cost functions

  • duopoly decisions of production

    The profits for each firm will be =18*4.5-4.5*4.5-4.5*4.5 - 0.5*4.5*4.5=30.375 Thank you for using Brainmass. This solution helps produce the reaction curve mathematically.

  • Equilibium Output in a Cournot Duopoly

    We also have a marginal cost of 4 given by differentiating the cost function. Inserting this value and the value for B into the equilibrium output equation will give us output for each firm.

  • Cournot Duopoly: Determining Equilibrium Price and Quantity

    Solution describes the steps to determine equilibrium price and quantity of two identical firms in the case of cournot duopoly.

  • Stackelberg Duopoly

    321631 Managerial Economics; Stackelberg Duopoly 11. The inverse demand curve for a Stackelberg duopoly is . The leader's cost structure is . The follower's cost structure is . a. Determine the reaction function for the follower. b.

  • Cournot Equilibrium, Monopoly, Duopoly

    216970 Cournot Equilibrium, Monopoly, Duopoly Let there be 3 identical firms in an indusrty. The inverse demand curve is given by P=1-Q where Q= q1+q2+q3. The marginal cost for each is zero. a) Compute the Cournot equilibrium.

  • Nash Equilibrium

    335826 Simple model of duopoly In a simple model of duopoly, two firms produce the same good, for which each firm charges either a low or a high price. Each firm wants to achieve the highest profits.

  • profits and payoffs

    177514 profits and payoffs for Air 'R' Us Please see attached. Untied and Air 'R' Us are the only two airlines operating flights between Collegeville and Bigtown. That is, they operate in a duopoly.

View More Related Solutions