# Cournot Oligopoly

Cournot Oligopoly

. Two firms compete on the quantity they produce of good a single comÂ¬modity. They face a demand function

p= f(x)

where p is the price at which they will sell the good, which depends on the total quantity produced, x= x1 + x2 (x1 is the quantity produced by firm i = 1, 2). Let the demand be linear:

p = Î² - Î³(x1+ x2)

The production cost for firm i is

C (xi) = -Î± (xi) ^2

and its revenues are

pxi

. Problem Set:

- Write the maximization problem of each firm (maximizing profÂ¬its, revenues minus costs), its best reply function and the Nash equilibrium quantities x1 and x2

- Write the problem of a single monopolist firm, that is, a firm choosing x1 + x2 and facing the same demand, cost and revenue functions.

- Is total quantity x1 + x2 larger or smaller in the monopolist case?

And total profits?

https://brainmass.com/economics/oligopoly/cournot-oligopoly-29839

#### Solution Preview

Cournot Oligopoly

Two firms compete on the quantity they produce of good a single comÂ¬modity. They face a demand function

p= f(x)

where p is the price at which they will sell the good, which depends on the total quantity produced, x= x1 + x2 (x1 is the quantity produced by firm i = 1, 2). Let the demand be linear:

p = Î² - Î³(x1+ x2)

The production cost for firm i is

C (xi) = -Î± (xi) ^2

and its revenues are

pxi

. Problem Set:

- Write the maximization problem of each firm (maximizing profÂ¬its, revenues minus costs), its best reply function ...

#### Solution Summary

Cournot Oligopoly is demonstrated.