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# Cournot Oligopoly

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Cournot Oligopoly

. Two firms compete on the quantity they produce of good a single com¬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 = β - γ(x1+ x2)

The production cost for firm i is
C (xi) = -α (xi) ^2
and its revenues are
pxi

. Problem Set:

- Write the maximization problem of each firm (maximizing prof¬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?

##### Solution Summary

Cournot Oligopoly is demonstrated.

##### Solution Preview

Cournot Oligopoly

Two firms compete on the quantity they produce of good a single com¬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 = β - γ(x1+ x2)

The production cost for firm i is
C (xi) = -α (xi) ^2
and its revenues are
pxi

. Problem Set:

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

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