Cournot Oligopoly:
Task: Two firms compete on the quantity they produce of good a single commodity. 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:
1) Write the maximization problem of each firm (maximizing profits, revenues minus costs), its best reply function and the Nash equilibrium quantities x1 and x2
2) Write the problem of a single monopolist firm, that is, a firm choosing x1 + x2 and facing the same demand, cost and revenue functions.
3) Is total quantity x1 + x2 larger or smaller in the monopolist case? And total profits?