Solution
Cournot Duopoly
Show the problem again
Two firms simultaneously choose quantities q₁ and q₂ of an identical good. The market price is P = 120 − (q₁ + q₂) and production is costless. What quantity does each firm produce in the Nash equilibrium?
Worked solution
Each firm produces 40. Firm 1 maximizes q₁(120 − q₁ − q₂), giving best response q₁ = (120 − q₂)/2. By symmetry q₁ = q₂ = q, so q = (120 − q)/2, yielding q = 40. Total output 80 gives P = 40 and profit 1600 each, more output and lower price than monopoly (60 at P = 60), but less competitive than the efficient outcome.
Source: Antoine Augustin Cournot, 'Recherches sur les principes mathematiques de la theorie des richesses' (1838). Statement written for AxiomIQ.