From Duopoly to “Infinite” Competition
The analysis of duopoly is generalized: the number of firms in a market is increased and costs of production are introduced. Supposing n firms, let φi(Di) be the cost of production of firm i.
Its profitpDi - φi(Di) is at a maximum when Di + pf(p) - φi'(Di)f'(p) = 0. Cournot shows that, in these circumstances, the price is lower than in monopoly conditions, in spite of a greater marginal cost.The “infinite” competition is a limit, when Di is negligible for all i, with respect to the total production f (p) and to its derivative f '(p) “so that the partial production Di could be deleted [from the total production] without any appreciable change in the price of the good” (Cournot 1838 [1980]: 69). In such a case the price equals the marginal cost. It is thus possible to consider the supply of each firm as a function of the price and, in addition, obtain a total supply which is necessarily an increasing function of price. The equilibrium price is determined by supply and demand.