Monopoly
When the cost of production is nil or when it only consists in overhead costs, the profit is maximal when the final revenue pf(p) is at a maximum. As f is a continuous function, the total revenue is a continuous function of price.
It is increasing or decreasing as the elasticity of demand - Cournot introduces the notion, if not the phrase - is smaller or greater than 1. When it is a maximum, the marginal revenue f (p) + pf(p) is nil. Cournot shows that there exists at least one maximum but that it is mathematically possible to have more than one solution - he discards however this possibility because he is convinced that “in real facts, and taking into account all the conditions of an economic system, there is no good, the price of which is not fully determined” ([1838] 1980: 82). A good model must only entail one solution.If the total cost is a function φ(p) of the quantity produced, the profitpf (p) - φ[f (p)] is a maximum when f (p) + pf(p) - φ'f'(p) = 0, that is, when marginal revenue equals marginal cost. Cournot contrasts manufactures on the one hand and agriculture and mining on the other, and many followed him in this. While in the former, marginal costs are taken to be decreasing - at least as long as the increase in production does not increase the prices of raw materials and wages - in agriculture and mining where marginal costs are taken to be increasing. The logical conclusion is that “powerful capitalists or great companies can... artificially constitute monopolies, with profits superior to the usual rate of profits” (Cournot, 1863 [1981]: 79). However, Cournot does not judge this evolution negatively. To be sure, the monopoly price is higher than the competitive price, but the consumer benefits from lower prices due to a decrease in costs.
Cournot then studies the effects of the introduction of a tax. If the tax is based on the net revenue of the monopoly, it affects neither the price of the good nor the quantity produced. Its only consequence is to lower the rent of the monopolist. If the tax is based on each unit produced, it increases the price and diminishes production. The producer’s loss is the reduction of his or her net income and is greater than the product of the tax. An idea advanced by Quesnay is thus met again: it is better to tax the net revenue than the products. However, what is the consumers’ loss? Cournot calculates the additional expense that the consumers, who still buy the good in spite of its higher price, have to meet. He abstracts from the loss experienced by the consumers who stop buying the good: “this kind of damage cannot be evaluated” (1838 [1980]: 103). Cournot deliberately closes a door that Dupuit was to open later to measure the consumer’s surplus.