Cournot and Duopoly Model

Cournot and Duopoly, Cournot Duopoly Model

Antoine Augustin Cournot (1801-1877), French mathematician and philosopher, in 1838 made the assumption of monopoly his starting point, and stated the law of demand in the form of a price-determined equation, D = F(p) — quantity demanded is a function of price. He argued that the maximum total value is obtained by multiply­ing quantity demanded by price. Beginning with the theory of price for a single monopolistic firm, he introduced (in lieu of a less perfect condition of monopoly) another monopolistic firm — the case of "duopoly," and attempted a determinate solution, concluding that the price would be lowered and lie between the monopoly price and the price under pure competition. Finally, he considered the case of joint demand for copper and zinc (to produce brass), assuming no other use for the two raw materials and each to be supplied by a monopoly, concluding that the price would be higher (as a result of increased unit costs), but hardly determinate. Cournot's mathematical studies led him to assume that diminishing unit costs make perfect competition impossible, and lead to monopoly in an industry. Cost he treats as money expense, with no allowance for disutility cost or for profit.

Little attention was paid to Cournot's approach at the time. His reasoning was criticized by Bertrand in 1883. Alfred Mar­shall refers to it critically in the first edition of his Principles, 1890. And Pareto and Edgeworth discuss it in 1896 and 1897. The general idea in this discussion was that Cournot had not sufficiently considered various possible assumptions, and that with two monopolies as sellers, the price would be unstable, possibly falling to zero if the supply could be increased indefinitely.