Cournot Monopoly Model Cournot Profit

Cournot's Micro Models, Cournot Monopoly Model

Cournot turned this method into the creation of numerous models of firm behavior based upon the demand curve. We shall consider two of these models: (1) the mo­nopoly model and (2) the duopoly (two producers) model. Cournot's major contri­butions may then be evaluated.

Cournot turned to an analysis of profit maximization by a proprietor of a mineral spring that has just been found to possess salubrious qualities known to no other. Sale of a single liter of the water might fetch as much as 100 francs, but, as Cournot demonstrated, the monopolist will not charge the highest price he could get for the water. Rather, he will adjust his price so as to maximize net receipts. Cournot demonstrated mathematically that, in the case of zero costs, the monopolist would maximize gross receipts. Assuming a demand function D = F(p) and also assuming the demand curve is always negatively sloped (i.e., dD/dp < n =" TR-" mr =" MC">
Figure 1
Cournot's monopoly model of a mineral-springs proprietor burdened with posi­tive costs of production clearly uncovered the "marginal principle," which is the cen­tral organizing principle of economic theory. To put the problem in the form of a ques­tion, when the monopolist faces costs of production, what price would he charge and what quantity would he sell to maximize profits? Cournot solved the problem in a straightforward fashion. Assuming that (D) was equal to the cost of making a num­ber of liters equal to D, Cournot's profit equation becomes k = pF(p) - (D.) Profit maximization requires that the slope of the profit function equal zero—or, in Cournot's notation, that D + dD/dp [p - d{ (D)]ldD} = 0. In plainer language, profit maxi­mization takes place where MR - MC = 0. As Cournot put it, "Whatever may be the abundance of the source of production, the producer will always stop when the in­crease in expense exceeds the increase in receipts" {Mathematical Principles, p. 59).
In reference to Figure , Cournot established that profits are at a maximum where MR = MC. Output produced will be Qc, and price will be Pc; further, Qc will be lower and Pc will be higher than in the case of zero costs. Alternatively, Cournot's monopoly theory might be interpreted as in Figure , which reproduces the total cost, total revenue, and profit function relevant to the mineral-springs proprietor. The proprietor will cease production at Qc in Figure , where the profit function ji, is at a maximum (Cournot included a second condition—that the slope of the profit function be zero at Qc and, further, that profits decline with either increases or de­creases in quantity). Note that the mineral spring is not operated to maximize gross returns at Qn but to maximize net returns at Qc. The geometrically inclined reader will determine that at Qc, the slope of the TC function is equal to the slope of the TR function, or MC = MR, as in Figure . Cournot's development of the theory of monopoly would, in short, compare most favorably with that of any modern text­book writer, for it is precisely Cournot's theory that modern writers on monopoly are explicating.