Dupuit Consumers Surplus Monopoly

Jules Dupuit Consumers' Surplus, Monopoly, and Discrimination

In the course of his economic writings, Dupuit was led to investigate some of the factors that give rise to monopoly pricing. Conditions existing in the French railroad companies were of particular interest to him, and as scores of later economists were to show, he pointed out that "the interest of ordinary capitals is regulated by the law of supply and demand . . . while the means of transportation are monopolies." Thus, generally speaking, "ways of communication," or forms of transportation, are shel­tered from competition.

He illustrated the point by a comparison between the economic principles that determine house rents and those affecting transport rates. Exorbitant rents for lodging, according to Dupuit, could not exist for very long, since "If it was known that house rental yields a revenue superior to the rental of other capitals, speculation would focus very quickly on the construction of houses and equilibrium would be established." Thus the entry and exit process prohibits monopoly rents over the long run in houses, but as Dupuit indicated, this freedom to enter the railroad industry is inhibited by certain factors indigenous to that industry. Enormous amounts of capital, in the first instance, restrict the possibility of entry to a limited number of persons. Also, be­cause of the uniqueness of the first enterprise, a "new one can survive only at the ex­pense of the first and ... the profit which is sufficient for one is not sufficient for two."

The analytical contribution to monopoly theory emerged when Dupuit addressed himself to the principles on which the simple monopolist, as constituted above, be­haves. He uncovered the rule of monopoly profit maximization in the course of his discussion of the effects on utility of tolls and transport charges. Table 1, repro­duced from an 1849 article, is useful in illustrating Dupuit's early conception of this well-known principle.

The data in Table 1 refer to a tariff or rate that a monopoly railroad may charge for passage. Here Dupuit was considering the case of an unregulated mo­nopolist free to charge a rate that would maximize profits. His monopolist was a profit maximizer, for "If the road or bridge or canal is private property, the owner com­pany has only one aim, and that is to get the largest possible income from the toll." Thus the monopolist facing the demand schedule of Table1 with no costs of pro­duction would charge a rate of 5 francs in order to maximize profits or gross receipts. The example was then extended to the monopolist with costs of production when Dupuit supposed that the "cost of traction" could be represented by 2 francs per unit of passage. These traction costs may be identified with variable costs, and in this case, as Dupuit correctly pointed out:


Dupuit correctly stated the principle of profit maximization in terms of net revenue and pointed out that if the level of traction costs increased, the profit-maximizing tariff would increase and output would decrease. The net receipts, additionally, are net only of variable expenses. Fixed costs, such as "certain administrative expenses, interest on construction expenditures, etc.," must also be covered in the long run. Con­sequently, Dupuit's net receipts are not long-run profits, as are his gross receipts (without costs of production). Dupuit, referring to what is our Table 1, said that "If fixed costs were more than 104 [francs] and it were possible to charge only one uniform rate, the railroad would be a losing proposition with any tariff."

In addition to an analysis of profit maximization, Dupuit's early treatment of mo­nopoly contained another important analytical tool, which was later used by Alfred Marshall. Specifically, both investigations posited a relation between monopoly rev­enue and consumers' surplus, given, of course, the constancy of the marginal utility of money. Making an implicit identification of the demand curve with a utility func­tion, Dupuit supplied a utility calculation for his railroad example. In this case the price that maximized net revenue would be a tariff of 6 francs, and the total utility (consumers' surplus, producers' surplus, and costs) pro­duced by this tariff would be 234 francs.

According to Dupuit, total utility always breaks down into three parts: lost util­ity, producers' surplus, and consumers' surplus. At the 6-franc tariff the total utility of 234 francs divides as follows. The lost utility equals 52 francs, the total variable costs of carriage (fixed costs are assumed nonexistent). The producers' surplus is identical to the net receipts of 104 francs. The consumers' surplus is the residual of 78 francs. The sum of the three parts equals 234, the total utility associated with 26 passengers (from Table 1).

If we momentarily depart from Dupuit's presentation and assume that the fixed cost is exactly 104, then monopoly revenue disappears. In the short run the 104 francs accruing to the owner of the railway is of the nature of an economic rent (i.e., pro­ducers' surplus) on fixed investment, but as Dupuit succinctly pointed out, these fixed costs must ultimately be met by the monopolist. Thus, under the assumption that the fixed costs are 104 francs there would be no monopoly revenue. A consumers' sur­plus is produced, however, in the amount of 78 francs.