Dupuit was the first economist to present a cogent discussion of the concept of marginal utility and to relate it to a demand curve. Fully utilizing his powers of observation and abstraction, Dupuit was able to show, as early as 1844, that the utility that an individual (and a collection of individuals) obtains from a homogeneous stock of goods is determined by the use to which the last units of the stock are put. In doing so, he clearly pointed out that the marginal utility of a stock of some particular good diminishes with increases in quantity. From observation Dupuit established that each consumer "attaches a different utility to the same object according to the quantity he can consume." He illustrated his point with a practical example of a technological improvement in water distribution to a town (in his essay "On Utility and Its Measure"):
Water is distributed in a city which, situated on a height, could procure it only with great pains. There was then such a value that the hectoliter per day was 50 francs by annual subscription. It is quite clear that every hectoliter of water consumed in these circumstances has a utility of at least 50 francs.
Dupuit suggested that each unit of a given quantity of water will have a different utility. But why should each increment of the same commodity possess a different utility? Dupuit continued his argument, supposing that as a result of the installation of pumps, costs of production for water drop by 20 francs:
What happens? First, the inhabitant who consumed a hectoliter will continue to do so and will realize a benefit of 20 francs on his first hectoliter; but it is highly probable that this lower price will encourage him to increase his consumption; instead of using it parsimoniously for his personal use, he will use it for needs less pressing, less essential, the satisfaction of which is worth more than 30 francs, since this sacrifice is necessary to obtain water, but is worth less than 50, since at this price he relinquished this consumption ("On Utility and Its Measure").
Each increment of the same commodity carries a different utility because additional units will allow "less pressing, less essential" needs to be met. The additional utility derived from additional units of the same commodity must decline.
Extending the example, Dupuit supposed that when the price fell to 20 francs, the individual would demand 4 hectoliters "to be able to wash his house every day; give them to him at 10 francs, he will ask for 10 to be able to water his garden; at 5 frs. he will ask for 20 to supply a water font; at 1 franc he would want 100 to have a continuous flow," and so on. It is the least pressing need for a commodity, not the most pressing need, that defines the exchange value of the entire stock of goods. Dupuit's argument can be conveniently summarized as in Figure 1.
Assume that the consumer is originally in equilibrium when the price of water is at p1 and the quantity taken is q1. Now assume with Dupuit that the price of water falls to p2. At the lower price for water the individual is in disequilibrium at point c. The marginal utility of the last unit of the consumer's existing stock is greater than the now-lower marginal utility of water represented by the lower price. In terms of price, what the consumer would pay for q1 of water is greater than the price he or she must pay for quantity q1 The same quantity of water (q1) could be bought at a lower total expenditure, but Dupuit assumed that the consumer would not do this. Attached to each incremental unit of water between quantity q1 and quantity q1 is a marginal satisfaction greater (albeit diminishing) than that which would obtain for the incremental unit corresponding to price p2. Thus in an effort to maximize total satisfaction, the individual will increase purchases of water up to, but not beyond, quantity q2 As suggested by the labeling of the vertical axis (marginal utility = price) of Figure 1, the marginal-utility curve is Dupuit's demand curve (courbe de consummation), and although most of his examples are concerned with transportation and communication, he considered the same laws to apply to all goods and services. He provided explicit directions in his article entitled "Tolls," which appeared in the 1852-1853 French Dictionary of Political Economy, on the manner in which a demand curve should be constructed:
Dupuit constructed such a demand curve in 1844, six years after Cournot's Researches was published, in a paper entitled "On the Measurement of the Utility of Public Works."
Like Cournot, Dupuit gave the equation for the curve of consumption as y =f(x) or, alternatively, Qd =f(p). Additionally, Dupuit (as Leon Walras and other economists were to do later) placed the independent variable, price, on the x axis and the dependent variable, quantity, on the y axis. Modern microeconomic diagrams, following Alfred Marshall's practice, reverse this procedure because Marshall treated marginal-demand price as a function of quantity. Dupuit's construction is reproduced as Figure 2.
Dupuit described his construction as follows:
It is obvious that this curve is identical in conception to that of Figure 1; that is, Dupuit's demand curve is a marginal-utility curve. Dupuit made his meaning clear, with reference to Figure 2, by stating that "The utility of.. . np articles is at least Op and ... for almost all of them the utility is greater than Op."
The relation that Dupuit posited between price, marginal utility, and quantity was, he thought, a "fact of experience" that "has been verified statistically." It was, in addition, a theory of powerful originality, for in linking the demand curve with utility it established a new approach to economic inquiry—welfare economics. Specifically, Dupuit agreed that the total area under the demand curve of Figure 2 (area OPN) represents the total utility produced by the commodity. At some price—say, Op"—there is some amount that consumers would be willing to pay for the commodity over and above what they must pay. The amount that they must pay is represented by area Op'n'r" in Figure 2, and it represents the firm's receipts (ignore for the present the other price-output combinations). In the case of zero costs (that described in Figure 2) areas Op"n"r" may be called "producers' surplus" or "producers' rents." The amount that consumers would be willing to pay over and above what they must pay is area p~n"P. In Dupuit's terms this is "utility remaining to consumers," and in modern terms it is called "consumers' surplus." Dupuit's numerical examples (see the following section) of these concepts will illustrate their importance and will at the same time demonstrate Dupuit's advances in monopoly and price discrimination.