Dupuit's Graphics

Discrimination: Dupuit's Graphics

Dupuit also expressed these ideas graphically. In Figure 1, suppose OM is the profit-maximizing price. The utility produced by the commodity or service depicted by the demand curve of Figure 1 would be distributed in the following manner: the monopoly revenue would equal the area OMTR; the consumers' surplus (or the utility remaining to consumers, in Dupuit's terminology) would equal area TMP; fi­nally, the lost utility, utilite perdue, would equal the triangle RTN.


Under conditions of competition this lost utility would result from scarcity of re­sources. However, since Dupuit assumed zero costs of production, lost utility in his example can only be attributable to restrictions of output under monopoly. The sig­nificance of Dupuit's theory of price discrimination is that he showed how economic welfare could be increased (i.e., lost utility could be reduced) by differential pric­ing.

Thus if the monopolist faced with the demand curve of Figure 1 was able to in­crease the total quantity sold to Or via discrimination, the total utility (the sum of consumers' surplus and monopoly revenue in the no-cost case) would equal the area OPnr, which is greater than OPTR by RTnr. The increase in monopoly receipts would clearly depend on the number of submarkets that the monopolist would be able to establish and invade. As Dupuit correctly pointed out:

Monopoly profits under discrimination (assuming no costs) have increased consid­erably over those that result from the simple monopoly price OM. Specifically, prof­its have been augmented by Mp'n'q' + Rqnr, and it is important to note that they could have been increased without increasing output above that established under the simple monopoly output OR. In other words, price discrimination could affect the distribution of welfare without affecting the total utility produced. But Dupuit believed that discrimination was desirable only if it increased quantity over that ob­tained under a single-price, simple monopoly system, for only in that event would utilite perdue be reduced.

With respect to Figure 1, Dupuit knew that output would increase if only one of the markets could be served at the simple monopoly price but more than one could be served with price discrimination. The market in which price Op' is charged would have been served in any event, given the simple monopoly profit-maximizing price OM. But the relatively weaker market delineated by price Rq would not have been entered at the simple monopoly price OM. Dupuit's implicit suggestion that output would increase (by Rr) if discrimination allowed the monopolist to enter markets not entered at the simple monopoly price was only much later given scientific treat­ment by A. C. Pigou and Joan Robinson. Yet it is certainly clear that Dupuit, as early as 1844, was at the threshold of output analysis under dis­crimination, which finally yielded to Robinson's expert treatment almost a century later.