Menger The Equimarginal Principle

Carl Menger, The Equimarginal Principle

Although Menger was preceded by Gossen, he presented one of the first clear dis­cussions of the equimarginal principle of welfare maximization. He first emphasized that satisfactions have different degrees of importance to people:
The maintenance of life depends neither on having a comfortable bed nor on having a chess­board, but the use of these goods contributes, and certainly in very different degrees, to the in­crease of our well-being. Hence there can also be no doubt that, when men have a choice be­tween doing without a comfortable bed or doing without a chessboard, they will forgo the latter much more readily than the former (Principles, p. 123).

This is the subjective factor in an economizing individual's valuation process, i.e., the extent to which different satisfactions have different degrees of importance. Menger also emphasized that within the same class of goods, satisfactions may vary in importance. The point is that people try to satisfy the more urgent needs before the less urgent, but they will combine the more complete satisfaction of more press­ing wants with the lesser satisfaction of less pressing wants.

Menger illustrated his theory with the use of numbers, shown in Table 1. The Roman numerals depict ten classes of wants, with want III less urgent than want II, want IV less urgent than want III, and so on. Menger assumed that an individual is able to rank satisfactions and to assign number indices to them (cardinal ranking). Thus the individual can say that consumption of the first unit of commodity I (food) yields 10 units of satisfaction, while the first unit of commodity V (say, tobacco) gives but 6. Further, satisfactions from consuming, say, goods IV and VII (or any other two goods) are independent. Some other resource (other than goods I to X) is being used, moreover, to obtain units of these ten goods, and additional unit amounts of each commodity may be obtained with an equal expenditure of the resource (for con­venience, we call this other resource "money," and we assume that the unit price of all goods is $1).

An economizing person, according to Menger, would behave in the following manner. If the individual possessed scarce means in the amount of $3 and spent it all on the commodity of highest importance (I), he or she would obtain 27 units of satisfaction. The individual would, however, seek to combine satisfactions obtained from commodities I and II. Buying 2 units of commodity I and 1 unit of commod­ity II, the individual would obtain 28 units of satisfaction. With, say, $15 at his or her command, the individual would allocate expenditures so that, at the margin, the satisfaction obtainable from commodities I through V would just equal 6, as can eas­ily be verified from Table 1. Thus Menger established an equimarginal princi­ple. That is, given scarce means (dollars, in our example), the individual will arrange his or her various consumptions so that at the margin, satisfactions are equal. In doing so, Menger's economizing individual, like that of Jevons, maximizes total satisfac­tion.

Menger, in rather Germanic prose, described an objective, concrete factor in the valuation process:

Accordingly, in every concrete case, of all the satisfactions secured by means of the whole quan­tity of a good at the disposal of an economizing individual, only those that have the least im­portance to him are dependent on the availability of a given portion of the whole quantity. Hence the value to this person of any portion of the whole available quantity of the good is equal to the importance to him of the satisfactions of least importance among those assured by the whole quantity and achieved with an equal portion (Principles, p. 132).


Thus it is the least urgent satisfaction obtainable from a given stock of goods that gives value to that good. For example, imagine a given quantity of water available to an individual. He or she puts the available stock to many uses, from the most ur­gent (maintaining life) to the least (watering his or her flower garden). The deter­mination of the value of any portion of water is in this case objective—it is in its least important use, gardening. Any given portion of the good could stand for any other portion, of course.

In extending value theory, Menger also considered the impact of differences in the quality of goods on their value. Like Jevons, moreover, he presented a theory of exchange and its limits, concluding that under certain cases, "If command of a cer­tain amount of A's goods were transferred to B and if command of a certain amount of B's goods were transferred to A, the needs of both economizing individuals could be better satisfied than would be the case in the absence of this reciprocal transfer" (Principles, pp. 177-178). His examples of isolated exchange are copious, eschew mathematical expression, and are often cumbersome. In addition, Menger analyzed the effects of competitive and monopoly structures upon price. Like Jevons, but un­like Dupuit, he did not relate utility (satisfactions, in Menger's terms) to the demand curve. Thus, along with Jevons, he ignored consumers' surplus. Yet a survey of Menger's overall contributions to utility and value theory reveals a contribution of clear originality in breadth and in choice of exposition. It remains to take a brief look at Menger's important development of the concept of imputation.

Imputation and Factor Values

One of Menger's most interesting and important contributions relates to his attempt to value higher-order goods (productive resources). Opportunity cost is clearly un­derstood in relation to the value of final goods to Menger's economizing individual. The value of a particular good to an individual is equal, in Menger's words, "to the importance he attaches to the satisfactions he would have to forgo if he did not have command of it." But Menger applied an opportunity cost concept to the valuation of higher-order goods as well. Menger's valuation experiments are best understood by means of a simple example.

Suppose a given amount of labor (a), capital (b), and land (c) combine to produce some output (x). Upon what does the value of any unit of productive resources— say, a unit of labor—depend? The value of a unit of labor is determined by the net loss of satisfaction resulting from the reduction in final output attributable to the unit of labor. The reduction in output depends, of course, on the degree to which the pro­ductive resources are substitutable. Productive relations may generally be of two sorts: (1) variable proportions, in which the proportions of different higher-order goods can be altered to produce a given output, and (2) fixed proportions, in which a fixed amount of one resource must be combined with a fixed amount of another resource to produce a given output. An example of the former might be the ability to alter proportions of fertilizer and land to produce a given amount of agricultural output. Fixed-proportion relations might be typified by the necessary proportions of hydrogen and oxygen to produce water. Menger clearly understood the importance of both types of productive relations and their significance for the valuation of higher-order goods, and, unlike Wieser and Bohm-Bawerk, he emphasized the very wide range within which proportions could be varied.

Returning to our example, how would Menger evaluate a unit of labor? He gives explicit directions:
Assuming in each instance that all available goods of higher order are employed in the most eco­nomic fashion, the value of a concrete quantity of a good of higher order is equal to the difference in importance between the satisfactions that can be attained when we have command of the given quantity of the good of higher order whose value we wish to determine and the satisfactions that would be attained if we did not have this quantity at our command (Principles, pp. 164-165).

In the case of variable proportions, the reduction in a unit of labor a would mean that the output of x (x°) would be reduced, say, to some x1. The remaining labor, capital, and land still produce x. The value of the unit of labor would then be the difference in total satisfaction when x1 was produced and when x1 was produced (or x° - x'). Menger's theory might be characterized as a marginal-value-productivity theory of input valuation.

If productive relations are arranged in rigidly fixed proportions, on the other hand, the reduction of a unit of labor would mean that no x would be produced. Would the value of a unit of labor (or of any of the other inputs), then, be the whole output of x? Assuming that resources are originally combined to produce goods for a max­imum of satisfaction, a recombination of the remaining labor, capital, and land could produce a different good—say, y—but it would result in lower total satisfaction. Thus Menger reasoned that the value of a unit of labor would be the difference between total satisfaction when the unit was used to produce x (x°) and total satisfaction when all resources but that unit were used to produce some other good, y. Unfortunately, it is difficult to develop a concept of marginal productivity under such circum­stances, and Wieser and Bohm-Bawerk all but ignored Menger's insistence on the applicability of variable proportions. Wieser, however, significantly enriched cer­tain of Menger's ideas on value and on the valuation of higher-order goods. It is to these developments that we now turn.