William Stanley Jevons Marjinal Utility

William Stanley Jevons Marginal Utility

Marginal Utility Following Bentham's lead, Jevons main­tained that the value of pleasure and pain varies according to four circumstances: (1) intensity, (2) duration, (3) certainty or uncertainty, and (4) nearness or remoteness. Jevons discussed each of these at length. Pain is simply the negative of pleasure, and in individual calculations the algebraic sum (i.e., net pleasure) is the meaningful quan­tity. Like Bentham before him, Jevons injected a probabilistic element into economic analysis when he discussed the ways in which the uncertainty of future events and future "anticipated feelings" affect behavior. In one especially telling passage, Jevons suggested how time preference and anticipation permeate economic quantities:

The cares of the moment are but ripples on the tide of achievement and hope. We may safely call that man happy who, however lowly his position and limited his possessions, can always hope for more than he has, and can feel that every moment of exertion tends to realize his as­pirations. He, on the contrary, who seizes the enjoyment of the passing moment without regard to coming times, must discover sooner or later that his stock of pleasure is on the wane, and that even hope begins to fail (Theory, p. 35).

This all-important element was nevertheless omitted from Jevons's theory of utility.
Jevons asserted that maximizing pleasure is the object of economics, or, in his own words, humans seek to procure the "greatest amount of what is desirable at the expense of the least that is undesirable." However, it is necessary to make this propo­sition more objective by attaching it to something more concrete, such as commodi­ties.

Jevons defined a commodity as an "object, substance, action, or service which can afford pleasure or ward off pain," and he denoted the "abstract quality whereby an object serves our purposes, and becomes entitled to rank as a commodity." Es­chewing any pretensions of direct measurability, Jevons claimed that behavior would reveal utility and preferences and that the investigator would not make value judg­ments. As he clearly noted, "Anything which an individual is found to desire and to labour for must be assumed to possess for him utility." Thus flagpole sitters, astronauts, kamikaze pilots, heroin addicts, and suicides might simply be regarded as max­imizing utility (under certain constraints, of course).

Jevons's formal analysis of utility relates commodities, as defined above, to util­ity. His theory of marginal utility is basically simple and straightforward. It may be explained and illustrated with the aid of the elementary arithmetic and graphs used by Jevons himself. Unlike any of his predecessors, Jevons clearly specified that a utility function is a relation between the commodities an individual con­sumes and an act of individual valuation. Utility is not, in sum, an intrinsic or in­herent quality that things possess. Instead, utility has meaning only in the act of valuation.

Jevons's vast improvements over Bentham's performance consist in the follow­ing features of his formal utility analysis: (1) his clear distinction between total util­ity and marginal utility, (2) his discussion of the nature of marginal utility, and (3) his establishment of the equimarginal principle, as it relates to alternative uses of the same commodity and to choices between commodities. Jevons unlocked Adam Smith's water-diamond paradox in distinguishing between total utility and what Jevons called the "degree of utility." The latter may be regarded as the same as mar­ginal utility. Both total and marginal utilities were related to the quantities of goods possessed, and only to those quantities.
Graphical Analysis Using a simple algebraic notation, Jevons's utility func­tion is expressed as U =f{X), to be read as "the utility of commodity X (food) is a function of the quantity of X the individual holds." It should be noted that all other goods are left out of the picture; i.e., it may be assumed either that they are nonex­istent or that their quantities are held constant. Assuming that one could add tiny por­tions of food to the individual's store—that is, "continuously," in the language of arithmetic—one might derive a utility function as depicted in Figure 1a. Here the total utility of food (the quantities of other things held constant) may be seen to rise as quantities are added up to X0, reach a maximum at that point, and then decline. But the utility of an additional unit of food, which Jevons called the "degree of util­ity," declines as units of food are added to the individual's consumption. Arith­metically, Jevons wrote du/dx, to be read as "the ratio of a small change in utility to a small change in X (food)." Figure 1b, which is derived from Figure 1a, demonstrates this idea. Further, he assumed that the marginal utility (used synony­mously with "degree of utility") of food was declining after the very first unit taken, although he was undoubtedly aware that this might not always be the case. Jevons's law may then be stated as follows: The degree of utility for a single commodity varies with the quantity possessed of that commodity and ultimately decreases as the quan­tity of that single commodity increases.

The Equimarginal Principle Jevons presented a clear understanding of the in­dividual's maximizing behavior in discussing a person's allocation of any given com­modity among alternative uses. If an individual starts with a fixed stock S of a com­modity X and the uses of that commodity are represented by x and y, then the stock must be divided up between those uses such that S - x + y. Now Jevons, in effect, asks the question: How does an individual decide how to allocate his fixed stock among the two uses? The answer is simple and intuitively reasonable. The quantity of X should be allocated to the two uses so that the increase in utility from adding an additional unit of X in use x just equals the increase in utility from adding an ad­ditional unit of X in use y. In Jevonian terms, the equimarginal condition implies that where MUX stands for the degree of utility of commodity X in use x, and similarly for y.

du / dx = du / dy or Mx = Muy

The equimarginal principle, first clearly explained by Jevons, also holds for the allocation of scarce, fixed means (say, income) among all goods in the individual consumer's budget. If x represents number of beers and z represents packs of ciga­rettes, then the consumer will allocate scarce income y such that the MUX = MUz, as­suming that beers and cigarettes are the same price and that all y is expended on these two goods. A more general formulation of the equimarginal principle, one that does not appear in Jevons but that accounts for different prices of n goods, is the one fa­miliar to every student of basic economics:

MUx / Px = MUz / Pz =MUn / Pn

Further, in order to ensure that all income is allocated among the individual's con­sumptions (which could include a savings account), an additional condition is ex­pressed:

PxX + PzZ+-- + PnN=Y

where PxX represents the individual's expenditure on X, PZZ represents the expen­diture on Z, etc. The sum of all these expenditures equals income Y. Although Jevons did not work out the details, his argument underlies the whole development of the theory of individual maximization behavior, which is at the core of contemporary theory.