Complete this in about one hour!
Jevons demonstrated that consumers’ demand behavior could be derived from consumer’s utility maximization. In a context of two commodities (X and Y), give a simple and brief proof that a utility-maximizing consumer would exchange the two commodities up to the point where the relative ratio of marginal utility between the two commodities exactly equals their relative price ratio (no numerical calculation is required, just explain the logic and reasoning).
Jevons’s Theory of Marginal Utility and Exchange
William Stanley Jevons (1835–1882) wrote on a wide variety of topics, ranging from meteorology to logic to economic theory. His Theory of Political Economy was his most important work in the last field. In 1860, in a letter to his brother, he wrote: “in the last few months I have fortunately struck out what I have no doubt is the true Theory of Economy, so thorough-going and consistent that I cannot read other books on the subject without indignation.”4 This “true theory” was finally published in 1871.
In the preface to the Theory, Jevons stated that “Bentham’s ideas … are … the starting point of the theory given in this work.”5 He had no doubt that utilitarianism was the only possible foundation for scientific economic theory: “In this work I have attempted to treat economy as a calculus of pleasure and pain, and have sketched out … the form which the science … must ultimately take.”6 The ultimate truth, on the basis of which he had felt such indignation toward other theories, was “ that value depends entirely upon utility.”7
When Jevons used the term value, he always meant simply exchange value, or price. Whereas labor theorists, such as Marx, had defined value as the labor embodied in a commodity, Jevons contemptuously rejected such a definition:
A student of economics has no hope of ever being clear and correct in his ideas of the science if he thinks of value as at all a thing or an object, or even as anything which lies in a thing or object…. The word value, so far as it can be correctly used, merely expresses the circumstance of its exchanging in a certain ratio for some other substance.8
Thus, Jevons was interested only in prices. He avowedly and proudly restricted his economic analysis to the sphere of circulation, the market. As Marx had pointed out some years before, within the sphere of the market all people are essentially identical. When Jevons wrote of people, he assiduously avoided any real discussion of superordinate or subordinate social relations. People, in Jevons’s view, had only two characteristics that defined them as economic agents; moreover, every person had both of these characteristics. Hence, there was an abstract, implicit equality among all persons. The first characteristic was that they derived utility from consuming commodities: “Anything which an individual is found to desire … must be assumed to possess for him utility. In the science of economics we treat men not as they ought to be, but as they are.”9 The second characteristic was that every person was a rational, calculating maximizer. And rational, calculating, maximizing behavior was the only element of human action to be studied by economics: “To satisfy our wants to the utmost with the least effort—to procure the greatest amount of what is desirable at the expense of the least that is undesirable—in other words, to maximize pleasure, is the problem of economics.”10
People received utility from consuming commodities. The error of previous economists, Jevons believed, lay in their failure to distinguish between the total utility a person derived from the consumption of a given quantity of some commodity and the “final degree of utility” (or, what in later neoclassical terminology came to be called the “marginal utility”) that the person derived from consuming the last small increment of that commodity. Although it was often true that total utility might continue to become greater as one consumed an increased quantity of a commodity, the final “degree of utility … ultimately decreases as that quantity increases.”11 It was this “final degree of utility,” or marginal utility, that concerned Jevons. This principle of diminishing marginal utility was to become the cornerstone of the neoclassical restatement of utilitarianism.
By introducing the notion of marginalism into utilitarian economics, Jevons had found a way in which the utilitarian view of human beings as rational, calculating maximizers could be put into mathematical terms. If the total utility one received from consuming a commodity depended on the quantity consumed, then this could be written as a mathematical function, TU = f(Q), which simply says total utility (TU) has some concrete mathematical relationship to the quantity (Q) consumed. In calculus, the first derivative of a function tells one how much the dependent variable (in this case, total utility) changes as a consequence of an infinitesimally small change in the independent variable (in this case, the quantity consumed). The first derivative of the total utility function gives one the marginal utility at any particular quantity consumed. The logic of maximization could be easily formulated in terms of calculus. The total utility function was maximized when the quantity was increased to that point at which marginal utility was equal to zero. This was not very profound. It simply meant that to maximize one’s utility from consuming a particular commodity, one should consume the commodity (if there were no costs of consumption) until one was satiated, that is, until one could derive no more utility from another small increment of the commodity.
When consumption involved costs, those costs could be stated in mathematical form. For example, if one possessed a commodity y and could only get another commodity x by giving up some y in exchange, then one could compare the ratios of one’s marginal utilities for the two commodities, MUx/MUy and the prices of the two commodities, Px/Py. If MUx/MUy was higher than Px/Py, then our individual could gain utility by trading some of his y for some x. If the process continued until the individual had exhausted the gains from exchange, he or she would have traded to the point at which MUx/MUy = Px/Py. To put the same thing differently, the ratio MUx/Px would tell one how much additional utility one would get (or give up) if one purchased (or sold) an additional dollar’s worth of commodity x. The two individuals would, Jevons asserted, buy and sell the commodities until the marginal utilities of each commodity had changed to the point where MUx/Px = MUy/Py. At that point, the last dollar’s worth of either x or y yielded the same increment to the individual’s total utility. If for an individual the ratio MUx/Px was greater than MUy/Py, then that individual would sell y and buy x, thereby losing less utility for giving up a dollar’s worth of y than he or she gained from the additional dollar’s worth of x. But as he or she gave up y and gained x, the principle of diminishing marginal utility meant that MUy would increase and MUx would decrease until MUx/Px = MUy/Py. At that point, no further gains from exchange could be realized. The reverse but identical process would have occurred if MUy/Py had been greater than MUx/Px.
All prior utilitarian theorists had realized that in voluntary exchange, an individual bought or sold as long as what he or she purchased gave more utility than the utility lost in what he or she sold. This had always been the basis for advocating free exchange and for the belief that exchange harmonized everyone’s interests. Jevons’s only addition to the theory had been to give this principle a mathematical formulation and to make explicit the distinction between total utility and marginal utility.12 Thus Jevons’s major addition to the ideas of the previous utilitarian economists can be summed up in his own words: “The nature of wealth and value is explained by the consideration of indefinitely small amounts of pleasure and pain.”13 “I contend that all economic writers must be mathematical so far as they are scientific at all.”14
Jevons attempted to show how marginal utility determined prices. But in doing so he tried to show how two “trading bodies” could arrive at equilibrium prices for two commodities. But the theoretical problem as he set it up did not yield any determinate solution, and it was left to other neoclassical economists to demonstrate how the marginal-utility theory could become a theory of prices. Jevons simply demonstrated how consumers arranged their exchanges, once prices were known, in order to maximize their individual utilities.
Jevons did not, however, derive from the Benthamite notion of diminishing marginal utility the egalitarian conclusions of Bentham. In our critique of Thompson’s utilitarianism, we argued that interpersonal comparisons of the relative intensities of the utility of wealth or income were impossible because pleasure was a purely subjective, personal experience. From this we concluded that utilitarianism could ethically compare two social situations only when unanimity prevailed among all participants. This, we argued, gave utilitarianism its highly conservative bent. The situations before and after an exchange are among the few situations in any social setting where such unanimity prevailed. If both parties participated in the exchange voluntarily, then it could be assumed that both benefited. This seemingly trivial conclusion has always been the basis of the utilitarian belief in the natural harmony of market capitalism.
Unlike Bentham, Thompson, and Mill, Jevons clearly recognized (and appreciated) this limitation of utilitarianism:
The reader will find … that there is never, in any single instance, an attempt made to compare the amount of feeling in one mind with that in another. I see no means by which such comparison can be accomplished. The susceptibility of one mind may, for what we know, be a thousand times greater than that of another…. Every mind is thus inscrutable to every other mind, and no common denominator of feeling seems to be possible. 15
Not surprisingly, Jevons felt certain that social harmony and not class conflict was the natural state of market capitalism. He asserted that “the supposed conflict of labour with capital is a delusion.” 16 Appealing to universal brotherhood, he added: “We ought not look at such subjects from a class point of view,” because “in economics at any rate [we] should regard all men as brothers.” 17 This “brotherhood” of social harmony arose, of course, because all people appear essentially equal and in the same light when seen exclusively as exchangers:
Each labourer must be regarded, like each landowner and each capitalist, as bringing into the common stock one part of the component elements, bargaining for the best share of the produce which the conditions of the market allow him to claim successfully. 18
He who pays a high price must either have a very great need of that which he buys, or very little need of that which he pays for it; on either supposition there is gain by exchange. In questions of this sort there is but one rule which can be safely laid down, namely that no one will buy a thing unless he expects advantage from the purchase; and perfect freedom of exchange, therefore, tends to the maximizing of utility. 19
Again the utility perspective had arrived at a new appreciation of the “invisible hand” that now, with Jevons’s new “scientific” and “mathematical” formulation, could be shown to maximize everyone’s utility in a world of brotherhood and harmony.
Jevons also developed a theory of capital that, like those of Ricardo and Marx, stressed the temporal dimension of production. A highly similar theory of capital was to become central to the later Austrian and Chicago schools of neoclassical economics (both of which grew out of the influence of Menger and reflected the spirit of Bastiat). This capital theory was developed only a few years later by a disciple of Menger—Eugen von Böhm-Bawerk. Because Böhm-Bawerk’s version was superior to that of Jevons, and because the theory is usually associated with Böhm-Bawerk, we will postpone a discussion until we consider his ideas in the next chapter.
The principal objective of Jevons’s capital theory was to refute Ricardo’s conclusion that the rate of profit varied inversely to the rate of wages. Ricardo’s conclusion obviously demonstrated the fundamental antagonism between capital and labor, and Jevons did not like it. Discussing Ricardo’s theory, Jevons wrote:
We thus arrive at the simple equation—
produce = profit + wages
A plain result also is drawn from the formula; for we are told that if wages rise profits must fall, and vice versa. But such a doctrine is radically fallacious…. The wages of a working man are ultimately coincident with what he produces, after the deduction of rent, taxes and the interest of capital. 20
It is the proper function of capitalists to sustain labour before the result is accomplished, and as many branches of industry require a large outlay long previous to any definite result being arrived at, it follows that capitalists must undertake the risk of any branch of industry where the ultimate profits are not accurately known…. The amount of capital will depend upon the amount of anticipated profits, and the competition to obtain the proper workmen will strongly tend to secure to the latter all their legitimate share in the ultimate produce. 21
Since competition would secure to the worker his “legitimate share,” Jevons hoped the trade unionist, who saw the capitalist as a class enemy, would “cease his exclusive strife against his true ally, his wealthy employer.” 22 Because the accumulation of capital benefited all workers, Jevons believed that the laborer should view the capitalists as “the trustee who holds his capital rather for the good of others than himself.” 23 The common interest of both the wealthy “trustee” and the laborer who “benefited” from the trustee’s wealth were both promoted by free exchange. Bastiat had asserted that economics was exchange—pure and simple. Jevons wrote:
Exchange is so important a process in the maximizing of utility … that some economists have regarded their science as treating of this operation alone…. I am perfectly willing to agree with the high importance attributed to exchange. It is impossible to have a correct idea of the science of economics without a perfect comprehension of the theory of exchange. 24
Jevons, however, did not want economics to be seen as explaining only exchange. Both Thompson and Hodgskin had argued, on utilitarian grounds, that exchange would be even more beneficial in an economy where workers owned their own means of production. Jevons did not want anyone to forget that capitalists’ ownership of capital was sacrosanct and that “it is the proper function of capitalists to sustain labour.” 25 Therefore, he extended Bastiat’s definition of economics (in a way with which Bastiat surely would have agreed): “Economics, then, is not solely the science of exchange or value: it is also the science of capitalization.” 26
It is not surprising that Jevons’s indignation toward prior economists, which he had expressed to his brother in the letter written in 1860, did not extend to all prior economists, but was directed primarily toward Ricardo and Mill:
When at length a true system of economics comes to be established, it will be seen that that able but wrong-headed man, David Ricardo, shunted the car of economic science on to a wrong line—a line, however, on which it was further urged toward confusion by his equally able and wrong-headed admirer, John Stuart Mill. There were economists, such as Malthus and Senior, who had a far better comprehension of the true doctrines. 27
Jevons’s The Theory of Political Economy is replete with condemnations of Ricardo and Mill and laudatory statements describing the doctrines of Malthus, Say, Senior, and Bastiat. “J.B. Say has correctly … defined utility,” 28 he wrote, and the doctrine was correctly developed by Senior “in his admirable treatise” and by “Bastiat, for instance, in his Harmonies of Political Economy.” 29 In another essay, while discussing Malthus’s theory of population, Jevons referred to Malthus as “one of the most humane and excellent of men.” 30
One of John Maynard Keynes’s favorite quotations from Malthus’s writings shows quite clearly what type of man Jevons considered to be “most humane and excellent.” The quotation is from Malthus’s Essay on Population, and it was in the context of discussing Malthus’s population theory that Jevons expressed his admiration of Malthus.
A man who is born into a world already possessed, if he cannot get subsistence from his parents on whom he has a just demand, and if the society does not want his labour, has no claim of right to the smallest portion of food, and, in fact, has no business to be where he is. At nature’s mighty feast there is no vacant cover for him. She tells him to be gone, and will quickly execute her own orders, if he does not work upon the compassion of some of her guests. If these guests get up and make room for him, other intruders immediately appear demanding the same favour. The report of a provision for all that come, fills the hall with numerous claimants. The order and harmony of the feast is disturbed, the plenty that before reigned is changed into scarcity; and the happiness of the guests is destroyed by the spectacle of misery and dependence in every part of the hall, and by the clamorous importunity of those, who are justly enraged at not finding the provision which they had been taught to expect. The guests learn too late their error, in counteracting those strict orders to all intruders, issued by the great mistress of the feast, who, wishing that all her guests should have plenty, and knowing that she could not provide for unlimited numbers, humanely refused to admit fresh comers when her table already was full. 31
One wonders what a person would have to have done or said for Jevons to have considered that person inhumane.
Rereading the doctrines of the four economists whom Jevons most admired, it strikes one as rather strange that Jevons’s ideas are frequently referred to as constituting a revolution in economic theory that marks a watershed dividing older from more modern views. The fundamental differences between the utility-theory perspective and the labor-theory perspective were clear before Jevons wrote anything, and his contribution was primarily to show that marginalism permitted the doctrines of Malthus, Say, Senior, and Bastiat to be stated with mathematical elegance and greater logical consistency. But the theoretical and ideological essence of the utility perspective remained unchanged.