William Stanley Jevons’ The Theory of Political Economy

Introduction

• In 1871 William Stanley Jevons published The Theory of Political Economy, which would prove to be one of the most influential books in the history of economic thought.

• This book developed the ideas that a young Jevons had sketched out in a paper presented to an 1862 meeting of the British Association entitled A Brief Account of a General Mathematical Theory of Political Economy, which envisioned transforming the discipline of economics.

• In that paper, a 26 or 27 year old Jevons had argued that the incorporation of mathematical techniques - in particular calculus - into economic theory would allow economists to explain all economic activity by deductively reasoning from a basic theory of utility.

• The paper garnered little attention.

• Jevons later published the essay in Journal of the Statistical Society of London in 1866.

• Still, it drew little attention.

• But Jevons’ 1871 Theory , which built on and refined the ideas Jevons had begun outlining in A Brief Account, would prove widely influential.

• It was widely reviewed throughout England, with reviews of Theory running in the pages of newspapers in London and Manchester.

• And two of the most eminent economists of the age, Alfred Marshall and John Elliot Cairnes, published their own reviews of Jevons’ treatise.

• Theory, coupled with the contemporaneous work of Leon Walras and Carl Menger, marked a turning point for economic thought: Jevons, Walras, and Menger would launch the marginalist revolution and set economics on the path toward becoming the heavily mathematical discipline it is today.

• (Related: Learn about the correspondences between Jevons and Walras on their efforts to transform economics.)

• The opening chapter of theory begins by making a case for the use of mathematics in economic theorizing.

• And subsequent chapters of the book expound Jevons’ utility theory-based approach to political economy.

The Role of Mathematics in Economics

• Jevons begins by arguing that economics is inherently mathematical because it deals with quantities (e.g. supply and demand) and the changes to them.

It is clear that Economics, if it is to be a science at all, must be a mathematical science. (pg. 3)

To me it seems that our science must be mathematical, simply because it deals with quantities. Wherever the things treated are capable of being greater or less, there the laws and relations must be mathematical in nature. The ordinary laws of supply and demand treat entirely of quantities of commodity demanded or supplied, and express the manner in which the quantities vary in connection with the price. In consequence of this fact the laws are mathematical. Economists cannot alter their nature by denying them the name; they might as well try to alter red light by calling it blue. (pg. 3 – 4)

Now there can be no doubt that pleasure, pain, labour, utility, value, wealth, money, capital, etc., are all notions admitting of quantity; nay, the whole of our actions in industry and trade certainly depend upon comparing quantities of advantage or disadvantage. (pg. 10)

• In particular, Jevons argues for a role for calculus in economics.

• He argues that, since the quantities economics deals with (e.g. supply and demand) are continuously changing, this lends itself to analysis by use of calculus – a branch of mathematics which studies the rates at which quantities change.

• Almost every other science, Jevons writes, makes use of calculus. So should economics.

My theory of Economics …. is purely mathematical in character. [B]elieving that the quantities with which we deal must be subject to continuous variation, I do not hesitate to use the appropriate branch of mathematical science, involving though it does the fearless consideration of infinitely small quantities. The theory consists in applying the differential calculus to the familiar notions of wealth, utility, value, demand, supply, capital, interest, labour, and all the other quantitative notions belonging to the daily operations of industry. As the complete theory of almost every other science involves the use of that calculus, so we cannot have a true theory of Economics without its aid. (pg. 3)

• Jevons suggests that ordinary language is limited in its ability to express complicated relations such as those dealt with by astronomers and economists. 

• In contrast, Jevons claims, mathematics constitutes a language that is capable of expressing such complicated relations, making it essential to economics.

[S]ome distinguished mathematicians have shown a liking for getting rid of their symbols, and expressing their arguments and results in language as nearly as possible approximating to that in common use. In his Système du Monde, Laplace attempted to describe the truths of physical astronomy in common language; and Thomson and Tait interweave their great Treatise on Natural Philosophy with an interpretation in ordinary words, supposed to be within the comprehension of general readers. (pg. 4)

These attempts, however distinguished and ingenious their authors, soon disclose the inherent defects of the grammar and dictionary for expressing complicated relations. The symbols of mathematical books are not different in nature from language; they form a perfected system of language, adapted to the notions and relations which we need to express. They do not constitute the mode of reasoning they embody; they merely facilitate its exhibition and comprehension. If, then, in Economics, we have to deal with quantities and complicated relations of quantities, we must reason mathematically; we do not render the science less mathematical by avoiding the symbols of algebra,—we merely refuse to employ, in a very imperfect science, much needing every kind of assistance, that apparatus of appropriate signs which is found indispensable in other sciences. (pg. 5)

• (Note that the questions of whether economics is a science and what role, if any, mathematics should play in economic theory are major topics of debate in the philosophy of economics.

• Here Jevons has provided his contribution to this discourse: economics is like the sciences and should make use of mathematics, as the sciences do.)

Many Opponents of Mathematics in Economics Confuse “Mathematical Science” For “Exact Science”

• Jevons argues that much of the opposition to the use of mathematics in economics stems from a confusion between “mathematical sciences” and “exact sciences.”

• Many opponents of the use of mathematics in economics, Jevons writes, believe that economists should not use mathematics because they lack precise data and are therefore incapable of obtaining precise answers to their problems.

• That is, economics is not what Jevons calls an “exact science.”

• Accepting that economics is not an “exact science,” Jevons nevertheless believes it is a “mathematical science.”

• He argues that, although some sciences may be more “exact” than others, no science is an “exact science.”

• To make his case, he points to astronomy.

• Astronomy, he claims, is more exact than other sciences because astronomers are capable of measuring very accurately (that is, very “exactly”) the positions of planets and stars.

• But astronomy is still not an “exact science” because, as accurate as its measurements may be, they are still only approximate.  

• There are thus, Jevons claims, no such thing as “exact sciences.”

• Therefore, Jevons argues, the requirement that a discipline must be capable of being precise in its conclusions if it is to deploy mathematical techniques is mistaken.

• Thus, Jevons concludes, it is wrong to say that economics should not be mathematical because it cannot yield precise conclusions.

• Economics is not an “exact science,” but it is still a “mathematical science.”

Many persons entertain a prejudice against mathematical language, arising out of a confusion between the ideas of a mathematical science and an exact science. They think that we must not pretend to calculate unless we have the precise data which will enable us to obtain a precise answer to our calculations; but, in reality, there is no such thing as an exact science, except in a comparative sense. Astronomy is more exact than other sciences, because the position of a planet or star admits of close measurement; but, if we examine the methods of physical astronomy, we find that they are all approximate. Every solution involves hypotheses which are not really true: as, for instance, that the earth is a smooth, homogeneous spheroid. Even the apparently simpler problems in statics or dynamics are only hypothetical approximations to the truth. (pg. 5 – 6)

We can calculate the effect of a crowbar, provided it be perfectly inflexible and have a perfectly hard fulcrum,—which is never the case. The data are almost wholly deficient for the complete solution of any one problem in natural science. (pg. 6)

The greater or less accuracy attainable in a mathematical science is a matter of accident, and does not affect the fundamental character of the science. (pg. 7)

If Physicists Waited for Precise Data Before Adopting the Use of Math, The Progress of Science Would Have Been Impaired

• Jevons further argues that if physicists had waited for access to precise data before adopting the use of mathematics, the progress of science would have been severely impaired.

Had physicists waited until their data were perfectly precise before they brought in the aid of mathematics, we should have still been in the age of science which terminated at the time of Galileo. (pg. 6)

• He claims that physical scientists often articulate mathematical theories without the availability of precise data.

When we examine the less precise physical sciences, we find that physicists are, of all men, most bold in developing their mathematical theories in advance of their data. Let any one who doubts this examine Airy's "Theory of the Tides," as given in the Encyclopædia Metropolitana; he will there find a wonderfully complex mathematical theory which is confessed by its author to be incapable of exact or even approximate application, because the results of the various and often unknown contours of the seas do not admit of numerical verification. In this and many other cases we have mathematical theory without the data requisite for precise calculation. (pg. 6 – 7)

The Two Classes of Sciences

• Having argued that there are no exact sciences, Jevons claims that there are only two types of sciences: logical sciences and mathematical sciences.

• Logical sciences are those which are concerned only with whether an event will happen or not happen, and therefore, rely only upon logic.

• Mathematical sciences are those which - in addition to being concerned with whether an event will happen or not happened and therefore relying on logic - are also concerned with time (i.e. when an event happens) and quantities.

• Economics, Jevons writes, falls into this latter category.

There can be but two classes of sciences—those which are simply logical, and those which, besides being logical, are also mathematical. If there be any science which determines merely whether a thing be or be not—whether an event will happen, or will not happen—it must be a purely logical science; but if the thing may be greater or less, or the event may happen sooner or later, nearer or farther, then quantitative notions enter, and the science must be mathematical in nature[.] (pg. 7)

The Laws of Economics Can Only Be Discerned by Considering Aggregates

• Jevons points out that, although his theory of political economy is rooted in consideration of individual minds, their sentiments, and the preferences these sentiments motivate (see below), his theory of political economy deals with aggregates (e.g. aggregate supply and aggregate demand).

I must here point out that, though the theory presumes to investigate the condition of a mind, and bases upon this investigation the whole of Economics, practically it is an aggregate of individuals which will be treated. (pg. 14-15)        

• This is because the laws which apply at the level of the individual also apply at the level of the nation.

The general forms of the laws of Economics are the same in the case of individuals and nations; and, in reality, it is a law operating in the case of multitudes of individuals which gives rise to the aggregate represented in the transactions of a nation. (pg. 15)

• And these laws cannot be discerned by observing only the actions of a limited number of limited: to detect the laws of economics, we must look at aggregate quantities.

Practically, however, it is quite impossible to detect the operation of general laws of this kind in the actions of one or a few individuals. The motives and conditions are so numerous and complicated, that the resulting actions have the appearance of caprice, and are beyond the analytic powers of science. (pg. 15)

• As an example, Jevons asks us to consider the price of sugar.

• He writes that, we should theoretically expect increases in the price of sugar to prompt every consumer of sugar to reduce their consumption of the commodity.

• But in actuality, what would happen is that some people would continue to consume sugar at the same level they had before the increase in its price, while others may cut back on their consumption dramatically.

• If we were to observe only the actions a few individuals took in the wake of an increase in the price of sugar, we may well assume that the economics of sugar are completely random.

• But when we look at the market for sugar in the aggregate, we will see a general tendency reveal itself: increases in the price of sugar lead to a reduction, in the aggregate, of sugar consumption.

• By looking at the aggregate, we could, Jevons writes, potentially detect continuous variation: that is, a continuous reduction in the aggregate demand for sugar as a response to continuous increases in its price.

• And this continuous relationship allows for expression using the mathematics of continuous change; that is, calculus.

• This is in contrast to the potential seemingly random discrete jumps we might observe if we only considered the actions of a few individuals (e.g. the few individuals sampled might cut their sugar consumption to near zero in response to some modest increase in the price of sugar).

With every increase in the price of such a commodity as sugar, we ought, theoretically speaking, to find every person reducing his consumption by a small amount, and according to some regular law. In reality, many persons would make no change at all; a few, probably, would go to the extent of dispensing with the use of sugar altogether so long as its cost continued to be excessive. It would be by examining the average consumption of sugar in a large population that we might detect a continuous variation, connected with the variation of price by a constant law. …. The use of an average, or, what is the same, an aggregate result, depends upon the high probability that accidental and disturbing causes will operate, in the long run, as often in one direction as the other, so as to neutralise each other. Provided that we have a sufficient number of independent cases, we may then detect the effect of any tendency, however slight. Accordingly, questions which appear, and perhaps are, quite indeterminate as regards individuals, may be capable of exact investigation and solution in regard to great masses and wide averages. (pg. 15 – 16)

Measuring Human Sentiment

• Jevons then turns to the measurement of human sentiment – in particular, pain and pleasure.

• For Jevons, such human sentiments drive all economic activity.

A unit of pleasure or of pain is difficult even to conceive; but it is the amount of these feelings which is continually prompting us to buying and selling, borrowing and lending, labouring and resting, producing and consuming[.] (pg. 12)

We Can’t Directly Measure Human Sentiment

• Jevons suggests that economists could not at the time he published (1871) and may never be able to directly measure pleasure and pain – the sentiments which he argues drive all economic activity.

I hesitate to say that men will ever have the means of measuring directly the feelings of the human heart. (pg. 12)

• (Related: Neuroeconomist Colin Camerer argued in 2007 that the development of new technologies – especially functional magnetic resonance imaging (fMRI) – for mapping activity in the human brain now allows us to measure such human sentiments.)

But We Can Measure Human Sentiment Indirectly

• However, Jevons writes, the inability to directly measure the human sentiments which he believes underlie all economic activity does not prohibit us from developing a mathematical theory of economics.

Many will object, no doubt, that the notions which we treat in this science are incapable of any measurement. We cannot weigh, nor gauge, nor test the feelings of the mind; there is no unit of labour, or suffering, or enjoyment. It might thus seem as if a mathematical theory of Economics would be necessarily deprived for ever of numerical data. (pg. 8)

[However] [i]f we trace the history of other sciences, we gather no lessons of discouragement. In the case of almost everything which is now exactly measured, we can go back to the age when the vaguest notions prevailed. (pg. 8)

• He points to advancements in other disciplines that can now measure quantities which were once unmeasurable – in particular, belief, electricity, and temperature.

• He argues that, prior to the development of probability theory, it would have been hard to measure belief and yet today we can express beliefs through the use of the mathematics of probability.

Previous to the time of Pascal, who would have thought of measuring doubt and belief? Who could have conceived that the investigation of petty games of chance would have led to the creation of perhaps the most sublime branch of mathematical science—the theory of probabilities? (pg. 8 – 9)

• He further likens the measurement of human sentiment to the measurement of electricity: there was a time when measuring quantities of electricity was not possible, but it is today.

There are sciences which, even within the memory of men now living, have become exactly quantitative. While Quesnay and Baudeau and Le Trosne and Condillac were founding Political Economy in France, and Adam Smith in England, electricity was a vague phenomenon, which was known, indeed, to be capable of becoming greater or less, but was not measured nor calculated: it is within the last forty or fifty years that a mathematical theory of electricity, founded on exact data, has been established. (pg. 9)

• Similarly, there was a time when we could not measure heat, but we can do so today.

We now enjoy precise quantitative notions concerning heat, and can measure the temperature of a body to less than 1/5,000 part of a degree Centigrade. Compare this precision with that of the earliest makers of thermometers, the Academicians del Cimento, who used to graduate their instruments by placing them in the sun’s rays to obtain a point of fixed temperature. (pg. 9)

• These developments, for Jevons, suggest that economists are not hopeless.

• He argues that, though economists cannot measure human sentiment directly, they can do so indirectly by measuring their effects, much like how gravity cannot be directly observed but is measured indirectly through its effects.

• And the effects of these human sentiments are outcomes in the market.

• Thus, we may indirectly measure human sentiment by observing market outcomes. [1]

[I]t is from the quantitative effects of the feelings [i.e. pain and pleasure] that we must estimate their comparative amounts. We can no more know nor measure gravity in its own nature than we can measure a feeling; but, just as we measure gravity by its effects in the motion of a pendulum, so we may estimate the equality or inequality of feelings by the decisions of the human mind. The will is our pendulum, and its oscillations are minutely registered in the price lists of the markets. (pg. 12)

And, Jevons writes, data on market outcomes is readily available.

In fact, when it comes to data on market outcomes, the problem economists face is not one of insufficient data but rather of an overabundance of it, scattered across different sources. [2]

"But where," the reader will perhaps ask, "are your numerical data for estimating pleasures and pains in Political Economy?" I answer, that my numerical data are more abundant and precise than those possessed by any other science, but that we have not yet known how to employ them. The very abundance of our data is perplexing. There is not a clerk nor book-keeper in the country who is not engaged in recording numerical facts for the economist. The private-account books, the great ledgers of merchants and bankers and public offices, the share lists, price lists, bank returns, monetary intelligence, Custom-house and other Government returns, are all full of the kind of numerical data required to render Economics an exact mathematical science. Thousands of folio volumes of statistical, parliamentary, or other publications await the labour of the investigator. (pg. 11)