Front Page Titles (by Subject) Numerical Determination of the Laws of Utility. - The Theory of Political Economy
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Numerical Determination of the Laws of Utility. - William Stanley Jevons, The Theory of Political Economy 
The Theory of Political Economy (London: Macmillan, 1888) 3rd ed.
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Numerical Determination of the Laws of Utility.
The future progress of Economics as a strict science must greatly depend upon our acquiring more accurate notions of the variable quantities concerned in the theory. We cannot really tell the effect of any change in trade or manufacture until we can with some approach to truth express the laws of the variation of utility numerically. To do this we need accurate statistics of the quantities of commodities purchased by the whole population at various prices. The price of a commodity is the only test we have of the utility of the commodity to the purchaser; and if we could tell exactly how much people reduce their consumption of each important article when the price rises, we could determine, at least approximately, the variation of the final degree of utility—the all-important element in Economics.
In such calculations we may at first make use of the simpler equation given on p. 113. For the first approximation we may assume that the general utility of a person's income is not affected by the changes of price of the commodity; so that, if in the equation
f x = m. y c
we may have many different corresponding values for x and m, we may treat yc, the utility of money, as a constant, and determine the general character of the function fx, the final degree of utility. This function would doubtless be a purely empirical one—a mere aggregate of terms devised so that their sum shall vary in accordance with statistical facts. The subject is too complex to allow of our expecting any simple precise law like that of gravity. Nor, when we have got the laws, shall we be able to give any exact explanation of them. They will be of the same character as the empirical formulæ used in many of the physical sciences—mere aggregates of mathematical symbols intended to replace a tabular statement.1 Nevertheless, their determination will render Economics a science as exact as many of the physical sciences; as exact, for instance, as Meteorology is likely to be for a very long time to come.
The method of determining the function of utility explained above will hardly apply, however, to the main elements of expenditure. The price of bread, for instance, cannot be properly brought under the equation in question, because, when the price of bread rises much, the resources of poor persons are strained, money becomes scarcer with them, and yc, the utility of money, rises. The natural result is, the lessening of expenditure in other directions; that is to say, all the wants of a poor person are supplied to a less degree of satisfaction when food is dear than when it is cheap. When in the long course of scientific progress a sufficient supply of suitable statistics has been at length obtained, it will become a mathematical problem of no great difficulty how to disentangle the functions expressing the degrees of utility of various commodities. One of the first steps, no doubt, will be to ascertain what proportion of the expenditure of poor people goes to provide food, at various prices of that food. But great difficulty is thrown in the way of all such inquiries by the vast differences in the condition of persons; and still greater difficulties are created by the complicated ways in which one commodity replaces or serves instead of another.
[]See Jevons' Principles of Science, chap. xxii., new ed., pp. 487-489, and the references there given.