Front Page Titles (by Subject) Variation of the Price of Corn. - The Theory of Political Economy
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Variation of the Price of Corn. - William Stanley Jevons, The Theory of Political Economy 
The Theory of Political Economy (London: Macmillan, 1888) 3rd ed.
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Variation of the Price of Corn.
As to Chalmers' ingenious remarks upon the consumption of nutmeg, he seems to be at least partially correct. To a certain extent he brings into view the principle explained above, that when only a small quantity of income is required to purchase a certain kind of commodity in sufficient abundance, the degree of utility of income will not be appreciably affected by the price paid, that is to say (p. 113) yc remains approximately constant. It follows that is constant, or in other words the final degree of utility of the small commodity purchased must be directly proportional to the price. If then the price rise much, either the consumer must relinquish the use of that commodity almost entirely, or else he must feel such need of it, that a small decrease of consumption is irksome to him; that is to say, looking to our curves of utility, either we must recede to a part of the curve very close to the axis of y, or else the curve must be one which rises rapidly as we move towards the origin. Now Chalmers assumes that with nutmeg the latter is the case. People accustomed to use it in his time were so fond of it that they would pay a much higher price rather than decrease their consumption considerably. This means that it possessed a high degree of utility to them, which could only be overbalanced by some serious increase in the value of yc, which would ultimately mean the need of the necessaries of life.
It is very curious that in this subject, which reaches to the very foundations of Political Economy, we owe more to early than later writers. Before our science could be said to exist at all, writers on Political Arithmetic had got about as far as we have got at present. In a pamphlet of 1737,1 it is remarked that "People who understand trade will readily agree with me, that the tenth part of a commodity in a market, more than there is a brisk demand for, is apt to lower the market, perhaps, twenty or thirty per cent, and that a deficiency of a tenth part will cause as exorbitant an advance." Sir J. Dalrymple,1 again, says: "Merchants observe, that if the commodity in market is diminished one-third beneath its mean quantity, it will be nearly doubled in value; and that if it is augmented one-third above its mean quantity, it will sink near one-half in its value; or that, by further diminishing or augmenting the quantity, these disproportions between the quantity and prices vastly increase." These remarks bear little signs of accuracy, indeed, for the writers have spoken of commodities in general as if they all varied in price in a similar degree. It is probable that they were thinking of corn or other kinds of the more necessary food. In the Spectator we find a conjecture,1 that the production of one-tenth part more of grain than is usually consumed would diminish the value of the grain one-half. I know nothing more strange and discreditable to statists and economists than that in so important a point as the relations of price and supply of the main article of food, we owe our most accurate estimates to writers who lived from one to two centuries ago.
There is a celebrated estimate of the variation of the price of corn which I have found quoted in innumerable works on Economics. It is commonly attributed to Gregory King, whose name should be held in honour as one of the fathers of statistical science in England. Born at Lichfield in 1648, King devoted himself much to mathematical studies, and was often occupied in surveying. His principal public appointments were those of Lancaster Herald and Secretary to the Commissioners of Public Accounts; but he is known to fame by the remarkable statistical tables concerning the population and trade of England, which he completed in the year 1696. His treatise was entitled Natural and Political Observations and Conclusions upon the State and Condition of England, 1696. It was never printed in the author's lifetime, but the contents were communicated in a most liberal manner to Dr. Davenant, who, making suitable acknowledgments as to the source of his information, founded thereupon his Essay upon the Probable Methods of making a People gainers in the Balance of Trade.1 Our knowledge of Gregory King's conclusions was derived from this and other essays of Davenant, until George Chalmers printed the whole treatise at the end of the third edition of his well-known Estimate of the Comparative Strength of Great Britain.
The estimate of which I am about to speak is given by Davenant in the following words:1 "We take it, that a defect in the harvest may raise the price of corn in the following proportions:—
So that when corn rises to treble the common rate, it may be presumed that we want above of the common produce; and if we should want , or half the common produce, the price would rise to near five times the common rate."
Though this estimate has always been attributed to Gregory King, I cannot find it in his published treatise; nor does Davenant, who elsewhere makes full acknowledgments of what he owes to King, here attribute it to his friend. It is therefore, perhaps, due to Davenant.
We may re-state this estimate in the following manner, taking the average harvest and the average price of corn as unity:—
Many writers have commented on this estimate. Thornton1 observes that it is probably exceedingly inaccurate, and that it is not clear whether the total stock, or only the harvest of a single year, is to be taken as deficient. Tooke,2 however, than whom on such a point there is no higher authority, believes that King's estimate "is not very wide of the truth, judging from the repeated occurrence of the fact that the price of corn in this country has risen from one hundred to two hundred per cent and upwards when the utmost computed deficiency of the crops has not been more than between one-sixth and one-third of an average."
I have endeavoured to ascertain the law to which Davenant's figures conform, and the mathematical function obtained does not greatly differ from what we might have expected. It is probable that the price of corn should never sink to zero, as, if abundant, it could be used for feeding horses, poultry, and cattle, or for other purposes for which it is too costly at present. It is said that in America corn, no doubt Indian corn, has been occasionally used as fuel. On the other hand, when the quantity is much diminished, the price should rise rapidly, and should become infinite before the quantity is zero, because famine would then be impending. The substitution of potatoes and other kinds of food renders the famine point very uncertain; but I think that a total deficiency of corn could not be made up by other food. Now a function of the form
fulfils these conditions; for it becomes infinite when x is reduced to b, but for greater values of x always decreases as x increases. An inspection of the numerical data shows that n is about equal to 2, and, assuming it to be exactly 2, I find that the most probable values of a and b are a = .824 and b = .12. The formula thus becomes
The following numbers show the degree of approximation between the first of these formulæ and the data of Davenant:—
I cannot undertake to say how nearly Davenant's estimate agrees with experience; but, considering the close approximation in the above numbers, we may safely substitute the empirical formula for his numbers; and there are other reasons already stated for supposing that this formula is not far from the truth. Roughly speaking, the price of corn may be said to vary inversely as the square of the supply, provided that this supply be not unusually small. I find that this is nearly the same conclusion as Whewell drew from the same numbers. He says:1 "If the above numbers were to be made the basis of a mathematical rule, it would be found that the price varies inversely as the square of the supply, or rather in a higher ratio."
There is further reason for believing that the price of corn varies more rapidly than in the inverse ratio of the quantity. Tooke estimates1 that in 1795 and 1796 the farmers of England gained seven millions sterling in each year by a deficiency of one-eighth part in the wheat crop, not including the considerable profit on the rise of price of other agricultural produce. In each of the years 1799 and 1800, again, farmers probably gained eleven millions sterling by deficiency. If the price of wheat varied in the simple inverse proportion of the quantity, they would neither gain nor lose, and the fact that they gained considerably agrees with our formula as given above.
The variation of utility has not been overlooked by mathematicians, who had observed, as long ago as the early part of last century—before, in fact, there was any science of Political Economy at all—that the theory of probabilities could not be applied to commerce or gaming without taking notice of the very different utility of the same sum of money to different persons. Suppose that an even and fair bet is made between two persons, one of whom has £10,000 a year, the other £100 a year; let it be an equal chance whether they gain or lose £50. The rich person will, in neither case, feel much difference; but the poor person will receive far more harm by losing £50 than he can be benefited by gaining it. The utility of money to a poor person varies rapidly with the amount; to a rich person less so. Daniel Bernoulli, accordingly, distinguished in any question of probabilities between the moral expectation and the mathematical expectation, the latter being the simple chance of obtaining some possession, the former the chance as measured by its utility to the person. Having no means of ascertaining numerically the variation of utility, Bernoulli had to make assumptions of an arbitrary kind, and was then able to obtain reasonable answers to many important questions. It is almost self-evident that the utility of money decreases as a person's total wealth increases; if this be granted, it follows at once that gaming is, in the long run, a sure way to lose utility; that every person should, when possible, divide risks, that is, prefer two equal chances of £50 to one similar chance of £100; and the advantage of insurance of all kinds is proved from the same theory. Laplace drew a similar distinction between the fortune physique, or the actual amount of a person's income, and the fortune morale, or its benefit to him."1
In answer to the objections of an ingenious correspondent, it may be remarked that when we say gaming is a sure way to lose utility, we take no account of the utility—that is, the pleasure attaching to the pursuit of gaming itself; we regard only the commercial loss or gain. If a person with a certain income prefers to run the risk of losing a portion of it at play, rather than spending it in any other way, it must no doubt be conceded that the political economist, as such, can make no conclusive objection. If the gamester is so devoid of other tastes that to spend money over the gaming-table is the best use he can discover for it, economically speaking, there is nothing further to be said. The question then becomes a moral, legislative, or political one. A source of amusement which, like gaming, betting, dram-drinking, or opium-eating, is not in itself always pernicious, may come to be regarded as immoral, if in a considerable proportion of cases it leads to excessive and disastrous results. But this question evidently leads us into a class of subjects which could not be appropriately discussed in this work treating of pure economic theory.
[]Quoted in Lauderdale's Inquiry into the Nature and Origin of Public Wealth, 2d ed., 1819, pp. 51, 52.
[]No. 200, quoted by Lauderdale, p. 50.
[]The Political and Commercial Works of Charles Davenant, vol. ii. p. 163.
[]Ibid., p. 224.
[]An Inquiry into the Nature and Effects of the Paper Credit of Great Britain, pp. 270, 271.
[]History of Prices, vol. i. pp. 13-15.
[]Six Lectures on Political Economy. Cambridge, 1862.
[]History of Prices.
[]Todhunter's History of the Theory of Probability, chap. xi., etc.