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• Preface to the First Edition (1871)
• Preface to the Second Edition (1879)
• Preface to the Third Edition By Harriet Jevons
• Errata
• Chapter I: Introduction
• Mathematical Character of the Science.
• Confusion Between Mathematical and Exact Sciences.
• Capability of Exact Measurement.
• Measurement of Feeling and Motives.
• Logical Method of Economics.
• Relation of Economics to Ethics.
• Chapter II: Theory of Pleasure and Pain
• Pleasure and Pain As Quantities.
• Pain the Negative of Pleasure.
• Anticipated Feeling.
• Uncertainty of Future Events.
• Chapter III: Theory of Utility
• Definition of Terms.
• The Laws of Human Want.
• Utility Is Not an Intrinsic Quality.
• Law of the Variation of Utility.
• Total Utility and Degree of Utility.
• Variation of the Final Degree of Utility.
• Disutility and Discommodity.
• Distribution of Commodity In Different Uses.
• Theory of Dimensions of Economic Quantities.
• Actual, Prospective, and Potential Utility.
• Distribution of a Commodity In Time.
• Chapter IV: Theory of Exchange
• Importance of Exchange In Economics.
• Ambiguity of the Term Value.
• Value Expresses Ratio of Exchange.
• Popular Use of the Term Value.
• Dimension of Value.
• Definition of Market.
• Definition of Trading Body.
• The Law of Indifference.
• The Theory of Exchange.
• Symbolic Statement of the Theory.
• Analogy to the Theory of the Lever.
• Impediments to Exchange.
• Illustrations of the Theory of Exchange.
• Problems In the Theory of Exchange.
• Complex Cases of the Theory.
• Competition In Exchange.
• Failure of the Equations of Exchange.
• Negative and Zero Value.
• Equivalence of Commodities.
• Acquired Utility of Commodities.
• The Gain By Exchange.
• Numerical Determination of the Laws of Utility.
• Opinions As to the Variation of Price.
• Variation of the Price of Corn.
• The Origin of Value.
• Chapter V: Theory of Labour
• Definition of Labour.
• Quantitative Notions of Labour.
• Symbolic Statement of the Theory.
• Dimensions of Labour.
• Balance Between Need and Labour.
• Distribution of Labour.
• Relation of the Theories of Labour and Exchange.
• Relations of Economic Quantities.
• Various Cases of the Theory.
• Joint Production.
• Over-production.
• Limits to the Intensity of Labour.
• Chapter VI: Theory of Rent
• Accepted Opinions Concerning Rent.
• Symbolic Statement of the Theory.
• Illustrations of the Theory.
• Chapter VII: Theory of Capital
• The Function of Capital.
• Capital Is Concerned With Time.
• Quantitative Notions Concerning Capital.
• Expression For Amount of Investment.
• Dimensions of Capital, Credit and Debit.
• Effect of the Duration of Work.
• Illustrations of the Investment of Capital.
• Fixed and Circulating Capital.
• Free and Invested Capital.
• Uniformity of the Rate of Interest.
• General Expression For the Rate of Interest.
• Dimension of Interest.
• Peacock On the Dimensions of Interest.
• Tendency of Profits to a Minimum.
• Advantage of Capital to Industry.
• Are Articles In the Consumers' Hands Capital?
• Chapter VIII: Concluding Remarks
• The Doctrine of Population.
• Relation of Wages and Profit.
• Professor Hearn's Views.
• The Noxious Influence of Authority.
• Appendix I
• Appendix Ii

Distribution of a Commodity in Time.

We have seen that, when a commodity is capable of being used for different purposes, definite principles regulate its application to those purposes. A similar question arises when a stock of commodity is in hand, and must be expended over a certain interval of time more or less definite. The science of Economics must point out the mode of consuming it to the greatest advantage—that is, with a maximum result of utility. If we reckon all future pleasures and pains as if they were present, the solution will be the same as in the case of different uses. If a commodity has to be distributed over n days' use, and v¹, v², etc., be the final degrees of utility on each day's consumption, then we ought clearly to have

v¹ = v² = v³ =...=vⁿ.

It may, however, be uncertain during how many days we may require the stock to last. The commodity might be of a perishable nature, so that if we were to keep some of it for ten days, it might become unserviceable, and its utility be sacrificed. Assuming that we can estimate more or less exactly the probability of its remaining good, let p¹, p², p³... p¹⁰, be these probabilities. Then, on the principle (p. 36) that a future pleasure or pain must be reduced in proportion to its want of certainty, we have the equations

v¹p¹ = r²p² =... = v¹⁰p¹⁰.

The general result is, that as the probability is less, the commodity assigned to each day is less, so that v, its final degree of utility, will be greater.

So far we have taken no account of the varying influence of an event according to its propinquity or remoteness. The distribution of commodity described is that which should be made and would be made by a being of perfect good sense and foresight. To secure a maximum of benefit in life, all future events, all future pleasures or pains, should act upon us with the same force as if they were present, allowance being made for their uncertainty. The factor expressing the effect of remoteness should, in short, always be unity, so that time should have no influence. But no human mind is constituted in this perfect way: a future feeling is always less influential than a present one. To take this fact into account, let q¹, q², q³, etc., be the undetermined fractions which express the ratios of the present pleasures or pains to those future ones from whose anticipation they arise. Having a stock of commodity in hand, our tendency will be to distribute it so that the following equations will hold true—

v¹p¹q¹ = v²p²q² = v³p³q³ =... = vⁿpⁿq^n.

It will be an obvious consequence of these equations that less commodity will be assigned to future days in some proportion to the intervening time.

An illustrative problem, involving questions of prospective utility and probability, is found in the case of a vessel at sea, which is insufficiently victualled for the probable length of the voyage to the nearest port. The actual length of the voyage depends on the winds, and must be uncertain; but we may suppose that it will almost certainly last ten days or more, but not more than thirty days. It is apparent that if the food were divided into thirty equal parts, partial famine and suffering would be certainly endured for the first ten days, to ward off later evils which may not be encountered. To consume one-tenth part of the food on each of the first ten days would be still worse, as almost certainly entailing starvation on the following days. To determine the most beneficial distribution of the food, we should require to know the probability of each day between the tenth and thirtieth days forming part of the voyage, and also the law of variation of the degree of utility of food. The whole stock ought then to be divided into thirty portions, allotted to each of the thirty days, and of such magnitudes that the final degrees of utility multiplied by the probabilities may be equal. Thus, let v¹, v², v³, etc., be the final degrees of utility of the first, second, third, and other days supplied, and p¹, p², p³, etc., the probabilities that the days in question will form part of the voyage; then we ought to have

p¹v¹ = p²v² = p³v³ =... = p²⁹v²⁹ = p³⁰v³⁰.

If these equations did not hold true, it would be beneficial to transfer a small portion from one lot to some other lot. As the voyage is supposed certainly to last the first ten days, we have

p¹ = p² =... = p¹⁰ = 1:

hence we must have

v¹ = v² =... = v¹⁰:

that is to say, the allotments to the first ten days should be equal. They should afterwards decrease according to some regular law; for, as the probability decreases, the final degree of utility should increase in inverse proportion.

CHAPTER IV

THEORY OF EXCHANGE