The Online Library of Liberty

A project of Liberty Fund, Inc.

• 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

General Expression for the Rate of Interest.

We may obtain a general expression for the rate of interest yielded by capital in any employment provided that we may suppose the produce for the same amount of labour to vary as some continuous function of the time elapsing between the expenditure of the labour and the enjoyment of the result. Let the time in question be t, and the produce for the same amount of labour the function of t denoted by Ft, which may be supposed always to increase with t. If we now extend the time to t + Dt, the produce will be F (t + Dt), and the increment of produce F (t + Dt) - Ft. The ratio which this increment bears to the increment of investment of capital will determine the rate of interest. Now, at the end of the time t, we might receive the product Ft, and this is the amount of capital which remains invested when we extend the time by Dt. Hence the amount of increased investment of capital is Dt · Ft; and, dividing the increment of produce by this last expression, we have

When we reduce the magnitude of Dt infinitely, the limit of the first factor of the above expression is the differential coefficient of Ft, so that we find the rate of interest to be represented by

The interest of capital is, in other words, the rate of increase of the produce divided by the whole produce; but this is a quantity which must rapidly approach to zero, unless means can be found of continually maintaining the rate of increase. Unless a body moves with a rapidly increasing speed, the space it moves over in any unit of time must ultimately become inconsiderable compared with the whole space passed over from the commencement. There is no reason to suppose that industry, generally speaking, is capable of returning any such vastly increasing produce from the greater application of capital. Every new machine or other great invention will usually require a fixation of capital for a certain average time, and may be capable of paying interest upon it; but when this average time is reached, it fails to afford a return to more prolonged investments.

To take an instance, let us suppose that the produce of labour in some case is proportional to the interval of abstinence t; then we have say Ft = a · t, in which a is an unknown constant. The differential coefficient F't is now a; and the rate of interest

or

or

; or the rate of interest varies inversely as the time of investment.