# The Theory of Interest

Fisher was one of America’s greatest mathematical economists. This book is still used a textbook and is an outstanding example of clearly written economic theory.

*The Theory of Interest, as determined by Impatience to Spend Income and Opportunity to Invest it* (New York: Macmillan, 1930).

**Copyright:**

The text is in the public domain.

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- Author: Irving Fisher

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#### Table of Contents

- CONTENTS
- ERRATA
- PREFACE
- SUGGESTIONS TO READERS
- PART I.: INTRODUCTION
- PART I, CHAPTER I: INCOME AND CAPITAL2
- §1. Subjective, or Enjoyment, Income
- §2. Objective, or Real, Income (Our "Living")
- §3. Cost of Living, a Measure of Real Income
- §4. Cost of an Article vs. Cost of Its Use
- §5. Measuring at the Domestic Threshold
- §6. Money Income
- §7. Capital Value
- §8. The Rate of Interest
- §9. Discounting is Fundamental
- §10. Costs, or Negative Income
- §11. The Discount Principle Applied
- §12. Double Entry Bookkeeping
- §13. Simplicity Underlying Complications
- §14. Capital Gain not Income
- §15. Capital-Income Relations
- §16. Application to this Book
- §17. Confusions to be Avoided
- §18. A Working Concept of the Rate of Interest
- PART I, CHAPTER II: MONEY INTEREST AND REAL INTEREST
- §1. Introduction
- §2. Assuming Foresight
- §3. Limitations of Theory
- §4. Real and Money Interest
- PART I, CHAPTER III: SOME COMMON PITFALLS
- §1. Introduction
- §2. The Exploitation Explanation of Interest
- §3. Interest Taking Survives all Opposition
- §4. Naïve Productivity Explanations
- §5. Two Other Pitfalls
- PART II.: THE THEORY IN WORDS
- PART II, CHAPTER IV: TIME PREFERENCE (HUMAN IMPATIENCE)
- §1. Preference for Present over Future Income
- §2. Reduction to Enjoyment Income
- §3. Impatience Depends on Income
- §4. Interest and Price Theory
- §5. Specifications of Income
- §6. The Influence of Mere Size
- §7. The Influence of Time Shape
- §8. The Influence of Risk
- §9. The Personal Factor
- §10. The Personal Factor Summarized
- §11. Income Rather Than Capital in the Leading Rôle
- §12. Impatience Schedules
- PART II, CHAPTER V: FIRST APPROXIMATION TO THE THEORY OF INTEREST Assuming Each Person's Income Stream Foreknown and Unchangeable Except by Loans
- §1. Hypotheses of First Approximation
- §2. Income Prescribed
- §3. Equalization of Impatience
- §4. Altering Income by Loans
- §5. Altering Income by Sale
- §6. Interest Ineradicable
- §7. "Marginal" Principle Is "Maximum" Principle
- §8. Market Equilibrium
- §9. Four Principles
- THE TWO IMPATIENCE PRINCIPLES
- A. Empirical Principle
- B. Principle of Maximum Desirability
- THE TWO MARKET PRINCIPLES
- A. Principle of Clearing the Market
- B. Principle of Repayment
- PART II, CHAPTER VI: SECOND APPROXIMATION TO THE THEORY OF INTEREST Assuming Income Modifiable (1) by loans and (2) by other means
- §1. The New Hypothesis
- §2. Optional Income Streams
- §3. The Two Kinds of Choice
- §4. Opportunity to Invest by Change of Use of Capital
- §5. The Reasoning not "Circular"
- §6. Summary
- THE TWO INVESTMENT OPPORTUNITY PRINCIPLES
- A. Empirical Principle
- B. Principle of Maximum Present Worth
- THE TWO IMPATIENCE PRINCIPLES
- A. Empirical Principle
- B. Principle of Maximum Desirability
- THE TWO MARKET PRINCIPLES
- A. Principle of Clearing the Market
- B. Principle of Repayment
- PART II, CHAPTER VII: THE INVESTMENT OPPORTUNITY PRINCIPLES
- §1. Eligible and Ineligible Options
- §2. The Method of Comparative Advantage
- §3. The Concept of Rate of Return Over Cost
- §4. The Principle of Return over Cost
- §5. Marginal Rate of Return Over Cost
- §6. The Illustration of Cutting a Forest
- §7. Other Similar Illustrations
- §8. The Case of Perpetual Returns
- §9. The General Case
- §10. Range of Choice Depends on Interest Rate
- §11. The Investment Opportunity Principles Summarized
- The Principle of Maximum Present Value.
- The Principle of Comparative Advantage.
- The Principle of Return over Cost.
- The Same Principle when the Options Differ by Continuous Gradations.
- §12. Interrelation of Human Impatience and Investment Opportunity
- PART II, CHAPTER VIII: DISCUSSION OF THE SECOND APPROXIMATION
- §1. Opportunity Reduced to Lowest Terms
- §2. Investment Opportunity Essential
- §3. Options Differing in Time Shape Only
- §4. The Imaginary "Hard-Tack" Illustration
- §5. The Imaginary "Figs" Example
- §6. The Imaginary "Sheep" Example
- §7. Opportunities as to Repairs, Renewals, Betterments
- §8. Opportunity to Change the Application of Labor
- §9. Fluctuations in Interest Rates Self-Corrective
- §10. Wide Opportunities Stabilize Interest
- PART II, CHAPTER IX: THIRD APPROXIMATION TO THE THEORY OF INTEREST Assuming Income Uncertain
- §1. More than One Rate of Interest
- §2. Relations Between the Various Rates
- §3. Limitations on Loans
- §4. Risk and Small Loans
- §5. Salability as a Safeguard
- §6. General Income Risks
- §7. Securities Classified as to Risk
- §8. Effect of Risk on the Six Principles
- THE TWO PRINCIPLES AS TO INVESTMENT OPPORTUNITY
- A. Empirical Principle
- B. Principle of Maximum Present Value
- THE TWO PRINCIPLES AS TO IMPATIENCE
- A. Empirical Principle
- B. The Principle of Maximum Desirability
- THE TWO MARKET PRINCIPLES
- A. Principle of Clearing the Market
- B. Principle of Repayment
- PART III.: THE THEORY IN MATHEMATICS
- PART III, CHAPTER X: FIRST APPROXIMATION IN GEOMETRIC TERMS
- §1. Introduction
- §2. The Map of This Year's and Next Year's Income
- §3. The Market Line
- §4. The Willingness Line
- §5. The Two Lines Compared
- §6. The Whole Family of Market Lines
- §7. Many Families of Willingness Lines
- §8. A Typical Family of Willingness Lines
- §9. Time Preference May be Negative
- §10. The Personal and Impersonal Influences on Impatience
- §11. Deciding Whether to Borrow or to Lend
- §12. Interest Fixed for an Individual
- §13. How an Individual Adjusts his Income Position to the Market
- §14. Market Equilibrium
- §15. The Four Principles as Charted
- §16. The Geometric Method
- §17. Relation to Supply and Demand
- PART III, CHAPTER XI: SECOND APPROXIMATION IN GEOMETRIC TERMS
- §1. Introduction
- §2. The Investment Opportunity Line
- §3. The Individual's Adjustment Without Loans
- §4. Individual Adjustment with Loans
- §5. The Double Adjustment Discussed
- §6. Market Equilibrium
- §7. The Nature of the Opportunity Line Discussed
- §8. Investment Opportunity and Impatience
- §9. Can Interest Disappear?
- §10. Does Interest Stimulate Saving?
- §11. Relation to Supply and Demand Curves
- PART III, CHAPTER XII: FIRST APPROXIMATION IN TERMS OF FORMULAS
- §1. Case of Two Years and Three Individuals
- §2. Impatience Principle A (Three Equations)
- §3. Impatience Principle B (Three Equations)
- §4. Market Principle A (Two Equations)
- §5. Market Principle B (Three Equations)
- §6. Counting Equations and Unknowns
- §7. Case of m Years and n Individuals
- §8. Impatience Principle A (n(m - 1) Equations)
- §9. Impatience Principle B (n(m - 1) Equations)
- §10. Market Principle A (m Equations)
- §11. Market Principle B (n Equations)
- §12. Counting Equations and Unknowns
- §13. Different Rates of Interest for Different Years
- PART III, CHAPTER XIII: SECOND APPROXIMATION IN TERMS OF FORMULAS
- §1. Introduction
- §2. Impatience Principle A. (n(m—1) Equations)
- §3. Impatience Principle B (n(m - 1) Equations)
- §4. Market Principle A. (m Equations)
- §5. Market Principle B. (n Equations)
- §6. Investment Opportunity Principle A. (n Equations)
- §7. Opportunity Principle B. (n(m—1) Equations)
- §8. Counting the Equations and Unknowns
- §9. Reconciling the Numbers of Equations and Unknowns
- §10. Zero or Negative Rates of Interest
- §11. The Formula Method Helpful
- PART III, CHAPTER XIV: THE THIRD APPROXIMATION UNADAPTED TO MATHEMATICAL FORMULATION
- §1. Introduction
- §2. The Six Sets of Formulas Incomplete
- §3. Conclusions
- PART IV.: FURTHER DISCUSSION
- PART IV, CHAPTER XV: THE PLACE OF INTEREST IN ECONOMICS
- §1. Interest Rates and Values of Goods
- §2. Interest Rates and Values of Services
- §3. Interest Rates and Wages
- §4. Interest and Functional Distribution
- §5. Interest and Personal Distribution
- §6. The Loan Market Is a Highway for Re-Distribution
- PART IV, CHAPTER XVI: RELATION OF DISCOVERY AND INVENTION TO INTEREST RATES
- §1. The First Effect of Each Important Discovery and Invention Is to Increase the Rate of Interest
- §2. Invention Causes Dispersion of Interest Rates
- §3. Invention Causes Revaluation of Capital
- §4. The Ultimate Effects of Invention on Interest Rate
- §5. The Present an Age of Invention
- §6. Mass Production of Inventions
- §7. Effects on Investment
- §8. Importance of Invention
- PART IV, CHAPTER XVII: PERSONAL AND BUSINESS LOANS
- §1. Personal Loans
- §2. Business Loans
- §3. Short Term Loans
- §4. Long Term Loans
- §5. Business vs. Personal Loans
- §6. Purpose of Borrowing to Increase Present Income
- §7. Public Loans
- PART IV, CHAPTER XVIII: SOME ILLUSTRATIVE FACTS
- §1. Introduction
- §2. Examples of Influence of Personal Characteristics
- §3. Examples of Influence of Poverty
- §4. Examples of Influence of Composition of Income
- §5. Examples of Influence of Risk
- §6. Examples of Influence of Time Shape
- §7. Rising Income Means High Interest Rates
- §8. Effect of Catastrophes on Interest
- §9. Examples of Influence of Periodicity of Income
- §10. Summary
- PART IV, CHAPTER XIX: THE RELATION OF INTEREST TO MONEY AND PRICES
- §1. Price Changes and Interest Rates
- §2. United States Coin and Currency Bonds
- §3. Gold and Rupee Bonds
- §4. Money Interest and Real Interest
- §5. Real Interest Varies More Than Money Interest
- §6. Interest Rates and Rates of Price Change
- §7. Short Term Interest Rates and Prices in the United States
- §8. Interest Rates and Price Indexes
- §9. Elimination of Trends
- §10. Relations of Prices and Interest Interpreted
- §11. Relations of Interest to Business and Prices
- §12. Interest Rates and Bank Reserves
- §13. Summary
- PART IV, CHAPTER XX: OBJECTIONS CONSIDERED73
- §1. Introduction
- §2. Income and Capital
- §3. Cost of Production as a Determinant of Capital Value
- §4. Impatience as Determinant of the Interest Rate
- §5. Productivity as a Determinant of Interest Rates
- §6. Technical Superiority of Present Goods
- §7. Interest as a Cost
- §8. Empirical and Institutional Influences on Interest Rates
- §9. Conclusion
- PART IV, CHAPTER XXI: SUMMARY
- §1. Interest and Purchasing Power of Money
- §2. The Six Principles
- §3. The Nature of Investment Opportunity
- §4. Investment Opportunity for Society as a Whole
- §5. Time Preference
- §6. Conclusion
- §7. The Future
- APPENDIX TO CHAPTER I
- §1 (to Ch. I, § 1) Quotations from Professor Canning's book
- APPENDIX TO CHAPTER X
- §1 (to Ch. X, § 2) [Geometric representation of incomes for three years]
- APPENDIX TO CHAPTER XII
- §1 (to Ch. XII, § 1) Algebraic expression of rate of time preference
- §2 (to Ch. XII,§3) Equality of marginal rate of time preference and rate of interest implies that desirability of income stream is made a maximum
- APPENDIX TO CHAPTER XIII
- §1 (to Ch. XIII, § 9) Rate of return over cost expressed in the notation of the calculus
- §2 (to Ch. XIII, § 9) Rate of return over cost derived by differential equations
- §3 (to Ch. XIII. § 7, also § 9) Mathematical proof that the principle of maximum present value is identical with the principle that the marginal rate of return over cost is equal to the rate of interest.
- §4 (to Ch. XIII, § 9) Geometrical explanation of the proposition expounded in § 3 of this Appendix
- §5 (to Ch. XIII, § 9) Maximum total desirability is found when rate of time preference is equal to the rate of interest
- §6 (to Ch. XIII, § 9) Walras and Pareto
- APPENDIX TO CHAPTER XIX
- §1 (to Ch. XIX, § 4) Tables giving basic data
- §2 (to Ch. XIX, § 6) Tables of interest rates
- APPENDIX TO CHAPTER XX
- §1 (to Ch. XX, § 17) Waiting as a Cost
- BIBLIOGRAPHY
- I. WORKS ON INTEREST THEORY.
- 1. Books:
- 2. Articles:
- II. OTHER WORKS DEALING WITH INTEREST.
- 1. Books:
- 2. Articles:

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