APPENDICES

APPENDIX TO CHAPTER I. INCOME AND CAPITAL

PAGB

§ 1. (to Ch. I, § 1). Quotations from Professor Canning’s book 507

APPENDIX TO CHAPTER X. FIRST APPROXIMATIONIN GEOMETRIC TERMS

§ 1 (to Ch. X, §2). Geometric Representation of Incomes forThree Years.508

APPENDIX TO CHAPTER XII. FIRST APPROXIMATIONIN TERMS OF FORMULAS

§1 (to Ch. XII, §1). Algebraic Expression of Rate of Time

Preference .510

§ 2 (to Ch. XII, § 3). Equality of Marginal Rate of TimePreference and Rate of Interest Implies That Desirabilityof Income Stream Is Made a Maximum.511

APPENDIX TO CHAPTER XIII. SECOND APPROXIMA-TION IN TERMS OF FORMULAS

§1 (to Ch. XIII, §9). Rate of Return Over Cost Express!®

in the Notation of the Calculus .513

§ 2 (to Ch. XIII, § 9). Rate of Return Over Cost Derived by

Differential Equations .513

§ 3 (to Ch. XIII, §7 and §9). Mathematical Proof That thePrinciple of Maximum Present Value Is Identical Withthe Principle That the Marginal Rate of Return Over

Cost Is Equal to the Rate of Interest . 514

§4 (to Ch. XIII, §9). Geometrical Explanation of the Propo-sition Expounded in § 3 of This Appendix .516

I 5 (to Ch. XIII, §9). Maximum Total Desirability Is FoundWhen Rate of Time Preference Is Equal to the Rate of In-terest .517

§ 6 (to Ch. XIII, § 9). Walras and Pareto. 518

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