Production Theory and Indivisible Commodities. (PSME-3), Volume 3 (Princeton Studies in Mathematical Economics)

One of the usual assumptions in economic theory is that an entity called a commodity can be measured or that the amount of it can be represented by any real number. The functions (or other types of mapping) with which the economist deals, such as production functions, demand curves, and cost functions are assumed to be defined for real number arrays and to behave properly with respect to various criteria of continuity. Assumptions of this sort imply an acceptance of commodity divisibility. However, it is possible that in many instances indivisible rather than divisible commodities are the more relevant factors. This book incorporates the notion of indivisibility in a limited way into an analysis of production and allocation in the belief that there is a large class of problems for which this type of analysis is relevant. Originally published in 1969. The **Princeton Legacy Library** uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. Preface Contents Chapter 1. Introduction 1.1 Indivisible Commodities 1.2 Efficiency and Pareto Optimality 1.3 The Problem of Attaining Efficiency 1.4 Plan of Attack Chapter 2. Production Possibilities, Attainability, Prices, Efficiency, and Profit Maximization 2.1 Introduction 2.2 Production Possibilities 2.3 Commodities 2.4 Resources and Attainability 2.5 Efficiency 2.6 Additivity and Inaction 2.7 Disposal 2.8 Closure 2.9 Properties of the Convex Hull F 2.10 Pricing 2.11 Profit Maximization 2.12 Pricing and Efficiency 2.13 The Missing Postulate 2.14 Conclusions Chapter 3. Indivisible Commodities and Returns to Scale 3.1 Introduction 3.2 The Meaning of an Indivisible Commodity 3.3 Integer Convexity 3.4 Geometric Interpretation of Integer Convexity 3.5 Joint Use and Joint Production 3.6 Returns to Scale 3.7 Profit Maximization and Increasing Returns 3.8 Conclusions Chapter 4. Substitution and Price Discrimination 4.1 Introduction 4.2 Substitution 4.3 Discriminatory Pricing 4.4 Profit Maximization and Discriminatory Pricing 4.5 Conclusion Chapter 5. Attaining Efficiency 5.1 Introduction 5.2 Constant Returns 5.3 Substitution 5.4 Near Profit Maximization 5.5 Discriminatory Pricing 5.6 Conclusions Chapter 6. Integer Activity Analysis 6.1 The Technology 6.2 The Linear Programming Case 6.3 A Digression into Some Number Theory 6.4 The Modified Integer Programming Problem 6.5 The Original Integer Programming Problem 6.6 Odd-Lot Pricing 6.7 Discriminatory Pricing 6.8 Conclusions Chapter 7. Conclusion 7.1 Pricing and Increasing Returns 7.2 Scope of the Analysis Appendix A.1 Vectors and Spaces A.2 Sets and Functions A.3 Cones Index One of the usual assumptions in economic theory is that an entity called a commodity can be measured or that the amount of it can be represented by any real number. The functions (or other types of mapping) with which the economist deals, such as production functions, demand curves, and cost functions are assumed to be defined for real number arrays and to behave properly with respect to various criteria of continuity. Assumptions of this sort imply an acceptance of commodity divisibility. However, it is possible that in many instances indivisible rather than divisible commodities are the more relevant factors. This book incorporates the notion of indivisibility in a limited way into an analysis of production and allocation in the belief that there is a large class of problems for which this type of analysis is relevant. Originally published in 1969. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.