Princeton Studies in Mathematical Economics – serie

While traditional price theory has successfully elucidated national income distribution in a perfectly competitive economy, little is known today about the overall working of a noncompetitive economy. This book moves to remedy the imbalance by sketching a general equilibrium theory of a noncompetitive economy. Developing his theory in the world of the standard Leontief system, Hukukane Nikaido attempts to construct objective demand functions reflecting the interdependence of economic agents in the real world upon which the monopolist's control of prices or output ultimately depends. Originally published in 1975. 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.

Can every allocation in the core of an economy be decentralized by a suitably chosen price system? Werner Hildenbrand shows that the answer is yes if the economy has "many" participating agents and if the influence of every individual agent on collective actions is "negligible." To give a general and precise definition of economics with this property he considers both economies with a continuum of agents, and a sequence of economies with an increasing number of participants. In both cases this leads to a measure theoretic formulation of economic equilibrium analysis. In the first part of the book the relevant mathematics is developed. In the second part the continuity and convexity properties of the total demand of a consumption sector are investigated. An important result is the equivalence between the core and the set of Walras equilibria for an exchange economy with a continuum of agents. The author then deals with limit theorems on the core for purely competitive sequences of exchange economies. In the last chapter the core and the set of Walras equilibria for a coalition production economy and the relation between these two equilibrium concepts are studied.Originally published in 1974. 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.

A sequel to his frequently cited Cost and Production Functions (1953), this book offers a unified, comprehensive treatment of these functions which underlie the economic theory of production. The approach is axiomatic for a definition of technology, by mappings of input vectors into subsets of output vectors that represent the unconstrained technical possibilities of production. To provide a completely general means of characterizing a technology, an alternative to the production function, called the Distance Function, is introduced. The duality between cost function and production function is developed by introducing a cost correspondence, showing that these two functions are given in terms of each other by dual minimum problems. The special class of production structures called Homothetic is given more general definition and extended to technologies with multiple outputs. Originally published in 1971. 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.

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.

The important data of economics are in the form of time series; therefore, the statistical methods used will have to be those designed for time series data. New methods for analyzing series containing no trends have been developed by communication engineering, and much recent research has been devoted to adapting and extending these methods so that they will be suitable for use with economic series. This book presents the important results of this research and further advances the application of the recently developed Theory of Spectra to economics. In particular, Professor Hatanaka demonstrates the new technique in treating two problems-business cycle indicators, and the acceleration principle existing in department store data. Originally published in 1964. 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.

The utility idea has had a long history in economics, especially in the explanation of demand and in welfare economics. In a comprehensive survey and critique of the Slutsky theory and the pattern to which it belongs in the economic context, S. N. Afriat offers a resolution of questions central to its main idea, including sufficient conditions as well. Originally published in 1980. 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.

While traditional price theory has successfully elucidated national income distribution in a perfectly competitive economy, little is known today about the overall working of a noncompetitive economy. This book moves to remedy the imbalance by sketching a general equilibrium theory of a noncompetitive economy. Developing his theory in the world of the standard Leontief system, Hukukane Nikaido attempts to construct objective demand functions reflecting the interdependence of economic agents in the real world upon which the monopolist's control of prices or output ultimately depends. Originally published in 1975. 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.

Can every allocation in the core of an economy be decentralized by a suitably chosen price system? Werner Hildenbrand shows that the answer is yes if the economy has "many" participating agents and if the influence of every individual agent on collective actions is "negligible." To give a general and precise definition of economics with this property he considers both economies with a continuum of agents, and a sequence of economies with an increasing number of participants. In both cases this leads to a measure theoretic formulation of economic equilibrium analysis. In the first part of the book the relevant mathematics is developed. In the second part the continuity and convexity properties of the total demand of a consumption sector are investigated. An important result is the equivalence between the core and the set of Walras equilibria for an exchange economy with a continuum of agents. The author then deals with limit theorems on the core for purely competitive sequences of exchange economies. In the last chapter the core and the set of Walras equilibria for a coalition production economy and the relation between these two equilibrium concepts are studied.Originally published in 1974. 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.

A sequel to his frequently cited Cost and Production Functions (1953), this book offers a unified, comprehensive treatment of these functions which underlie the economic theory of production. The approach is axiomatic for a definition of technology, by mappings of input vectors into subsets of output vectors that represent the unconstrained technical possibilities of production. To provide a completely general means of characterizing a technology, an alternative to the production function, called the Distance Function, is introduced. The duality between cost function and production function is developed by introducing a cost correspondence, showing that these two functions are given in terms of each other by dual minimum problems. The special class of production structures called Homothetic is given more general definition and extended to technologies with multiple outputs. Originally published in 1971. 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.

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.

Game theory has brought into economics an uncertainty principle similar to the one brought into physics by the quantum theory. Professor Barch's main purpose in this book is to show how one can construct realistic economic theories by taking uncertainty into account instead of dismissing it. He brings together a number of recent developments in different fields of economics and other social sciences in which uncertainty and chance play a central role and shows that they really constitute an entity. These developments include the revisions of utility, the introduction of game theory as a basic tool, and the view of the foundations of probability theory adopted by modern Bayesian statisticians. Originally published in 1968. 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.