Value, Capital and Growth

J. N. Wolfe, Gabriel R. Ricci, J. N. Wolfe, Gabriel R. Ricci

• Publisher: Routledge
• Year: 2017
• Print ISBN: 9781138540224
• eBook ISBN: 9781351300186
• Topic: Economia
• Subtopic: Teoria economica

Value, Capital and Growth was written as a mark of honor to Sir John Hicks on the occasion of his retirement as Drummond Professor of Political Economy at the University of Oxford. As the title implies, most of the essays are directed to the development of the three great topics of modern economic theory to which he contributed--Value, Capital, and Growth. More specifically, there are important papers on general equilibrium, aggregation, and index numbers-- all topics of deep interest in international economics.The volume is particularly noteworthy for a number of papers exploring hitherto unrealized implications of general equilibrium models. There are also several papers dealing with mathematical economics as they relate to trade and development, which will be of great interest to students of those fields. Few theorists possessed Hicks catholicity in economics and his interest in and appetite for all branches of applied economics, and especially comparative economic history. His interests ranged from Italian Renaissance banking to academic publishing and the export and import of scholarly works,The international eminence of the contributors and the quality of their work ensure that this volume is a fitting tribute to a great economist and that it will be studied carefully for many years. No effort was spared to present the work in a style and format worthy of the subject and of the occasion. The volume includes masterful contributions by Kenneth Arrow, Jagdish Bhagwati, Roy Harrod, Paul A. Samuelson, Robert M. Solow, and Alan A. Walters among others, and contains a full biographical and bibliographical data base on Hicks.J.N. Wolfe was professor of economics at the University of Edinburgh until his retirement.

1

Optimal Capital Policy with Irreversible Investment

Kenneth J. Arrow

Introduction

It is Sir John Hicks’s Value and Capital which taught us clearly the formulation of capital theory as an optimization problem for the firm. He set a general framework within which all subsequent work has taken place.

If one may generalize a bit roughly, the principal subsequent innovation has been the more explicit recognition of the recursive nature of the production process. As a rough empirical generalization, the links between inputs and outputs at different points of time are built up out of links between successive time points. In discrete-time (period) analysis, this means that outputs at time t +1 are determined directly by inputs at time t, independent of earlier inputs; the latter may still have an indirect influence by affecting the availability of the inputs at time t. In continuous-time analysis, which will be employed here, the basic production relation is between the stocks of capital goods and the flows of current inputs and outputs; the earlier past is controlling only in that the stock of capital goods is a cumulation of past flows.

This recursive aspect of the production process simplifies analysis and computation, as was first recognized in the context of inventory theory in the magisterial work of Massé (1946) (unfortunately ignored in the English-language literature) and independently by Arrow, Harris and Marschak (1951). Subsequently, the mathematician Bellman (1957) recognized the basic principle of recursive optimization common to inventory theory, sequential analysis of statistical data, and a host of other control processes in the technological and economic realms and developed the set of computational methods and principles known as dynamic programming. Finally, the Russian mathematician Pontryagin and his associates (1962) developed an elegant theory of control of recursive processes related both to Bellman’s work and to the classical calculus of variations. The Pontr-yagin principle, which will be used in this paper, has the great advantage of yielding economically interesting results very naturally.

This paper follows several others investigating under various hypotheses the optimal policy of a firm with regard to the holding of fixed capital (Arrow, Beckmann and Karlin, 1958; Arrow, 1962b; Nerlove and Arrow, 1962; Arrow, 1964). Assume, for simplicity, that there is only one type of capital good, all other inputs and outputs being flows. Then for any fixed stock of capital goods, there is at any moment a most profitable current policy with regard to flow variables; we assume the flow optimization to have taken place and therefore have defined...

Table of contents

• Cover Page
• Title Page
• Copyright
• Contents
• Introduction by J.N. Wolfe
• 1 Optimal Capital Policy with Irreversible Investment
• 2 Trade Liberalization among LDCs, Trade Theory, and Gatt Rules
• 3 Income, Wealth, and the Theory of Consumption
• 4 Taste and Quality Change in the Pure Theory of the True Cost-of-Living Index
• 5 Measuring the Quantities of Fixed Factors
• 6 What is a Model?
• 7 Normal Backwardation
• 8 Wicksell on the Facts: Prices and Interest Rates, 1844 to 1914
• 9 A Partial Theoretical Solution of the Problems of the Incidence of Import Duties
• 10 Time, Interest, and the Production Function
• 11 The Principle of Two-stage Maximization in Price Theory
• 12 Two Classical Monetary Models
• 13 Information and Period Analysis in Economic Decisions
• 14 On Hicksian Stability
• 15 Accumulation Programs of Maximum Utility and the von Neumann Facet
• 16 Free Trade and Development Economics
• 17 An Economic Test of Sir John Hicks’s Theory of Biased Induced Inventions
• 18 Hicksian Stability, Currency Markets, and the Theory of Economic Policy
• 19 Two Generalizations of the Elasticity of Substitution
• 20 Short-run Adjustment of Employment to Output
• 21 Time Preference, the Consumption Function, and Optimum Asset Holdings
• 22 The Demand for Money Expectations and Short and Long Rates
• Sir John Hicks: Biographical and Bibliographical Data
• List of Works Referred to