经济分析基础 (1947)

Foundations of Economic Analysis is a book by Paul A. Samuelson published in 1947 (Enlarged ed., 1983) by Harvard University Press. It is based on Samuelson's 1941 doctoral dissertation at Harvard University. The book sought to demonstrate a common mathematical structure underlying multiple branches of economics from two basic principles: maximizing behavior of agents (such as of utility by consumers and profits by firms) and stability of equilibrium as to economic systems (such as markets or economies). Among other contributions, it advanced the theory of index numbers and generalized welfare economics. It is especially known for definitively stating and formalizing qualitative and quantitative versions of the "comparative statics" method for calculating how a change in any parameter (say, a change in tax rates) affects an economic system. One of its key insights about comparative statics, called the correspondence principle, states that stability of equilibrium implies testable predictions about how the equilibrium changes when parameters are changed.

Introduction

The front page quotes the motto of J. Willard Gibbs: "Mathematics is a language." The book begins with this statement:

The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features. This fundamental principle of generalization by abstraction was enunciated by the eminent American mathematician E. H. Moore more than thirty years ago. It is the purpose of the pages that follow to work out its implications for theoretical and applied economics.

Its other stated purpose (p. 3) is to show how operationally meaningful theorems can be described with a small number of analogous methods. Thus, "a general theory of economic theories" (1983, p. xxvi).

Topical outline

The body of the book is 353 pages. Topics and applications covered (all in terms of theory) include the following.

Part I introduction equilibrium systems (such as for a market or economy)

maximizing behavior (such as to profits by a firm and utility by a consumer) in the calculus sales-tax increase on equilibrium for a firm comparative statics (changes in prices and quantities and other equilibrium variables when underlying conditions change)

cost and production consumer's behavior transformations, elasticities, composite commodities, index numbers, and rationing cardinal utility, constancy of the marginal utility of income, and consumer's surplus welfare economics

Part II stability of equilibrium systems, dynamics (disturbances in equilibrium), and comparative statics the Keynesian system linear and nonlinear systems

Malthusian and optimum population dynamics the business cycle endogenous models mixed exogenous-endogenous theories mixed systems of a linear-stochastic type conclusions (on neoclassical theory from Walras to hints of the future in comparative dynamics, the comparative-statics counterpart of dynamic systems)

Methods and analysis

Samuelson's Foundations demonstrates that economic analysis benefits from the parsimonious and fruitful language of mathematics. In its original version as a dissertation submitted to the David A. Wells Prize Committee of Harvard University in 1941, it was subtitled "The Observational Significance of Economic Theory" (p. ix).

One unifying theme, on the striking formal similarities of analysis in seemingly diverse fields, occurred only in the course of writing on them — from consumer's behavior and production economics of the firm to international trade, business cycles, and income analysis. It dawned on the author that he was prodigal "in proving essentially the same theorems" over and over. His failure of initial intuition, so he suggests, might be less surprising in light of the few economic writings then extant concerned with formulating meaningful theorems – hypotheses about empirical data—that could conceivably be refuted by empirical data (pp. 3–5).

Samuelson (pp. 5, 21–24) finds three sources of meaningful theorems sufficient to illuminate his purposes:

maximizing behavior of economic units (as to utility for a consumer and profit for a firm)

economic systems (including markets and economies) in stable equilibrium qualitative properties between two or more variables, such as an alleged technological relation or psychological law (indexed by the sign of the relevant functional relationship).

Part I conjectures that meaningful theorems for economic units (for example individual households or firms, and for their respective aggregates are almost all derivable from general conditions of equilibrium. The equilibrium conditions can in turn be stated as maximization conditions. So, meaningful theorems reduce to maximization conditions. The calculus of the relations is at a high level of abstraction but with the advantage of numerous applications. Finally, Part I illustrates that there are meaningful theorems in economics, which apply to diverse fields.

Part II concentrates on aggregation of economic units into equilibrium of the system. But the symmetry conditions required for direct maximization of the system, whether a market or even the simplest model of the business cycle, are lacking, in contrast to an economic unit or its corresponding aggregate. What can be hypothetically derived (or rejected in some cases) is a stable equilibrium of the system. (This is an equilibrium of the system such that, if a variable disturbs equilibrium, the system converges to equilibrium.) Stability of equilibrium is proposed as the principal source of operationally meaningful theorems for economic systems (p. 5).