Foundations of Economic Analysis


Foundations of Economic Analysis is a book by Paul A. Samuelson published in 1947 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 and stability of equilibrium as to economic systems. 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 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:
Its other stated purpose is to show how operationally meaningful theorems can be described with a small number of analogous methods. Thus, "a general theory of economic theories".

Topical outline

The body of the book is 353 pages. Topics and applications covered include the following.
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".
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.
Samuelson finds three sources of meaningful theorems sufficient to illuminate his purposes:
  • maximizing behavior of economic units
  • economic systems in stable equilibrium
  • qualitative properties between two or more variables, such as an alleged technological relation or psychological law.
Part I conjectures that meaningful theorems for economic units is a stable equilibrium of the system. Stability of equilibrium is proposed as the principal source of operationally meaningful theorems for economic systems.
Analogies from physics are conspicuous, such as the Le Chatelier principle and correspondence principle, but they are given a nontrivially generalized formulation and application. They and mathematical constructions, such as Lagrangian multipliers, are given an operational economic interpretation. The generalized Le Chatelier principle is for a maximum condition of equilibrium: where all unknowns of the function are independently variable, auxiliary constraints reduce the response to a parameter change. Thus, factor-demand and commodity-supply elasticities are hypothesized to be lower in the short run than in the long run because of the fixed-cost constraint in the short run. In the course of analysis, comparative statics, changes in equilibrium of the system that result from a parameter change of the system, is formalized and most clearly stated. The correspondence principle is that the stability of equilibrium for a system implies meaningful theorems in comparative statics. Alternatively, the hypothesis of stability imposes directional restrictions on the movement of the system. The correspondence is between comparative statics and the dynamics implied by stability of equilibrium.
Chapter VIII on welfare economics is described as an attempt "to give a brief but fairly complete survey of the whole field of welfare economics". This Samuelson does in 51 pages, including his exposition of what became known as the Bergson–Samuelson social welfare function. Theorems derived in welfare economics, he notes, are deductive implications of assumptions that are not refutable, thus not meaningful in a certain sense. Still, the social welfare function can represent any index of the economic measures of any logically possible ethical belief system that is required to order any feasible social configurations as "better than", "worse than", or "indifferent to" each other. It also definitively elucidates the notion of Pareto optimality and the "germ of truth in Adam Smith's doctrine of the invisible hand".
The final pages of the book outline possible directions analytical methods might take, including for example models that show how:
Samuelson closes by expressing hope in the future use of comparative dynamics to:

Appendices

There are two mathematical appendices totalling 83 pages. The first gathers and develops "very briefly" and "without striving for rigor" results on maximization conditions and quadratic forms used in the book and not conveniently collected elsewhere. The other is on difference equations and other functional equations.

Enlarged edition

The 1983 enlarged edition includes an additional 12-page "Introduction" and a new 145-page appendix with some post-1947 developments in analytical economics, including how conclusions of the book are affected by them.

Assessments

  • Kenneth Arrow describes Foundations as "the only example I know of a doctoral dissertation that is a treatise, perhaps I should say of a treatise that has so much originality in every part that it is entitled to be accepted as a thesis."
  • Richard N. Cooper writes that the book "drastically redirected the advanced study of economics toward greater and more productive use of mathematics."
  • Notwithstanding the important work of Arrow, Kotaro Suzumura affirms the Bergson-Samuelson social welfare function as "logically impeccable."
  • The Nobel Prize is applicable to Foundations: "for the scientific work through which has developed static and dynamic economic theory and actively contributed to raising the level of analysis in economic science."
  • Samuelson himself assessed Foundations five decades later.
  • Roger E. Backhouse writes that "Samuelson's Foundations played a major role in defining how economic theory was undertaken for many years after the Second World War." He cites Samuelson on Joseph Schumpeter, Wassily Leontief, Gottfried Haberler, and Alvin Hansen in "teach him modern economic analysis but mak it clear that the main influence on Foundations was E. B. Wilson." "As economics became progressively more mathematical," he writes, "with graduate students increasingly expected to construct formal models of maximizing consumers and firms, Foundations was widely seen as the canonical exposition of such methods."