''Foundations of Economic Analysis'' is a book by Paul A. Samuelson published in 1947 (Enlarged ed., 1983) by

Harvard University Press Harvard University Press (HUP) is a publishing house established on January 13, 1913, as a division of Harvard University, and focused on academic publishing. It is a member of the Association of American University Presses. After the reti ...

. It is based on Samuelson's 1941 doctoral dissertation at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

. The book sought to demonstrate a common mathematical structure underlying multiple branches of economics from two basic principles:

maximizing Maximization is a style of decision-making characterized by seeking the best option through an exhaustive search through alternatives. It is contrasted with satisficing, in which individuals evaluate options until they find one that is "good enough" ...

behavior of agents (such as of

utility As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosoph ...

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 In Statistics, Economics and Finance, an index is a statistical measure of change in a representative group of individual data points. These data may be derived from any number of sources, including company performance, prices, productivity, an ...

and generalized

welfare economics Welfare economics is a branch of economics that uses microeconomic techniques to evaluate well-being (welfare) at the aggregate (economy-wide) level. Attempting to apply the principles of welfare economics gives rise to the field of public econ ...

. It is especially known for definitively stating and formalizing

qualitative Qualitative descriptions or distinctions are based on some quality or characteristic rather than on some quantity or measured value. Qualitative may also refer to: *Qualitative property, a property that can be observed but not measured numericall ...

and quantitative versions of the "

comparative statics In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous parameter. As a type of ''static analysis'' it compares two different equilibrium states, after the p ...

" method for calculating how a change in any

parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...

(say, a change in tax rates) affects an economic system. One of its key insights about comparative statics, called the

correspondence principle In physics, the correspondence principle states that the behavior of systems described by the theory of quantum mechanics (or by the old quantum theory) reproduces classical physics in the limit of large quantum numbers. In other words, it says ...

, states that

stability Stability may refer to: Mathematics * Stability theory, the study of the stability of solutions to differential equations and dynamical systems ** Asymptotic stability ** Linear stability ** Lyapunov stability ** Orbital stability ** Structural st ...

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 Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in t ...

: "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

by a consumer) in the calculus : sales-tax increase on equilibrium for a firm *

(changes in

prices and quantities In economics, nominal value is measured in terms of money, whereas real value is measured against goods or services. A real value is one which has been adjusted for inflation, enabling comparison of quantities as if the prices of goods had not c ...

and other equilibrium variables when underlying conditions change) * cost and production * consumer's behavior * transformations, elasticities, composite commodities,

, and rationing *

cardinal utility In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine transformations. Two utility indices are related by an affine transformation if for the value u(x_i) of one in ...

, constancy of the marginal utility of income, and consumer's surplus *

: 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 Endogenous substances and processes are those that originate from within a living system such as an organism, tissue, or cell. In contrast, exogenous substances and processes are those that originate from outside of an organism. For example, ...

models : mixed

exogenous In a variety of contexts, exogeny or exogeneity () is the fact of an action or object originating externally. It contrasts with endogeneity or endogeny, the fact of being influenced within a system. Economics In an economic model, an exogen ...

theories : mixed systems of a linear-

stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...

type * conclusions (on neoclassical theory from Walras to hints of the

future The future is the time after the past and present. Its arrival is considered inevitable due to the existence of time and the laws of physics. Due to the apparent nature of reality and the unavoidability of the future, everything that currentl ...

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 ''market''s 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). Analogies from physics (and biology) are conspicuous, such as the :Le Chatelier principle: Economics and

, 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 ("just-binding" in leaving initial equilibrium unchanged) reduce the response to a parameter change. Thus, factor-demand and commodity-supply elasticities are hypothesized to be lower in the

short run In economics, the long-run is a theoretical concept in which all markets are in equilibrium, and all prices and quantities have fully adjusted and are in equilibrium. The long-run contrasts with the short-run, in which there are some constraints an ...

than in the

long run In economics, the long-run is a theoretical concept in which all markets are in equilibrium, and all prices and quantities have fully adjusted and are in equilibrium. The long-run contrasts with the short-run, in which there are some constraints an ...

because of the fixed-cost constraint in the short run. In the course of analysis, ''

'', changes in equilibrium of the system that result from a

change of the system, is formalized and most clearly stated (Kehoe, 1987, p. 517). The ''correspondence principle'' is that the ''stability'' of equilibrium for a system (such as a market or economy) implies meaningful theorems in comparative statics. Alternatively, the hypothesis of stability imposes directional restrictions on the movement of the system (Samuelson, pp. 258, 5). The correspondence is between comparative

statics Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with t ...

and the dynamics implied by stability of equilibrium. Chapter VIII on

is described as an attempt "to give a brief but fairly complete survey of the whole field of welfare economics" (p. 252). 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 (

cardinal Cardinal or The Cardinal may refer to: Animals * Cardinal (bird) or Cardinalidae, a family of North and South American birds **'' Cardinalis'', genus of cardinal in the family Cardinalidae **'' Cardinalis cardinalis'', or northern cardinal, ...

or not) of the economic measures of any logically possible ethical belief system that is required to

order Order, ORDER or Orders may refer to: * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of ...

any (hypothetically) feasible social configurations as "better than", "worse than", or "indifferent to" each other (p. 221). It also definitively elucidates the notion of

Pareto optimality Pareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engine ...

and the "germ of truth in Adam Smith's doctrine of the

invisible hand The invisible hand is a metaphor used by the British moral philosopher Adam Smith that describes the unintended greater social benefits and public good brought about by individuals acting in their own self-interests. Smith originally mentio ...

" (Samuelson, 1983, p. xxiv; Fischer, 1987, p. 236). The final pages of the book (pp. 354–55) outline possible directions analytical methods might take, including for example models that show how: * deficit financing could produce positive short-run effects on the economy that are swamped by adverse long-run effects on capital accumulation (seriously reconsidered later as crowding out) * declines in age-specific mortality affect the net reproductive rate (whose implications for

population growth Population growth is the increase in the number of people in a population or dispersed group. Actual global human population growth amounts to around 83 million annually, or 1.1% per year. The global population has grown from 1 billion in 1800 to ...

are less abstract than they might first appear). Samuelson closes by expressing hope in the future use of ''comparative dynamics'' to: : aid in the attack upon diverse problems – from the trivial behavior of a single small commodity, to the fluctuations of important components of the business cycle, and even to the majestic problems of economic development.

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 In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, :4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong to ...

used in the book and not conveniently collected elsewhere (p. 389). The other is on

difference equations In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter ...

("for the dynamic economist") 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 Kenneth Joseph Arrow (23 August 1921 – 21 February 2017) was an American economist, mathematician, writer, and political theorist. He was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972. In economi ...

(1983) 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 (1997) writes that the book "drastically redirected the advanced study of economics toward greater and more productive use of mathematics." * Notwithstanding the important

work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an anim ...

of Arrow,

Kotaro Suzumura was a Japanese economist and professor emeritus of Hitotsubashi University and Waseda University. He graduated from Hitotsubashi University in 1966. His research interests were in social choice theory and welfare economics. He was also a Fel ...

(1987) affirms the Bergson-Samuelson social welfare function as "logically impeccable." * The Nobel Prize
citation
is applicable to ''Foundations'': "for the scientific work through which amuelsonhas 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 Roger Edward Backhouse, (born 19 January 1951) is a British economist, economic historian and academic. Since 1996, he has been Professor of the History and Philosophy of Economics at the University of Birmingham. Backhouse is an Associate Edito ...

(2015) 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 Joseph Alois Schumpeter (; February 8, 1883 – January 8, 1950) was an Austrian-born political economist. He served briefly as Finance Minister of German-Austria in 1919. In 1932, he emigrated to the United States to become a professor at H ...

Wassily Leontief Wassily Wassilyevich Leontief (russian: Васи́лий Васи́льевич Лео́нтьев; August 5, 1905 – February 5, 1999), was a Soviet-American economist known for his research on input–output analysis and how changes in one ...

Gottfried Haberler Gottfried von Haberler (; July 20, 1900 – May 6, 1995) was an Austrian-American economist. He worked in particular on international trade. One of his major contributions was reformulating the Ricardian idea of comparative advantage in a neocl ...

, and

Alvin Hansen Alvin Harvey Hansen (August 23, 1887 – June 6, 1975) was an American economist who taught at the University of Minnesota and was later a chair professor of economics at Harvard University. Often referred to as "the American Keynes", he was a w ...

in "teach nghim modern economic analysis but mak ngit clear that the main influence on ''Foundations'' was

he mathematician and physicist He or HE may refer to: Language * He (pronoun), an English pronoun * He (kana), the romanization of the Japanese kana へ * He (letter), the fifth letter of many Semitic alphabets * He (Cyrillic), a letter of the Cyrillic script called ''He'' in ...

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."Backhouse, Roger E. (2015). "Revisiting Samuelson's "Foundations of Economic Analysis," ''Journal of Economic Literature'', 53(2)
p. 347.
/ref>

Notes

References

* Allen, R. G. D. (1949), "The Mathematical Foundations of Economic Theory," ''Quarterly Journal of Economics'', 63(1)
pp. 111–127.
* Boulding, Kenneth E., 1948. "Samuelson's ''Foundations'': The Role of Mathematics in Economics," ''Journal of Political Economy'', 56(3), pp
187-199.
* Carter, C. F., 1950. eview ''Economic Journal'', 60(238), pp
51
55. * Flood, Merrill M., 1950. eview ''Bulletin of the American Mathematical Society'', 56(3), pp
266–267
* May, Kenneth, 1948. eview ''Science & Society'', 13(1), pp
93
95. * Metzler, Lloyd, 1948. eview ''American Economic Review'' 38(5), pp
905
10. * Samuelson, Paul A., 1947, Enlarged ed., 1983. ''Foundations of Economic Analysis''
Description.
Harvard University Press. * _____, 1998. "How ''Foundations'' Came to Be," ''Journal of Economic Literature'', 36(3), pp
1375–1386
* Savage, L. J., 1948. "Samuelson's ''Foundations'': Its Mathematics," ''Journal of Political Economy'', 56(3), pp
200-202.
* Stigler, George J., 1948. eview ''Journal of the American Statistical Association'', 43(244), pp
603-605.
* Tintner, Gerhard (1948). "''Foundations of Economic Analysis'', Paul A. Samuelson," ''Journal of the American Statistical Association'', 43(243), pp
497-99.

External links

link to Nobel Prize lecture

in which the first 3 areas discussed apply to ''Foundations'' {{DEFAULTSORT:Foundations Of Economic Analysis 1947 non-fiction books Costs Production economics Consumer theory Comparative statics Welfare economics 1947 in economics Books about philosophy of economics