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Encyclopedia > Foundations of Economic Analysis

Foundations of Economic Analysis is a book by Paul A. Samuelson published in 1947 (Enlarged ed., 1983). With a portent of the author's gift for concision, the book begins: Paul Samuelson (born May 15, 1915) is an American economist known for his work in many fields of economics. ...

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). Eliakim Hastings Moore (January 26 1862, Marietta, Ohio – December 30 1932, Chicago, Illinois) was an American mathematician. ... An operational definition is a description of something — such as a variable, term or object — in terms of the specific process or set of validation tests used to determine its presence and quantity. ...

Contents


Topical outline

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

Part I
sales-tax increase on equilibrium for a firm
Part II
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

General Equilbrium (linear) supply and demand curves. ... The supply and demand model describes how prices vary as a result of a balance between product availability at each price (supply) and the desires of those with purchasing power at each price (demand). ... In economics, profit maximization is the process by which a firm determines the price and output level that returns the greatest profit. ... Consumer theory is a theory of economics. ... Comparative statics is the comparison of two different equilibrium states, before and after a change in one of the variables. ... The supply and demand model describes how prices vary as a result of a balance between product availability at each price (supply) and the desires of those with purchasing power at each price (demand). ... An isoquant map where Q3 > Q2 > Q1. ... Consumer theory is a theory of economics. ... In economics, elasticity is the ratio of the incremental percentage change in one variable with respect to an incremental percentage change in another variable. ... // Definition A composite good is an abstraction used in economics that represents all other choices of consumption that can be made. ... Cardinal utility theory states that the utility (satisfaction) gained from a particular good or service can be measured in the same way as distance, temperature and time can. ... Welfare economics is a branch of economics that uses microeconomic techniques to simultaneously determine the allocational efficiency of a macroeconomy and the income distribution consequences associated with it. ... General Equilbrium (linear) supply and demand curves. ... The IS curve moves to the right, causing higher interest rates and expansion in the real economy (real GDP). ... In an economic model, an endogenous change is one that comes from inside the model and is explained by the model itself. ... Exogenous (or exogeneous) (from the Greek words exo and gen, meaning outside and production) refers to an action or object coming from outside a system. ... In an economic model, an endogenous change is one that comes from inside the model and is explained by the model itself. ... Stochastic, from the Greek stochos or goal, means of, relating to, or characterized by conjecture; conjectural; random. ... General Equilbrium (linear) supply and demand curves. ... Marie-Ésprit-Léon Walras (December 16, 1834 in Évreux, France - January 5, 1910 in Clarens, near Montreux, Switzerland) was a French economist, considered by Joseph Schumpeter as the greatest of all economists. He was a mathematical economist associated with the creation of the general equilibrium theory. ... Exogenous growth model, also known as the Neo-classical model or Solow growth model is a term used to sum up the contributions of various authors to a model of long-run economic growth within the framework of neoclassical economics. ...

Methods and analysis

The front motto of the book is that of J. Willard Gibbs: "Mathematics is a Language." The book attempts to show how its purposes can be parsimoniously and fruitfully met in the 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). Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American physical chemist. ...


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 aurhor 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. 3-4). The Logic of Scientific Discovery is a 1959 book by Karl Popper. ...


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 a market and an economy) in stable equilibrium
  • qualitative properties in equilibrium states between two or more variables, such as an alleged technological relation or psychological law (indexed by the sign of the relevant derivative).

Part I hypothesizes that meaningful theorems for economic units 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. In mathematics, the derivative is defined as the instantaneous rate of change of a function. ... In mathematics, particularly in calculus, a stationary point is a point on the graph of a function where the tangent to the graph is parallel to the x-axis or, equivalently, where the derivative of the function equals zero (known as a critical number). ...


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 principle source of operationally meaningful theorems for economic systems (p. 5).


Analogies from physics (and biology) 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 Lagrangean 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 than in the long run because of the fixed-cost constraint in the short run) (pp. 36, 38; Hatta, 1987, p. 155). The correspondence principle is that the stability of equilibrium for a system (such as a market or economy) implies meaningful theorems in comparative statics (changes in equilibrium of the system that result from a parameter change of the system), and conversely. Alternatively, the hypothesis of stability imposes directional restrictions on the movement of the system (Samuelson, pp. 258, 5). The correspondence is between (comparative) statics and the dynamics implied by stability of equilibrium. In chemistry, Le Chateliers principle can be used to predict the effect of a change in conditions on a chemical equilibrium. ... In physics, the correspondence principle is a principle, first invoked by Niels Bohr in 1923, which states that the behavior of quantum mechanical systems reduce to classical physics in the limit of large quantum numbers. ... Fig. ... Comparative statics is the comparison of two different equilibrium states, before and after a change in one of the variables. ... Statics is the branch of physics concerned with physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at rest under the action of external forces of equilibrium. ...

The starting point of the analysis is the postulate of maximizing behavior. The point is not (or not only) that everyone is out to maximize (Fischer, 1987, p. 235), even if true. Rather, first- and in particular higher-order (derivative) conditions of equilibrium at the maximum imply local behavioral relations (Samuelson, p. 16). The stability of equilibrium with sufficient other hypothetical qualitative restrictions then generates testable hypotheses (pp. 16, 28-29). Even where there is no context for purposive maximizing behavior, reduction to a maximization problem may be a convenient device for developing properties of the equilibrium, from which, however, no "teleological or normative welfare significance" is warranted (pp. 52-53).

The chapter on welfare economics 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 or not) of the economic measures of any logically possible ethical belief system that is required to order any (hypothetically) feasible social configurations as "better than," "worse than," or "indifferent to" each other (p. 221). It also definitively elucidates (Fischer, 1987, p. 236) the notion of Pareto optimality and the "germ of truth in Adam Smith's doctrine of the Invisible Hand" (Samuelson, 1983, p. xxiv). Teleology (telos: end, purpose) is the philosophical study of design, purpose, directive principle, or finality in nature or human creations. ... Normative economics is the branch of economics that incorporates value judgments about what the economy should be like or what particular policy actions should be recommended to achieve a desirable goal. ... Welfare economics is a branch of economics that uses microeconomic techniques to simultaneously determine the allocational efficiency of a macroeconomy and the income distribution consequences associated with it. ... A social welfare function, in welfare economics, is a function which gives a measure of the material welfare of society, given a number of economic variables as inputs. ... Cardinal utility theory states that the utility (satisfaction) gained from a particular good or service can be measured in the same way as distance, temperature and time can. ... In mathematics, a total order or linear order on a set X is any binary relation on X that is antisymmetric, transitive, and total. ... Pareto efficiency, or Pareto optimality, is a central concept in game theory with broad applications in economics, engineering and the social sciences. ... The invisible hand is a metaphor created by Adam Smith to illustrate how those who seek wealth, by following their individual self-interest, inadvertently stimulate the economy and assist the poor. ...


The final pages of the book (pp. 354-55) 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: Deficit spending is the amount by which a government, private company, or individuals spending exceeds income over a particular period of time, also called simply deficit, or budget deficit, the opposite of budget surplus. ... In economics, crowding out theoretically occurs when the government expands its borrowing more to finance increased expenditure or tax cuts in excess of revenue (i. ... Mortality rate (the word mortality comes from mortal, which originates from Latin mors, death) is the number of deaths (from a disease or in general) per 1000 people and typically reported on an annual basis. ... Demography is the study of human population dynamics. ... Countries by population growth rate Population growth is changing of the amount of population over time. ...

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 maxima and quadratic forms used in the book and not conveniently collected elsewhere (p. 389). The other is on difference equations ("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 (1983, p. 19) 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 of Arrow, Kotaro Suzumura (1987, p. 420) affirms the Bergson-Samuelson social welfare function as "logically impeccable."
  • The Nobel Prize citation is applicable to Foundations: "for the scientific work through which [Samuelson] has developed static and dynamic economic theory and actively contributed to raising the level of analysis in economic science."

Social Choice and Individual Values is a book written by Kenneth Arrow first published in 1951. ...

See also

Neoclassical economics refers to a general approach (a metatheory) to economics based on supply and demand which depends on individuals (or any economic agent) operating rationally, each seeking to maximize their individual utility or profit by making choices based on available information. ... Paul Anthony Samuelson Paul A. Samuelson (born May 15, 1915, in Gary, Indiana) is an American economist known for his work in many fields of economics. ... A social welfare function, in welfare economics, is a function which gives a measure of the material welfare of society, given a number of economic variables as inputs. ...

References

  • Arrow, Kenneth J. (1983), "Contribution to Welfare Economics," E. Cary Brown and Robert M. Solow, ed., Paul Samuelson and Modern Economic Theory, pp. 15-30.
  • Cooper, Richard N. (1997), Foreign Affairs, Sept./Oct.
  • Fischer, Stanley (1987), “Samuelson, Paul Anthony," The New Palgrave: A Dictionary of Economics, v. 4, pp. 234-41.
  • Hatta, Tatsuo (1987), "Le Chatelier principle," The New Palgrave: A Dictionary of Economics, v. 3, pp. 155-57.
  • Samuelson, Paul A. (1947, Enlarged ed. 1983). Foundations of Economic Analysis, Harvard University Press. ISBN 0-674-31301-1
  • Suzumura, Kotaro (1987), “social welfare function," The New Palgrave: A Dictionary of Economics, v. 4, pp. 418-20.

Kenneth Arrow Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Bank of Sweden Prize in Economic Sciences in 1972. ... Robert Merton Solow (born August 23, 1924) is an American economist particularly known for his work on the theory of economic growth. ... Richard N. Cooper was acting United States Secretary of State under President Jimmy Carter for one day in 1980. ... Stanley Fischer, Governor of the Bank of Israel Stanley Fischer (1943-) is an economist and the current Governor of the Bank of Israel. ...

External links

  • "Maximum Principles in Analytical Economics", link to Nobel Prize lecture
  • Nobel Prize presentation speech, in which the first 3 areas discussed apply to Foundations
  • A History of Economic Thought biography from The New School

 
 

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