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.
The front page quotes the motto of J. Willard Gibbs: "Mathematics is a language." The book begins with this statement:
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).
The body of the book is 353 pages. Topics and applications covered (all in terms of theory) 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" (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:
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 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 ("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. [1] 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 (Kehoe, 1987, p. 517). [2] 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 and the dynamics implied by stability 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 ( [3] ) 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). |
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" (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 the notion of Pareto optimality and the "germ of truth in Adam Smith's doctrine of the invisible hand" (Samuelson, 1983, p. xxiv; Fischer, 1987, p. 236 [3] ).
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:
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 (p. 389). The other is on difference equations ("for the dynamic economist") and other functional equations.
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.
Microeconomics is a branch of economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms. Microeconomics focuses on the study of individual markets, sectors, or industries as opposed to the national economy as a whole, which is studied in macroeconomics.
Neoclassical economics is an approach to economics in which the production, consumption, and valuation (pricing) of goods and services are observed as driven by the supply and demand model. According to this line of thought, the value of a good or service is determined through a hypothetical maximization of utility by income-constrained individuals and of profits by firms facing production costs and employing available information and factors of production. This approach has often been justified by appealing to rational choice theory.
In microeconomics, supply and demand is an economic model of price determination in a market. It postulates that, holding all else equal, in a competitive market, the unit price for a particular good or other traded item such as labor or liquid financial assets, will vary until it settles at a point where the quantity demanded will equal the quantity supplied, resulting in an economic equilibrium for price and quantity transacted. The concept of supply and demand forms the theoretical basis of modern economics.
In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium. General equilibrium theory contrasts with the theory of partial equilibrium, which analyzes a specific part of an economy while its other factors are held constant. In general equilibrium, constant influences are considered to be noneconomic, or in other words, considered to be beyond the scope of economic analysis. The noneconomic influences may change given changes in the economic factors however, and therefore the prediction accuracy of an equilibrium model may depend on the independence of the economic factors from noneconomic ones.
This aims to be a complete article list of economics topics:
Paul Anthony Samuelson was an American economist who was the first American to win the Nobel Memorial Prize in Economic Sciences. When awarding the prize in 1970, the Swedish Royal Academies stated that he "has done more than any other contemporary economist to raise the level of scientific analysis in economic theory". Economic historian Randall E. Parker has called him the "Father of Modern Economics", and The New York Times considers him to be the "foremost academic economist of the 20th century."
In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the values of economic variables will not change. For example, in the standard text perfect competition, equilibrium occurs at the point at which quantity demanded and quantity supplied are equal.
Welfare economics is a field of economics that applies microeconomic techniques to evaluate the overall well-being (welfare) of a society. This evaluation is typically done at the economy-wide level, and attempts to assess the distribution of resources and opportunities among members of society.
An economic model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes. Frequently, economic models posit structural parameters. A model may have various exogenous variables, and those variables may change to create various responses by economic variables. Methodological uses of models include investigation, theorizing, and fitting theories to the world.
In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous parameter.
Paul Robert Milgrom is an American economist. He is the Shirley and Leonard Ely Professor of Humanities and Sciences at the Stanford University School of Humanities and Sciences, a position he has held since 1987. He is a professor in the Stanford School of Engineering as well and a Senior Fellow at the Stanford Institute for Economic Research. Milgrom is an expert in game theory, specifically auction theory and pricing strategies. He is the winner of the 2020 Nobel Memorial Prize in Economic Sciences, together with Robert B. Wilson, "for improvements to auction theory and inventions of new auction formats".
There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information, and in perfect competition, will be Pareto optimal. The requirements for perfect competition are these:
Michio Morishima was a Japanese heterodox economist and public intellectual who was the Sir John Hicks Professor of Economics at the London School of Economics from 1970 to 1988. He was also professor at Osaka University and member of the British Academy. In 1976 he won the Order of Culture.
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The Sonnenschein–Mantel–Debreu theorem is an important result in general equilibrium economics, proved by Gérard Debreu, Rolf Mantel, and Hugo F. Sonnenschein in the 1970s. It states that the excess demand curve for an exchange economy populated with utility-maximizing rational agents can take the shape of any function that is continuous, has homogeneity degree zero, and is in accordance with Walras's law. This implies that the excess demand function does not take a well-behaved form even if each agent has a well-behaved utility function. Market processes will not necessarily reach a unique and stable equilibrium point.
Qualitative economics is the representation and analysis of information about the direction of change in some economic variable(s) as related to change of some other economic variable(s). For the non-zero case, what makes the change qualitative is that its direction but not its magnitude is specified.
Value and Capital is a book by the British economist John Richard Hicks, published in 1939. It is considered a classic exposition of microeconomic theory. Central results include:
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
In economics, non-convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences and convex budget sets and on producers with convex production sets; for convex models, the predicted economic behavior is well understood. When convexity assumptions are violated, then many of the good properties of competitive markets need not hold: Thus, non-convexity is associated with market failures, where supply and demand differ or where market equilibria can be inefficient. Non-convex economies are studied with nonsmooth analysis, which is a generalization of convex analysis.
James Patrick Quirk was a Caltech professor of economics.