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Neoclassical economics is a term variously used for approaches to economics focusing on the determination of prices, outputs, and income distributions in markets through supply and demand, often mediated through a hypothesized maximization of utility by income-constrained individuals and of profits by cost-constrained firms employing available information and factors of production, in accordance with rational choice theory. Neoclassical economics dominates microeconomics, and together with Keynesian economics forms the neoclassical synthesis which dominates mainstream economics today. Although neoclassical economics has gained widespread acceptance by contemporary economists, there have been many critiques of neoclassical economics, often incorporated into newer versions of neoclassical theory as awareness of economic criteria changes.
The term was originally introduced by Thorstein Veblen in 1900, in his article 'Preconceptions of Economic Science', to distinguish marginalists in the tradition of Alfred Marshall from those in the Austrian School.
"No attempt will here be made even to pass a verdict on the relative claims of the recognized two or three main "schools" of theory, beyond the somewhat obvious finding that, for the purpose in hand, the so-called Austrian school is scarcely distinguishable from the neo-classical, unless it be in the different distribution of emphasis. The divergence between the modernized classical views, on the one hand, and the historical and Marxist schools, on the other hand, is wider, so much so, indeed, as to bar out a consideration of the postulates of the latter under the same head of inquiry with the former." - Veblen
It was later used by John Hicks, George Stigler, and others to include the work of Carl Menger, William Stanley Jevons, John Bates Clark and many others. Today it is usually used to refer to mainstream economics, although it has also been used as an umbrella term encompassing a number of other schools of thought, notably excluding institutional economics, various historical schools of economics, and Marxian economics, in addition to various other heterodox approaches to economics.
Neoclassical economics is characterized by several assumptions common to many schools of economic thought. There is not a complete agreement on what is meant by neoclassical economics, and the result is a wide range of neoclassical approaches to various problem areas and domains—ranging from neoclassical theories of labor to neoclassical theories of demographic changes. As expressed by E. Roy Weintraub, neoclassical economics rests on three assumptions, although certain branches of neoclassical theory may have different approaches:
- People have rational preferences among outcomes that can be identified and associated with a value.
- Individuals maximize utility and firms maximize profits.
- People act independently on the basis of full and relevant information.
From these three assumptions, neoclassical economists have built a structure to understand the allocation of scarce resources among alternative ends—in fact understanding such allocation is often considered the definition of economics to neoclassical theorists. Here's how William Stanley Jevons presented "the problem of Economics".
"Given, a certain population, with various needs and powers of production, in possession of certain lands and other sources of material: required, the mode of employing their labour which will maximize the utility of their produce."
From the basic assumptions of neoclassical economics comes a wide range of theories about various areas of economic activity. For example, profit maximization lies behind the neoclassical theory of the firm, while the derivation of demand curves leads to an understanding of consumer goods, and the supply curve allows an analysis of the factors of production. Utility maximization is the source for the neoclassical theory of consumption, the derivation of demand curves for consumer goods, and the derivation of labor supply curves and reservation demand. Market supply and demand are aggregated across firms and individuals. Their interactions determine equilibrium output and price. The market supply and demand for each factor of production is derived analogously to those for market final output to determine equilibrium income and the income distribution. Factor demand incorporates the marginal-productivity relationship of that factor in the output market.  
Neoclassical economics emphasizes equilibria, where equilibria are the solutions of agent maximization problems. Regularities in economies are explained by methodological individualism, the position that economic phenomena can be explained by aggregating over the behavior of agents. The emphasis is on microeconomics. Institutions, which might be considered as prior to and conditioning individual behavior, are de-emphasized. Economic subjectivism accompanies these emphases. See also general equilibrium.
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Classical economics, developed in the 18th and 19th centuries, included a value theory and distribution theory. The value of a product was thought to depend on the costs involved in producing that product. The explanation of costs in Classical economics was simultaneously an explanation of distribution. A landlord received rent, workers received wages, and a capitalist tenant farmer received profits on their investment. This classic approach included the work of Adam Smith and David Ricardo.
However, some economists gradually began emphasizing the perceived value of a good to the consumer. They proposed a theory that the value of a product was to be explained with differences in utility (usefulness) to the consumer. (In England, economists tended to conceptualize utility in keeping with the Utilitarianism of Jeremy Bentham and later of John Stuart Mill.)
The third step from political economy to economics was the introduction of marginalism and the proposition that economic actors made decisions based on margins. For example, a person decides to buy a second sandwich based on how full they are after the first one, a firm hires a new employee based on the expected increase in profits the employee will bring. This differs from the aggregate decision making of classical political economy in that it explains how vital goods such as water can be cheap, while luxuries can be expensive.
The marginal revolution 
The change in economic theory from classical to neoclassical economics has been called the 'marginal revolution', although it has been argued that the process was slower than the term suggests. It is frequently dated from William Stanley Jevons's Theory of Political Economy (1871), Carl Menger's Principles of Economics (1871), and Léon Walras's Elements of Pure Economics (1874–1877). Historians of economics and economists have debated:
- Whether utility or marginalism was more essential to this revolution (whether the noun or the adjective in the phrase "marginal utility" is more important)
- Whether there was a revolutionary change of thought or merely a gradual development and change of emphasis from their predecessors
- Whether grouping these economists together disguises differences more important than their similarities.
In particular, Jevons saw his economics as an application and development of Jeremy Bentham's utilitarianism and never had a fully developed general equilibrium theory. Menger did not embrace this hedonic conception, explained diminishing marginal utility in terms of subjective prioritization of possible uses, and emphasized disequilibrium and the discrete; further Menger had an objection to the use of mathematics in economics, while the other two modeled their theories after 19th century mechanics. Walras' conception of utility, like that of Menger, was that of usefulness in general, rather than the hedonic conception of Bentham or of Mill; and Walras was more interested in the interaction of markets than in explaining the individual psyche.
Alfred Marshall's textbook, Principles of Economics (1890), was the dominant textbook in England a generation later. Marshall's influence extended elsewhere; Italians would compliment Maffeo Pantaleoni by calling him the "Marshall of Italy". Marshall thought classical economics attempted to explain prices by the cost of production. He asserted that earlier marginalists went too far in correcting this imbalance by overemphasizing utility and demand. Marshall thought that "We might as reasonably dispute whether it is the upper or the under blade of a pair of scissors that cuts a piece of paper, as whether value is governed by utility or cost of production".
Marshall explained price by the intersection of supply and demand curves. The introduction of different market "periods" was an important innovation of Marshall’s:
- Market period. The goods produced for sale on the market are taken as given data, e.g. in a fish market. Prices quickly adjust to clear markets.
- Short period. Industrial capacity is taken as given. The level of output, the level of employment, the inputs of raw materials, and prices fluctuate to equate marginal cost and marginal revenue, where profits are maximized. Economic rents exist in short period equilibrium for fixed factors, and the rate of profit is not equated across sectors.
- Long period. The stock of capital goods, such as factories and machines, is not taken as given. Profit-maximizing equilibria determine both industrial capacity and the level at which it is operated.
- Very long period. Technology, population trends, habits and customs are not taken as given, but allowed to vary in very long period models.
Marshall took supply and demand as stable functions and extended supply and demand explanations of prices to all runs. He argued supply was easier to vary in longer runs, and thus became a more important determinant of price in the very long run.
Further developments 
An important change in neoclassical economics occurred around 1933. Joan Robinson and Edward H. Chamberlin, with the near simultaneous publication of their respective books, The Economics of Imperfect Competition (1933) and The Theory of Monopolistic Competition (1933), introduced models of imperfect competition. Theories of market forms and industrial organization grew out of this work. They also emphasized certain tools, such as the marginal revenue curve.
Joan Robinson's work on imperfect competition, at least, was a response to certain problems of Marshallian partial equilibrium theory highlighted by Piero Sraffa. Anglo-American economists also responded to these problems by turning towards general equilibrium theory, developed on the European continent by Walras and Vilfredo Pareto. J. R. Hicks's Value and Capital (1939) was influential in introducing his English-speaking colleagues to these traditions. He, in turn, was influenced by the Austrian School economist Friedrich Hayek's move to the London School of Economics, where Hicks then studied.
These developments were accompanied by the introduction of new tools, such as indifference curves and the theory of ordinal utility. The level of mathematical sophistication of neoclassical economics increased. Paul Samuelson's Foundations of Economic Analysis (1947) contributed to this increase in mathematical modelling.
The interwar period in American economics has been argued to have been pluralistic, with neoclassical economics and institutionalism competing for allegiance. Frank Knight, an early Chicago school economist attempted to combine both schools. But this increase in mathematics was accompanied by greater dominance of neoclassical economics in Anglo-American universities after World War II.
Hicks' book, Value and Capital had two main parts. The second, which was arguably not immediately influential, presented a model of temporary equilibrium. Hicks was influenced directly by Hayek's notion of intertemporal coordination and paralleled by earlier work by Lindhal. This was part of an abandonment of disaggregated long run models. This trend probably reached its culmination with the Arrow-Debreu model of intertemporal equilibrium. The Arrow-Debreu model has canonical presentations in Gérard Debreu's Theory of Value (1959) and in Arrow and Hahn's "General Competitive Analysis" (1971).
Many of these developments were against the backdrop of improvements in both econometrics, that is the ability to measure prices and changes in goods and services, as well as their aggregate quantities, and in the creation of macroeconomics, or the study of whole economies. The attempt to combine neo-classical microeconomics and Keynesian macroeconomics would lead to the neoclassical synthesis which has been the dominant paradigm of economic reasoning in English-speaking countries since the 1950s. Hicks and Samuelson were for example instrumental in mainstreaming Keynesian economics.
Macroeconomics influenced the neoclassical synthesis from the other direction, undermining foundations of classical economic theory such as Say's Law, and assumptions about political economy such as the necessity for a hard-money standard. These developments are reflected in neoclassical theory by the search for the occurrence in markets of the equilibrium conditions of Pareto optimality and self-sustainability.
Neoclassical economics is sometimes criticized for having a normative bias. In this view, it does not focus on explaining actual economies, but instead on describing a "utopia" in which Pareto optimality applies.
The assumption that individuals act rationally may be viewed as ignoring important aspects of human behavior. Many see the "economic man" as being quite different from real people. Many economists, even contemporaries, have criticized this model of economic man. Thorstein Veblen put it most sardonically. Neoclassical economics assumes a person to be,
"a lightning calculator of pleasures and pains, who oscillates like a homogeneous globule of desire of happiness under the impulse of stimuli that shift about the area, but leave him intact."
Large corporations might perhaps come closer to the neoclassical ideal of profit maximization, but this is not necessarily viewed as desirable if this comes at the expense of neglect of wider social issues. The response to this is that neoclassical economics is descriptive and not normative. It addresses such problems with concepts of private versus social utility.
Problems exist with making the neoclassical general equilibrium theory compatible with an economy that develops over time and includes capital goods. This was explored in a major debate in the 1960s—the "Cambridge capital controversy"—about the validity of neoclassical economics, with an emphasis on the economic growth, capital, aggregate theory, and the marginal productivity theory of distribution. There were also internal attempts by neoclassical economists to extend the Arrow-Debreu model to disequilibrium investigations of stability and uniqueness. However a result known as the Sonnenschein-Mantel-Debreu theorem suggests that the assumptions that must be made to ensure that the equilibrium is stable and unique are quite restrictive.
Neoclassical economics is also often seen as relying too heavily on complex mathematical models, such as those used in general equilibrium theory, without enough regard to whether these actually describe the real economy. Many see an attempt to model a system as complex as a modern economy by a mathematical model as unrealistic and doomed to failure. A famous answer to this criticism is Milton Friedman's claim that theories should be judged by their ability to predict events rather than by the realism of their assumptions. Mathematical models also include those in game theory, linear programming, and econometrics. Critics of neoclassical economics are divided into those who think that highly mathematical method is inherently wrong and those who think that mathematical method is potentially good even if contemporary methods have problems.
In general, allegedly overly unrealistic assumptions are one of the most common criticisms towards neoclassical economics. It is fair to say that many (but not all) of these criticisms can only be directed towards a subset of the neoclassical models (for example, there are many neoclassical models where unregulated markets fail to achieve Pareto-optimality and there has recently been an increased interest in modeling non-rational decision making).
See also 
- Antonietta Campus (1987), "marginal economics", The New Palgrave: A Dictionary of Economics, v. 3, p. 323.
- Clark, B. (1998). Principles of political economy: A comparative approach. Westport, Connecticut: Praeger.
- Colander, David; The Death of Neoclassical Economics.
- Aspromourgos, T. (1986). On the origins of the term ‘neoclassical’. Cambridge Journal of Economics, 10(3), 265 -270. 
- Veblen, T. (1900). 'The Preconceptions of Economic Science - III', The Quarterly Journal of Economics, 14(2), 240-269. (Term on pg. 261).
- George J. Stigler (1941 ). Production and Distribution Theories. New York: Macmillan. Preview.
- Fonseca G. L.; “Introduction to the Neoclassicals”, The New School.
- E. Roy Weintraub. (2007). Neoclassical Economics. The Concise Encyclopedia Of Economics. Retrieved September 26, 2010, from http://www.econlib.org/library/Enc1/NeoclassicalEconomics.html
- William Stanley Jevons (1879, 2nd ed., p. 289), The Theory of Political Economy. Italics in original.
- Philip H. Wicksteed The Common Sense of Political Economy
- Christopher Bliss (1987), "distribution theories, neoclassical", The New Palgrave: A Dictionary of Economics, v. 1, pp. 883-886.
- Robert F. Dorfman (1987), "marginal productivity theory", The New Palgrave: A Dictionary of Economics, v. 3, pp. 323-25.
- C.E. Ferguson (1969). The Neoclassical Theory of Production and Distribution. Cambridge. Description, ch. 1 excerpt, pp. 1-10 (press +), & review excerpt.
- Roger E. Backhouse (2008). "marginal revolution," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
- William Jaffé (1976) "Menger, Jevons, and Walras De-Homogenized", Economic Inquiry, V. 14 (December): 511-525
- Philip Mirowski (1989) More Heat than Light: Economics as Social Physics, Physics as Nature's Economics, Cambridge University Press.
- Philip Mirowski (1989) More Heat than Light: Economics as Social Physics, Physics as Nature's Economics, Cambridge University Press, p 234-5.
- Olivier Jean Blanchard (1987). "neoclassical synthesis", The New Palgrave: A Dictionary of Economics, v. 3, pp. 634-36.
- Thorstein Veblen (1898) Why Is Economics Not an Evolutionary Science?, reprinted in The Place of Science in Modern Civilization (New York, 1919), p. 73.
- Friedman argued for this in essays III, IV and V in "Essays in Positive Economics". http://www.econ.umn.edu/~schwe227/teaching.s11/files/articles/friedman-1953.pdf
- Neoclassical economics from the Concise Library of Economics
- Introduction to neoclassical economics at Drexel