54-488: In welfare economics , the theory of the second best concerns the situation when one or more optimality conditions cannot be satisfied. The economists Richard Lipsey and Kelvin Lancaster showed in 1956 that if one optimality condition in an economic model cannot be satisfied, it is possible that the next-best solution involves changing other variables away from the values that would otherwise be optimal. Politically,
108-857: A Fulbright Distinguished Chair , in 1995 he taught economics at the University of Siena . He was also a founding member of the Pontifical Academy of Social Sciences and a member of the board at the Santa Fe Institute . At various stages in his career he was a Fellow of Churchill College, Cambridge . He was one of the founding editors of the Annual Review of Economics , which was first published in 2009. Four of his former students have gone on to become Nobel Prize winners, namely John Harsanyi , Eric Maskin , Roger Myerson , and Michael Spence . A collection of Arrow's papers
162-445: A competitive equilibrium for some set of prices. More generally, it suggests that redistribution should, if possible, be achieved without affecting prices (which should continue to reflect relative scarcity ), thus ensuring that the final (post-trade) result is efficient. Put into practice, such a policy might resemble predistribution . Because of welfare economics' close ties to social choice theory , Arrow's impossibility theorem
216-422: A competitive market equilibrium, provided that a social planner uses a social welfare function to choose the most equitable efficient outcome and then uses lump sum transfers followed by competitive trade to achieve it. Arrow's impossibility theorem which is closely related to social choice theory , is sometimes considered a third fundamental theorem of welfare economics. Welfare economics typically involves
270-400: A competitive market equilibrium. These restrictions are stronger than for the first fundamental theorem, with convexity of preferences and production functions a sufficient but not necessary condition. A direct consequence of the second theorem is that a benevolent social planner could use a system of lump sum transfers to ensure that the "best" Pareto efficient allocation was supported as
324-573: A left-leaning philosophy. He graduated from Townsend Harris High School and then earned a bachelor's degree in mathematics from the City College of New York in 1940, where he was a member of Sigma Phi Epsilon . He then attended Columbia University for graduate studies, obtaining a master's degree in mathematics in June 1941. At Columbia, Arrow studied under Harold Hotelling , who influenced him to switch fields to economics. He served as
378-476: A measure would still be concerned with the distribution of income ( distributive efficiency ) but not the distribution of final utilities. In normative terms, such authors were writing in the Benthamite tradition. The ordinal-behaviorist approach, originally called the new welfare economics , is based on the work of Pareto , Kaldor , Hicks , and Scitovsky . It explicitly recognizes the differences between
432-531: A millionaire. At the other extreme is the Max-Min, or Rawlsian utility function. According to the Max-Min criterion, welfare is maximized when the utility of those society members that have the least is the greatest. No economic activity will increase social welfare unless it improves the position of the society member that is the worst off. Most economists specify social welfare functions that are intermediate between these two extremes. The social welfare function
486-437: A number of conditions that can lead to inefficiency. They include: Note that if one of these conditions leads to inefficiency, another condition might help by counteracting it. For example, if a pollution externality leads to overproduction of tires, a tax on tires might restore the efficient level of production. A condition inefficient in the "first-best" might be desirable in the second-best . To determine whether an activity
540-420: A social utility frontier represents an efficient allocation of an economy's resources; that is, it is a Pareto optimum in factor allocation, in production, in consumption, and in the interaction of production and consumption (supply and demand). In the diagram below, the curve MN is a social utility frontier. Point D corresponds with point C from the earlier diagram. Point D is on the social utility frontier because
594-807: A weather officer in the United States Army Air Forces from 1942 to 1946. From 1946 to 1949 Arrow was a graduate student at Columbia, and also worked as a research associate at the Cowles Commission . During that time he also served as an assistant professor of economics at the University of Chicago and worked at the RAND Corporation in California . He left Chicago to become an acting assistant professor of economics and statistics at Stanford University . In 1951, he earned his PhD from Columbia. He served in
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#1732791589388648-408: Is endogenously to economic activities, and thus belong inside the model. Endogenous growth theory started with Paul Romer 's 1986 paper, borrowing from Arrow's 1962 " learning-by-doing " model which introduced a mechanism to eliminate diminishing returns in aggregate output. A literature on this theory has developed subsequently to Arrow's work. In other pioneering research, Arrow investigated
702-452: Is a curve that slopes downward to the right. The intermediate form of social indifference curve can be interpreted as showing that as inequality increases, a larger improvement in the utility of relatively rich individuals is needed to compensate for the loss in utility of relatively poor individuals. A crude social welfare function can be constructed by measuring the subjective dollar value of goods and services distributed to participants in
756-530: Is a field of economics that applies microeconomic techniques to evaluate the overall well-being (welfare) of a society. The principles of welfare economics are often used to inform public economics , which focuses on the ways in which government intervention can improve social welfare . Additionally, welfare economics serves as the theoretical foundation for several instruments of public economics, such as cost–benefit analysis . The intersection of welfare economics and behavioral economics has given rise to
810-457: Is a necessary, but not a sufficient condition for social welfare. Each Pareto optimum corresponds to a different income distribution in the economy. Some may involve great inequalities of income. So how do we decide which Pareto optimum is most desirable? This decision is made, either tacitly or overtly, when we specify the social welfare function . This function embodies value judgements about interpersonal utility. The social welfare function shows
864-484: Is an efficiency goal that is standard in economics. A situation is Pareto-efficient only if no individual can be made better off without making someone else worse off. An example of an inefficient situation would be if Smith owns an apple but would prefer to consume an orange while Jones owns an orange but would be prefer to consume an apple. Both could be made better off by trading. A Pareto-efficient state of affairs can only come about if four criteria are met: There are
918-531: Is delivered through the aggregate of individual preferences rather than the formation of government or income, especially those that exist because of neutrality, presented a challenge to reconcile conflicting interests in revenue sharing. The neutral results, avoiding special utility issues, restricted the social analyzes to structural utility issues. This restriction did not exclude important information about an individual’s social status or position needed to make an income allocation decision. Sen recommended expanding
972-530: Is housed at the Rubenstein Library at Duke University . Arrow's monograph Social Choice and Individual Values derives from his 1951 PhD thesis. If we exclude the possibility of interpersonal comparisons of utility, then the only methods of passing from individual tastes to social preferences which will be satisfactory and which will be defined for a wide range of sets of individual orderings are either imposed or dictatorial. In what he named
1026-520: Is known as Kaldor–Hicks efficiency . If the two conditions disagree, that yields the Scitovsky paradox . There are many combinations of consumer utility, production mixes, and factor input combinations consistent with efficiency. In fact, there are an infinity of consumption and production equilibria that yield Pareto optimal results. There are as many optima as there are points on the aggregate production–possibility frontier . Hence, Pareto efficiency
1080-475: Is maximized. Such point is called "the point of bliss". This point is Z where the social utility frontier MN is tangent to the highest possible social indifference curve labelled SI. Kenneth Arrow Kenneth Joseph Arrow (August 23, 1921 – February 21, 2017) was an American economist , mathematician and political theorist . He received the John Bates Clark Medal in 1957, and
1134-460: Is moving the economy towards Pareto efficiency, two compensation tests have been developed. Policy changes usually help some people while hurting others, so these tests ask what would happen if the winners were to compensate the losers. Using the Kaldor criterion , the change is desirable if the maximum amount the winners would be willing to pay is greater than the minimum the losers would accept. Under
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#17327915893881188-546: Is something of a balance between the amounts of goods and services that some individuals want to supply and the amounts that other, different individuals want to sell. Would-be buyers ordinarily count correctly on being able to carry out their intentions, and would-be sellers do not ordinarily find themselves producing great amounts of goods that they cannot sell. This experience of balance is indeed so widespread that it raises no intellectual disquiet among laymen; they take it so much for granted that they are not disposed to understand
1242-405: Is sometimes listed as a third fundamental theorem. Utility functions can be derived from the points on a contract curve. Numerous utility functions can be derived, one for each point on the production possibility frontier (PQ in the diagram above). A social utility frontier (also called a grand utility frontier ) can be obtained from the outer envelope of all these utility functions. Each point on
1296-438: Is typically translated into social indifference curves so that they can be used in the same graphic space as the other functions that they interact with. A utilitarian social indifference curve is linear and downward sloping to the right. The Max-Min social indifference curve takes the shape of two straight lines joined so as they form a 90-degree angle. A social indifference curve drawn from an intermediate social welfare function
1350-724: The American Philosophical Society . He was the joint winner of the Nobel Memorial Prize in Economics with John Hicks in 1972 and the 1986 recipient of the von Neumann Theory Prize . He was one of the recipients of the 2004 National Medal of Science , the nation's highest scientific honor, presented by President George W. Bush for his contributions to research on the problem of making decisions using imperfect information and his research on bearing risk. He has received honorary doctorates from
1404-547: The Hicks criterion , the change is desirable if the maximum the losers would be willing to offer the winners to prevent the change is less than the minimum the winners would accept as a bribe to give up the change. The Hicks compensation test is from the losers' point of view; the Kaldor compensation test is from the winners'. If both conditions are satisfied, the proposed change will move the economy toward Pareto optimality. This idea
1458-677: The Nobel Memorial Prize in Economic Sciences in 1972, along with John Hicks . In economics, Arrow was a major figure in postwar neoclassical economic theory. Four of his students ( Roger Myerson , Eric Maskin , John Harsanyi , and Michael Spence ) went on to become Nobel laureates themselves. His contributions to social choice theory , notably his “impossibility theorem ", and his work on general equilibrium analysis are significant. His work in many other areas of economics, including endogenous growth theory and
1512-480: The Pareto principle , totalitarianism , and free will Arrow concluded that there is no rational way to articulate individual preferences forms together resulting in a harmonious social status of the various social societies. Amartya Sen later emphasized the nature of the sequential gain approach, and Arrow's theory emphasized it. Sen said collective action often arises in social decision-making, because Arrow's theory
1566-431: The University of Chicago and psychotherapist, who died in 2015; they had two children, David Michael (b. 1962), an actor, and Andrew Seth (b. 1965), an actor/singer. Arrow was well known for being a polymath, possessing prodigious knowledge of subjects far removed from economics. On one occasion (recounted by Eric Maskin ), in an attempt to artificially test Arrow's knowledge, the junior faculty agreed to closely study
1620-419: The liberal paradox which argued that given a status of "Minimal Liberty" there was no way to obtain Pareto optimality , nor to avoid the problem of social choice of neutral but unequal results. Work by Arrow and Gérard Debreu and simultaneous work by Lionel McKenzie offered the first rigorous proofs of the existence of a market clearing equilibrium . For this work and his other contributions, Debreu won
1674-410: The 1930s and 40s, has largely collapsed since the discovery of Arrow's impossibility theorem and utility representation theorems have shown them to be mathematically self-contradictory , violating the principle of transitive preferences . Situations are considered to have distributive efficiency when goods are distributed to the people who can gain the most utility from them. Pareto efficiency
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1728-476: The 1983 Nobel Prize in Economics. Arrow went on to extend the model and its analysis to include uncertainty , the stability . His contributions to the general equilibrium theory were influenced by Adam Smith 's Wealth of Nations . Written in 1776, The Wealth of Nations is an examination of economic growth brought forward by the division of labor, by ensuring interdependence of individuals within society. In 1974, The American Economic Association published
1782-589: The General Impossibility Theorem, he theorized that, unless we accept to compare the levels of utility reached by different individuals, it is impossible to formulate a social preference ordering that satisfies all of the following conditions: The theorem has implications for welfare economics and theories of justice , and for voting theory (it extends the Condorcet paradox ). Following Arrow's logical framework, Amartya Sen formulated
1836-675: The Management Sciences . In 2007 he was the first Witten Lecturer at the Witten/Herdecke University as the awardee of the Witten Lectures in Economics and Philosophy. Arrow was a brother to the economist Anita Summers , uncle to economist and former Treasury Secretary and Harvard President Larry Summers , and brother-in-law of the late economists Robert Summers and Paul Samuelson . In 1947, he married Selma Schweitzer, graduate in economics at
1890-696: The University of Chicago (1967), the University of Vienna (1971) the City University of New York (1972). On 2 June 1995 he received an honorary doctorate from the Faculty of Social Sciences at Uppsala University , Sweden . He was elected a Foreign Member of the Royal Society (ForMemRS) in 2006. He was elected to the 2002 class of Fellows of the Institute for Operations Research and
1944-711: The Welfare Economics of Medical Care", in the American Economic Review); later researchers investigated many other markets, particularly second-hand assets, online auctions and insurance. Arrow was awarded the John Bates Clark Medal in 1957 and was elected a Fellow of the American Academy of Arts and Sciences in 1959. In 1968, he was elected to both the United States National Academy of Sciences and
1998-405: The derivation or assumption of a social welfare function , which can then be used to rank economically feasible allocations of resources based on the social welfare they generate. Until 1951, the objective of welfare economics remained largely uncontested. Economists viewed welfare economics as the branch of the discipline concerned with delineating the actions a governing body should undertake. It
2052-600: The economics of information , was also foundational. Arrow was born on August 23, 1921, in New York City . Arrow's mother, Lilian (Greenberg), was from Iași , Romania , and his father, Harry Arrow, was from nearby Podu Iloaiei . The family was of Romanian-Jewish descent, and very supportive of Kenneth’s education. Growing up during the Great Depression , he embraced socialism in his youth. He would later move away from socialism, but his views retained
2106-457: The economy. The field of welfare economics is associated with two fundamental theorems. The first states that given certain assumptions, competitive markets (price equilibria with transfers, e.g. Walrasian equilibria ) produce Pareto efficient outcomes. The assumptions required are generally characterised as "very weak". More specifically, the existence of competitive equilibrium implies both price-taking behaviour and complete markets , but
2160-576: The efficiency aspect of the discipline and the distribution aspect and treats them differently. Questions of efficiency are assessed with criteria such as Pareto efficiency and Kaldor–Hicks efficiency , while questions of income distribution are covered in the specification of the social welfare function Further, efficiency dispenses with cardinal measures of utility, replacing it with ordinal utility , which merely ranks commodity bundles (with an indifference-curve map, for example). The consensus in favor of such approaches, pushed by behavioralists of
2214-613: The government on the staff of the Council of Economic Advisers in the 1960s with Robert Solow . In 1968, he left Stanford for Harvard University , where he was appointed Professor of Economics; it was during his tenure there that he received the Nobel Prize in Economics. Arrow returned to Stanford in 1979 and became the Joan Kenney Professor of Economics and Professor of Operations Research. He retired in 1991. As
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2268-548: The government to intervene in a way that is contrary to usual policy. This suggests that economists need to study the details of the situation before jumping to the theory-based conclusion that an improvement in market perfection in one area implies a global improvement in efficiency. Even though the theory of the second best was developed for the Walrasian general equilibrium system, it also applies to partial equilibrium cases. Welfare economics Welfare economics
2322-525: The marginal rate of substitution at point C is equal to the marginal rate of transformation at point A. Point E corresponds with point B in the previous diagram, and lies inside the social utility frontier (indicating inefficiency) because the MRS at point C is not equal to the MRT at point A. Although all the points on the grand social utility frontier are Pareto efficient, only one point identifies where social welfare
2376-468: The mechanism by which it occurs. In 1951, Arrow presented the first and second fundamental theorems of welfare economics and their proofs without requiring differentiability of utility, consumption, or technology, and including corner solutions. Arrow was one of the precursors of endogenous growth theory , which seeks to explain the source of technical change, which is a key driver of economic growth. Until this theory came to prominence, technical change
2430-586: The only additional assumption is the local non-satiation of agents' preferences – that consumers would like, at the margin, to have slightly more of any given good. The first fundamental theorem is said to capture the logic of Adam Smith's invisible hand , though in general there is no reason to suppose that the "best" Pareto efficient point (of which there are a set) will be selected by the market without intervention, only that some such point will be. The second fundamental theorem states that given further restrictions, any Pareto efficient outcome can be supported as
2484-432: The paper written by Kenneth Arrow, General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice , where he states: From the time of Adam Smith's Wealth of Nations in 1776, one recurrent theme of economic analysis has been the remarkable degree of coherence among the vast numbers of individual and seemingly separate decisions about the buying and selling of commodities. In everyday, normal experience, there
2538-565: The problems caused by asymmetric information in markets. In many transactions, one party (usually the seller) has more information about the product being sold than the other party. Asymmetric information creates incentives for the party with more information to cheat the party with less information; as a result, a number of market structures have developed, including warranties and third party authentication , which enable markets with asymmetric information to function. Arrow analysed this issue for medical care (a 1963 paper entitled "Uncertainty and
2592-427: The relative importance of the individuals that comprise society. A utilitarian welfare function (also called a Benthamite welfare function) sums the utility of each individual in order to obtain society's overall welfare. All people are treated the same, regardless of their initial level of utility. One extra unit of utility for a starving person is not seen to be of any greater value than an extra unit of utility for
2646-420: The scope of data used in welfare research and emphasized the need for explicit discussion of ethics and morality in welfare economics. The early Neoclassical approach was developed by Edgeworth , Sidgwick , Marshall , and Pigou . It assumes the following: With these assumptions, it is possible to construct a social welfare function simply by summing all the individual utility functions. Note that such
2700-403: The subfield of behavioral welfare economics. Two fundamental theorems are associated with welfare economics. The first states that competitive markets, under certain assumptions, lead to Pareto efficient outcomes. This idea is sometimes referred to as Adam Smith's invisible hand . The second theorem states that with further restrictions, any Pareto efficient outcome can be achieved through
2754-649: The theory implies that if it is infeasible to remove a particular market distortion, introducing one or more additional market distortions in an interdependent market may partially counteract the first, and lead to a more efficient outcome . In an economy with some uncorrectable market failure in one sector, actions to correct market failures in another related sector with the intent of increasing economic efficiency may actually decrease overall economic efficiency. In theory, at least, it may be better to let two market imperfections cancel each other out rather than making an effort to fix either one. Thus, it may be optimal for
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#17327915893882808-578: The underlying social welfare function. By postulating W as W(UA, UB) and assuming W to be a positive function of each individual's utility, it was shown that maximum welfare occurred when allocative efficiency was achieved, and the marginal contribution to welfare of each individual was equalized. But this decision did not last long. In 1951, Kenneth Arrow tested whether rational collective selection rules could derive social welfare functions from individuals in preference to social states. He argued that rational law satisfies four conditions: partial universality,
2862-418: Was assumed to occur exogenously — that is, it was assumed to occur outside economic activities, and was outside (exogenous) to common economic models. At the same time there was no economic explanation for why it occurred. Endogenous-growth theory provided standard economic reasons for why firms innovate, leading economists to think of innovation and technical change as determined by economic actors, that
2916-559: Was commonly accepted that the term "maximizing welfare" held a specific meaning rooted in the philosophical framework of utilitarianism. Within the profession, there was ongoing debate regarding whether utility was an ordinal or cardinal concept. This debate seemed to have been addressed by Abram Bergson 's seminal paper in 1938, "A Reformulation of Certain Aspects of Welfare Economics." Bergson demonstrated that economic efficiency conditions could be precisely formulated without fully specifying
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