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Welfare economics is a branch of economics that uses microeconomic techniques to evaluate economic well-being especially relative to competitive general equilibrium within an economy as to economic efficiency and the resulting income distribution1 associated with it. It analyzes social welfare however measured in terms of economic activities of the individuals that comprise the theoretical society considered. As such individuals with associated economic activities are the basic units for aggregating to social welfare whether of a group a community or a society and there is no "social welfare" apart from the "welfare" associated with its individual units.

Welfare economics typically takes individual preferences as given and stipulates a welfare improvement in Pareto efficiency terms from social state A to social state B if at least one person prefers B and no one else opposes it. There is no requirement of a unique quantitative measure of the welfare improvement implied by this. Another aspect of welfare treats income/goods distribution including equality as a further dimension of welfare.2

Social welfare refers to the overall welfare of society. With sufficiently strong assumptions it can be specified as the summation of the welfare of all the individuals in the society. Welfare may be measured either cardinally in terms of "utils" or dollars or measured ordinally in terms of Pareto efficiency. The cardinal method in "utils" is seldom used in pure theory today because of aggregation problems that make the meaning of the method doubtful except on widely challenged underlying assumptions. In applied welfare economics such as in cost-benefit analysis money-value estimates are often used particularly where income-distribution effects are factored into the analysis or seem unlikely to undercut the analysis.

Since the early 1980s economists have been interested in a number of new approaches and issues in welfare economics. The capabilities approach to welfare argues that what people are free to do or be should also be included in welfare assessments and the approach has been particularly influential in development policy circles where the emphasis on multi-dimensionality and freedom has shaped the evolution of the Human Development Index. Economists have also been interested in using life satisfaction to measure what Kahneman and colleagues call experienced utility. What follows for the most part therefore refers to a particular approach to welfare economics possibly best referred to as 'neo-classical' or 'traditional' welfare economics. Other classifying terms or problems in welfare economics include externalities equity justice inequality and altruism. Contents 1 Two approaches 2 Efficiency 3 Income distribution 4 A simplified seven-equation model 5 Efficiency between production and consumption 6 Social welfare maximization 7 Welfare economics in relation to other subjects 8 Paretian welfare economics 9 Criticisms 10 See also 11 Notes 12 References Two approaches There are two mainstream approaches to welfare economics: the early Neoclassical approach and the New welfare economics approach. The early Neoclassical approach was developed by Edgeworth Sidgwick Marshall and Pigou. It assumes that: Utility is cardinal that is scale-measurable by observation or judgment. Preferences are exogenously given and stable. Additional consumption provides smaller and smaller increases in utility (diminishing marginal utility). All individuals have interpersonally comparable utility functions (an assumption that Edgeworth avoided in his Mathematical 'Psychics). With these assumptions it is possible to construct a social welfare function simply by summing all the individual utility functions. The New Welfare Economics approach is based on the work of Pareto Hicks and Kaldor. It explicitly recognizes the differences between 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 the Kaldor-Hicks compensation tests while questions of income distribution are covered in social welfare function specification. Further efficiency dispenses with cardinal measures of utility replacing it with ordinal utility which merely ranks commodity bundles such as represented by an indifference-curve map is adequate for this analysis. Efficiency Situations are considered to have distributive efficiency when goods are distributed to the people who can gain the most utility from them. Many economists use Pareto efficiency as their efficiency goal. According to this measure of social welfare a situation is optimal only if no individuals can be made better off without making someone else worse off. This ideal state of affairs can only come about if four criteria are met: The marginal rates of substitution in consumption are identical for all consumers. This occurs when no consumer can be made better off without making others worse off. The marginal rate of transformation in production is identical for all products. This occurs when it is impossible to increase the production of any good without reducing the production of other goods. The marginal resource cost is equal to the marginal revenue product for all production processes. This takes place when marginal physical product of a factor must be the same for all firms producing a good. The marginal rates of substitution in consumption are equal to the marginal rates of transformation in production such as where production processes must match consumer wants. There are a number of conditions that most economists agree may lead to inefficiency. They include: Imperfect market structures such as a monopoly monopsony oligopoly oligopsony and monopolistic competition. Factor allocation inefficiencies in production theory basics. Market failures and externalities; there is also social cost. Price discrimination and price skimming. Asymmetric information principal-agent problems. Long run declining average costs in a natural monopoly. Certain types of taxes and tariffs. To determine whether an activity is moving the economy towards Pareto efficiency two compensation tests have been developed. Any change usually makes some people better off while making others worse off so these tests ask what would happen if the winners were to compensate the losers. Using the Kaldor criterion an activity will contribute to Pareto optimality if the maximum amount the gainers are prepared to pay is greater than the minimum amount that the losers are prepared to accept. Under the Hicks criterion an activity will contribute to Pareto optimality if the maximum amount the losers are prepared to offer to the gainers in order to prevent the change is less than the minimum amount the gainers are prepared to accept as a bribe to forgo the change. The Hicks compensation test is from the losers' point of view while the Kaldor compensation test is from the gainers' point of view. If both conditions are satisfied both gainers and losers will agree that the proposed activity will move the economy toward Pareto optimality. This is referred to as Kaldor-Hicks efficiency or the Scitovsky criterion. See also: first welfare theorem Income distribution There are many combinations of consumer utility production mixes and factor input combinations consistent with efficiency. In fact there are an infinity of consumer and production equilibria that yield Pareto optimal results. There are as many optima as there are points on the aggregate production possibilities frontier. Hence Pareto efficiency 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 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 a millionaire. At the other extreme is the Max-Min or Rawlsian utility function (Stiglitz 2000 p102). 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 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 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 the economy (see also consumer surplus). A simplified seven-equation model The basic welfare economics problem is to find the theoretical maximum of a social welfare function subject to various constraints such as the state of technology in production available natural resources national infrastructure and behavioural constraints such as consumer utility maximization and producer profit maximization. In the simplest possible economy this can be done by simultaneously solving seven equations. This simple economy would have only two consumers (consumer 1 and consumer 2) only two products (product X and product Y) and only two factors of production going into these products (labour (L) and capital (K)). The model can be stated as: maximize social welfare: Wf(U1 U2) subject to the following set of constraints: K Kx + Ky (The amount of capital used in the production of goods X and Y) L Lx + Ly (The amount of labour used in the production of goods X and Y) X X(Kx Lx) (The production function for product X) Y Y(Ky Ly) (The production function for product Y) U1 U1(X1 Y1) (The preferences of consumer 1) U2 U2(X2 Y2) (The preferences of consumer 2) The solution to this problem yields a Pareto optimum. In a more realistic example of millions of consumers millions of products and several factors of production the math gets more complicated. Also finding a solution to an abstract function does not directly yield a policy recommendation! In other words solving an equation does not solve social problems. However a model like the one above can be viewed as an argument that solving a social problem (like achieving a Pareto-optimal distribution of wealth) is at least theoretically possible. Efficiency between production and consumption The relation between production and consumption in a simple seven equation model (2x2x2 model) can be shown graphically. In the diagram below the aggregate production possibility frontier labeled PQ shows all the points of efficiency in the production of goods X and Y. If the economy produces the mix of good X and Y shown at point A then the marginal rate of transformation (MRT) X for Y is equal to 2. Point A defines the boundaries of an Edgeworth box diagram of consumption. That is the same mix of products that are produced at point A can be consumed by the two consumers in this simple economy. The consumers' relative preferences are shown by the indifference curves inside the Edgeworth box. At point B the marginal rate of substitution (MRS) is equal to 2 while at point C the marginal rate of substitution is equal to 3. Only at point B is consumption in balance with production (MRSMRT). The curve 0BCA (often called the contract curve) inside the Edgeworth box defines the locus of points of efficiency in consumption (MRS1MRS ). As we move along the curve we are changing the mix of goods X and Y that individuals 1 and 2 choose to consume. The utility data associated with each point on this curve can be used to create utility functions. Social welfare maximization 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 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 B from the earlier diagram. Point D is on the social utility frontier because the marginal rate of substitution at point B is equal to the marginal rate of transformation at point A. Point E corresponds with point C 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 is maximized. This is point Z where the social utility frontier MN is tangent to the highest possible social indifference curve labelled SI. Welfare economics in relation to other subjects Welfare economics uses many of the same techniques as microeconomics and can be seen as intermediate or advanced microeconomic theory. Its results are applicable to macroeconomic issues so welfare economics is somewhat of a bridge between the two branches of economics. Cost-benefit analysis is a specific application of welfare economics techniques but excludes the income distribution aspects. Political science also looks into the issue of social welfare (political science) but in a less quantitative manner. Human development theory explores these issues also and considers them fundamental to the development process itself. Paretian welfare economics Paretian welfare economics rests on the assumed value judgment that if a particular change in the economy leaves at least one individual better off and no individual worse off social welfare may be said to have increased. (One individual being better off than other individuals and not leaving other individuals worse off is possible in societies where political power is not related to economic power.)citation needed In this sense an individualistic approach to social welfare is defined with concern extending to all individuals in society and with an explicit rejection of any organic concept of the State.3 Criticisms Some such as economists in the tradition of the Austrian School doubt whether a cardinal utility function or cardinal social welfare function is of any value. The reason given is that it is difficult to aggregate the utilities of various people that have differing marginal utility of money such as the wealthy and the poor. Also the economists of the Austrian School question the relevance of pareto optimal allocation considering situations where the framework of means and ends is not perfectly known since neoclassical theory always assumes that the ends-means framework is perfectly defined. Some even question the value of ordinal utility functions. They have proposed other means of measuring well-being as an alternative to price indices "willingness to pay" functions and other price oriented measures.citation needed These price based measures are seen as promoting consumerism and productivism by many.citation needed It should be noted that it is possible to do welfare economics without the use of prices however this is not always done.citation needed Value assumptions explicit in the social welfare function used and implicit in the efficiency criterion chosen make welfare economics a highly normative and subjective field. This can make it controversial. However perhaps most significant of all are concerns about the limits of a utilitarian apporach to welfare economics. According to this line of argument utilities are not the only claim or welfare output that matters to people and so a comprehensive approach to welfare economics should include such factors. The capabilities appraoch to welfare is an attempt to construct a more comprehensive approach to welfare economics one in which functionings happiness and capabilities are the three key aspects of welfare outcomes that people should seek to promote and foster. See also Arrow's impossibility theorem ClowardPiven strategy Compensation principle Consumer surplus Cost-benefit analysis Deadweight loss Distribution (economics) Economics terminology that differs from common usage Equity (economics) Feminist economics Gini coefficient Income inequality metrics Important publications in welfare economics Justice (economics) Kaldor-Hicks efficiency List of business ethics political economy and philosophy of business topics List of economics topics Laffer curve Lorenz curve Microeconomics National Income (national income accounting) Pareto efficiency Price ceiling Price floor Social welfare function Social welfare (political science) Notes Deardorff's Glossary of International Economics (2006). "Welfare economics." I.M.D. Little A Critique of Welfare Economics (1950). There are many such proposed measures of welfare including the Theil index and those in Amartya Sen On Economic Inequality Annexe with James E. Foster (1997) Clarendon Press Oxford ISBN 0-19-828193-5. Chareles K. Rowley and Alan T. Peacock Welfare Economics: A Liberal Restatement York Studies in Economics Martin Robertson 1975 References Arrow Kenneth J. (1951 2nd ed. 1963). Social Choice and Individual Values Yale University Press New Haven. Arrow Kenneth J. and Grard Debreu ed. 2002. Landmark Papers in General Equilibrium Theory Social Choice and Welfare. Edward Elgar Publishing ISBN 978 1 84064 569 9. Description and table of contents. AtkinsonAnthony B. (1975). The Economics of Inequality Oxford University Press London. Bator Francis M. (1957). "The Simple Analytics of Welfare Maximization" American Economic Review 47(1) p p. 22-59. Calsamiglia Xavier and Alan Kirman (1993). "A Unique Informationally Efficient and Decentralized Mechanism with Fair Outcomes" Econometrica 61(5) p p. 1147-1172. Chipman John S. and James C. Moore (1978). "The New Welfare Economics 1939-1974" International Economic Review 19(3) p p. 547-584. Mishan E. J. (1980). "The New Welfare Economics: An Alternative View" International Economic Review 21(3) p p. 691-705. Feldman Allan M. (1987). "equity" The New Palgrave: A Dictionary of Economics v. 2 pp. 18384. (1987 2008). "welfare economics" The New Palgrave: A Dictionary of Economics v. 4 pp. 88995. Abstract. Feldman Allan M. and Roberto Serrano 1980 2006. Welfare Economics and Social Choice Theory 2nd ed. ISBN 0-387-29367-1 ISBN 978-0-387-29367-7 Arrow-serachable chapter previews. Graaff Johannes de Villiers (1957; rev. ed. 1968). Theoretical Welfare Economics ISBN 978-0-521-09446-7 Cambridge UK: Cambridge University Press. Harberger Arnold C. (1971) "Three Basic Postulates for Applied Welfare Economics: An Interpretive Essay" Journal of Economic Literature 9(3) p p. 785-797. Just Richard et al. (2004) The Welfare Economics of Public Policy Edward Elgar Publishing Cheltenham and Northampton. Kuenne Robert E. ed. (2000) Readings in Social Welfare: Theory and Policy Wiley. Description and scroll to chapter-preview links. Little I.M.D. (1950; 2002). A Critique of Welfare Economics Oxford. Preview. ISBN 0-19-828119-6. Ng Yew-Kwang (1979; rev. ed. 1983). Welfare economics. London: Macmillan. O'Connell John F. (1982) Welfare Economic Theory Auburn House Publishing Boston. Samuelson Paul A. (1947 Enlarged ed. 1983). "Welfare Economics" Foundations of Economic Analysis Harvard University Press Cambridge MA ch. VIII pp. 20353. (1977). "Reaffirming the Existence of 'Reasonable' Bergson-Samuelson Social Welfare Functions" Economica N.S. 44(173) p p. 81-88. Reprinted in (1986) The Collected Scientific Papers of Paul A. Samuelson pp. 47-54. (1981). "Bergsonian Welfare Economics" in S. Rosefielde (ed.) Economic Welfare and the Economics of Soviet Socialism: Essays in Honor of Abram Bergson Cambridge University Press Cambridge pp. 22366. Reprinted in (1986) The Collected Scientific Papers of Paul A. Samuelson pp. 3 -46. Sen Amartya K. (1963). "Distribution Transitivity and Little's Welfare Criteria" Economic Journal 73(292) p. 771-78. (1982). Choice Welfare and Measurement MIT Press. Description and scroll to chapter-preview links. Suzumura Kotaro (1980). "On Distributional Value Judgments and Piecemeal Welfare Criteria" Economica 47(186) p p. 125-39. 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