Welfare economics is a branch of economics Economics is the social science that is concerned with the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek οἰκονομία from οἶκος (oikos, "house") + νόμος (nomos, "custom" or "law"), hence "rules of the house(hold)". Current that uses microeconomic Microeconomics is a branch of economics that studies how the individual parts of the economy, the household and the firms, make decisions to allocate limited resources, typically in markets where goods or services are being bought and sold. Microeconomics examines how these decisions and behaviours affect the supply and demand for goods and techniques to simultaneously determine allocative efficiency Allocative efficiency is a theoretical measure of the benefit or utility derived from a proposed or actual choice in the distribution or apportionment of resources within an economy and the income distribution Distribution in economics refers to the way total output or income is distributed among individuals or among the factors of production (Samuelson and Nordhaus, 2001, p. 762). In general theory and the national income and product accounts, each unit of output corresponds to a unit of income. One use of national accounts is for classifying factor associated with it.^{[citation needed]} It analyzes social welfare, however measured In economics, a social welfare function is a real-valued function that ranks conceivable social states from lowest to highest. Inputs of the function include any variables considered to affect welfare of the society (Sen, 1970, p. 33). In using welfare measures of persons in the society as inputs, the social welfare function is individualistic in, 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 Methodological individualism is a widely-used term in the social sciences. Its advocates see it as a philosophical method aimed at explaining and understanding broad society-wide developments as the aggregation of decisions by individuals. It has also been regarded as a form of "methodological reductionism," a reduction of the 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 Pareto efficiency, or Pareto optimality, is a concept in economics with applications in all areas of the discipline as well as engineering and other social sciences. The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency and income distribution. Informally, Pareto efficient 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 Distribution in economics refers to the way total output or income is distributed among individuals or among the factors of production (Samuelson and Nordhaus, 2001, p. 762). In general theory and the national income and product accounts, each unit of output corresponds to a unit of income. One use of national accounts is for classifying factor, including equality Economic inequality comprises all disparities in the distribution of economic assets and income. The term typically refers to inequality among individuals and groups within a society, but can also refer to inequality among countries. Economic Inequality generally refers to equality of outcome, and is related to the idea of equality of opportunity, as a further dimension of welfare.^[1]

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 Under both definitions the process involves, whether explicitly or implicitly, weighing the total expected costs against the total expected benefits of one or more actions in order to choose the best or most profitable option. The formal process is often referred to as either CBA or BCA (Benefit-Cost 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 The Capability Approach began life in the 1980s as an approach to welfare economics. In this approach, Amartya Sen brought together a range of ideas that were hitherto excluded from (or inadequately formulated in) traditional approaches to the economics of 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 Articles in economics journals are usually classified according to the JEL classification codes, a system originated by the Journal of Economic Literature . The JEL is published quarterly by the American Economic Association (AEA) and contains survey articles and information on recently published books and dissertations. The AEA maintains EconLit, or problems in welfare economics include externalities In economics, an externality is a cost or benefit, not transmitted through prices, incurred by a party who did not agree to the action causing the cost or benefit. A benefit in this case is called a positive externality or external benefit, while a cost is called a negative externality or external cost, equity In welfare economics, equity may be distinguished from economic efficiency in overall evaluation of social welfare. Although 'equity' has broader uses, it may be posed as a counterpart to economic inequality in yielding a "good" distribution of welfare. It has been studied in experimental economics as inequity aversion, justice 'Just' in many usages, including economic ones, may express ethical acceptance of some possible social state against which other possible social states are measured. By contrast, the usage of justice in economics is as a subcategory of welfare economics with models frequently representing the ethical-social requirements of a given theory. That, inequality Economic inequality comprises all disparities in the distribution of economic assets and income. The term typically refers to inequality among individuals and groups within a society, but can also refer to inequality among countries. Economic Inequality generally refers to equality of outcome, and is related to the idea of equality of opportunity, and altruism.

Two approaches

There are two mainstream approaches to welfare economics: the early Neoclassical approach and the New welfare economics approach.

The early Neoclassical 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 as mediated through a hypothesized maximization of income-constrained utility by individuals and of cost-constrained profits of firms employing available approach was developed by Edgeworth Francis Ysidro Edgeworth was an Irish philosopher/politician/economist who made significant contributions to the methods of statistics during the 1880s. From 1891 onward he was the editor of a leading academic journal in economics and his own writings in economics were influential, Sidgwick Henry Sidgwick was an English utilitarian philosopher. He was one of the founders and first president of the Society for Psychical Research, a member of the Metaphysical Society, and promoted the higher education of women. His work in economics has also had a lasting influence, Marshall Alfred Marshall was an English economist and one of the most influential economists of his time, being one of the founders of neoclassical economics. His book, Principles of Economics (1890), brings the ideas of supply and demand, of marginal utility and of the costs of production into a coherent whole. It became the dominant economic textbook in, and Pigou Arthur Cecil Pigou was an English economist. As a teacher and builder of the school of economics at the University of Cambridge he trained and influenced many Cambridge economists who went on to fill chairs of economics around the world. His work covered various fields of economics, particularly welfare economics but also including industrial. It assumes that:

• Utility is cardinal In economics, cardinal utility refers to a property of mathematical indices that preserve preference orderings uniquely up to linear transformations. Two utility indices are related by a linear transformation if for every point on one index, the corresponding point on the other index satisfies a relationship of the form , where and are constants, 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 In economics, the marginal utility of a good or service is the utility gained from an increase (or decrease) in the consumption of that good or service. In general, preferences display diminishing marginal utility. That is, the first unit of consumption of a good or service yields more utility than the second and subsequent units. The concept of).
• 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 In economics, a social welfare function is a real-valued function that ranks conceivable social states from lowest to highest. Inputs of the function include any variables considered to affect welfare of the society (Sen, 1970, p. 33). In using welfare measures of persons in the society as inputs, the social welfare function is individualistic in simply by summing all the individual utility functions.

The New Welfare Economics approach is based on the work of Pareto Vilfredo Federico Damaso Pareto , born Wilfried Fritz Pareto, was an Italian industrialist, sociologist, economist, and philosopher. He made several important contributions to economics, particularly in the study of income distribution and in the analysis of individuals' choices. "His legacy as an economist was profound. Partly because of him,, Hicks Sir John Richard Hicks was a British economist and one of the most important and influential economists of the twentieth century. The most familiar of his many contributions in the field of economics were his statement of consumer demand theory in microeconomics, and the IS/LM model (1937), which summarized a Keynesian view of macroeconomics. His, 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 Pareto efficiency, or Pareto optimality, is a concept in economics with applications in all areas of the discipline as well as engineering and other social sciences. The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency and income distribution. Informally, Pareto efficient 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 Ordinal utility theory states that while the utility of a particular good and service cannot be measured using a numerical scale, different alternatives can be ordered into worse, equal or better. Goods are often considered in ‘bundles’ or ‘baskets’. For example, does individual A prefer 3 apples and 2 oranges or 3 oranges and 2 apples?, 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 In welfare economics, distributive efficiency occurs when goods and services are received by those who have the greatest need for them. Abba Lerner first proposed the idea of distributive efficiency in his 1944 book The Economics of Control when goods are distributed to the people who can gain the most utility from them.

Many economists use Pareto efficiency Pareto efficiency, or Pareto optimality, is a concept in economics with applications in all areas of the discipline as well as engineering and other social sciences. The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency and income distribution. Informally, Pareto efficient 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 Under the standard assumption of neoclassical economics that goods and services are continuously divisible, the marginal rates of substitution will be the same regardless of the direction of exchange, and will correspond to the slope of an indifference curve passing through the consumption bundle in question, at that point: mathematically, it is 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 economics, a production-possibility frontier , sometimes called a "production-possibility curve" or "product transformation curve", is a graph that shows the different rates of production of two goods and/or services that an economy can produce efficiently during a specified period of time with a limited quantity of 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 Production refers to the economic process of converting of inputs into outputs. Production uses resources to create a good or service that is suitable for exchange. This can include manufacturing, storing, shipping, and packaging. Some economists define production broadly as all economic activity other than consumption. They see every commercial 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 In economics, a monopoly (from Greek monos / μονος + polein / πωλειν (to sell)) exists when a specific individual or an enterprise has sufficient control over a particular product or service to determine significantly the terms on which other individuals shall have access to it. (This is in contrast to a monopsony which relates to a, monopsony In economics, a monopsony (from Ancient Greek μόνος "single" + ὀψωνία (opsōnia) "purchase") is a market form in which only one buyer faces many sellers. It is an example of imperfect competition, similar to a monopoly, in which only one seller faces many buyers. As the only purchaser of a good or service, the ", oligopoly In Economics, an oligopoly is a market form in which a market or industry is dominated by a small number of sellers . The word is derived, by analogy with "monopoly", from the Greek ὀλίγοι (oligoi) "few" + πωλειν (polein) "to sell". Because there are few sellers, each oligopolist is likely to be aware of, oligopsony An oligopsony (from Ancient Greek ὀλίγοι "few" + ὀψωνία (opsōnia) "purchase") is a market form in which the number of buyers is small while the number of sellers in theory could be large. This typically happens in market for inputs where a small number of firms are competing to obtain factors of production. It, and monopolistic competition Monopolistic competition is a form of imperfect competition where many competing producers sell products that are differentiated from one another . In monopolistic competition firms can behave like monopolies in the short-run, including using market power to generate profit. In the long-run, other firms enter the market and the benefits of.
• Factor allocation inefficiencies in production theory basics Production refers to the economic process of converting of inputs into outputs. Production uses resources to create a good or service that is suitable for exchange. This can include manufacturing, storing, shipping, and packaging. Some economists define production broadly as all economic activity other than consumption. They see every commercial.
• Market failures and externalities In economics, an externality is a cost or benefit, not transmitted through prices, incurred by a party who did not agree to the action causing the cost or benefit. A benefit in this case is called a positive externality or external benefit, while a cost is called a negative externality or external cost; there is also social cost Social cost, in economics, is generally defined in opposition to "private cost". In economics, theorists model individual decision-making as measurement of costs and benefits. Rational choice theory often assumes that individuals consider only the costs they themselves bear when making decisions, not the costs that may be borne by others.
• Imperfect Price discrimination Price discrimination or price differentiation exists when sales of identical goods or services are transacted at different prices from the same provider. In a theoretical market with perfect information, perfect substitutes, and no transaction costs or prohibition on secondary exchange to prevent arbitrage, price discrimination can only be a and price skimming Price skimming is a pricing strategy in which a marketer sets a relatively high price for a product or service at first, then lowers the price over time. It is a temporal version of price discrimination/yield management. It allows the firm to recover its sunk costs quickly before competition steps in and lowers the market price.
• Asymmetric information, principal-agent problems In political science and economics, the principal–agent problem or agency dilemma treats the difficulties that arise under conditions of incomplete and asymmetric information when a principal hires an agent, such as the problem that the two may not have the same interests, while the principal is, presumably, hiring the agent to pursue the.
• Long run declining average costs in a natural monopoly Natural monopolies arise where the largest supplier in an industry, often the first supplier in a market, has an overwhelming cost advantage over other actual and potential competitors. This tends to be the case in industries where capital costs predominate, creating economies of scale which are large in relation to the size of the market, and.
• 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 Kaldor-Hicks efficiency is a measure of economic efficiency that captures some of the intuitive appeal of Pareto efficiency, but has less stringent criteria and is hence applicable to more circumstances. Under Kaldor-Hicks efficiency, an outcome is considered more efficient if a Pareto optimal outcome can be reached by arranging sufficient or the Scitovsky criterion.

See also: first welfare theorem There are two fundamental theorems of welfare economics. The first states that any competitive equilibrium or Walrasian equilibrium leads to a Pareto efficient allocation of resources. The second states the converse, that any efficient allocation can be sustainable by a competitive equilibrium. Despite the apparent symmetry of the two theorems, in

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 In economics, a production-possibility frontier or "transformation curve" is a graph that shows the different rates of production of two goods that an individual or group can efficiently produce with limited productive resources. The PPF shows the maximum obtainable amount of one commodity for any given amount of another commodity or. 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 In economics, a social welfare function is a real-valued function that ranks conceivable social states from lowest to highest. Inputs of the function include any variables considered to affect welfare of the society (Sen, 1970, p. 33). In using welfare measures of persons in the society as inputs, the social welfare function is individualistic in. This function embodies value judgements about interpersonal utility. The social welfare function is a way of mathematically stating the relative importance of the individuals that comprise society.

A utilitarian welfare function (also called a Benthamite Jeremy Bentham was an English jurist, philosopher, and legal and social reformer. He became a leading theorist in Anglo-American philosophy of law, and a political radical whose ideas influenced the development of welfarism. He is best known for his advocacy of utilitarianism and animal rights, and the idea of the panopticon 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 John Rawls 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: W=f(U¹ U²) subject to the following set of constraints:

K = K^x + K^y (The amount of capital used in the production of goods X and Y)

L = L^x + L^y (The amount of labour used in the production of goods X and Y)

X = X(K^x L^x) (The production function for product X)

Y = Y(K^y L^y) (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 (MRS=MRT). The curve 0BCA (often called the contract curve) inside the Edgeworth box defines the locus of points of efficiency in consumption (MRS¹=MRS ²). 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.) 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^[2].

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.

See also

• Arrow's impossibility theorem
• Cloward–Piven strategy
• Compensation principle
• Consumer surplus
• Cost-benefit analysis
• Distribution (economics)
• 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
• Lorenz curve
• Microeconomics
• National Income (national income accounting)
• Pareto efficiency
• Social welfare function
• Social welfare (political science)

Sources

• Arrow, Kenneth J. (1951, 2nd ed., 1963). Social Choice and Individual Values, Yale University Press, New Haven.
• Arrow, Kenneth J., and Gérard 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.
• Atkinson,Anthony 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), pp. 22-59.
• Calsamiglia, Xavier, and Alan Kirman (1993). "A Unique Informationally Efficient and Decentralized Mechanism with Fair Outcomes," Econometrica, 61(5) , pp. 1147-1172.
• Chipman, John S., and James C. Moore (1978). "The New Welfare Economics 1939-1974," International Economic Review, 19(3), pp. 547-584.
• Feldman, Allan M. (1987). "equity," The New Palgrave: A Dictionary of Economics, v. 2, pp. 183-84.
• _____ (1987). "welfare economics," The New Palgrave: A Dictionary of Economics, v. 4, pp. 889-95.
• 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.
• Harberger, Arnold C. (1971) "Three Basic Postulates for Applied Welfare Economics: An Interpretive Essay," Journal of Economic Literature, 9(3), pp. 785-797.
• Just, Richard et al. (2004), The Welfare Economics of Public Policy, Edward Elgar Publishing, Cheltenham and Northampton.
• 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. 203-53.
• _____ (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. 223-66.
• Sen, Amartya K. (1963). "Distribution, Transitivity and Little's Welfare Criteria," Economic Journal, 73(292), p. 771-78.
• Suzumura, Kotaro (1980). "On Distributional Value Judgments and Piecemeal Welfare Criteria," Economica, 47(186), pp. 125-39.
• Sustainable National Income at wikinfo

References

1. ^ 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.
2. ^ Chareles K. Rowley and Alan T. Peacock, Welfare Economics: A Liberal Restatement, York Studies in Economics, Martin Robertson, 1975

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