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# social welfare

social welfare or public charity, organized provision of educational, cultural, medical, and financial assistance to the needy. Modern social welfare measures may include any of the following: the care of destitute adults; the treatment of the mentally ill; the rehabilitation of criminals; the care of destitute, neglected, and delinquent children; the care and relief of the sick or handicapped; the care and relief of needy families; and supervisory, educational, and constructive activity, especially for the young.

## Early Forms of Assistance

Among the Greeks and Romans public assistance was given chiefly to those holding full citizenship. It was early connected with religion, as among the Hebrews and, from them, among the Christians and later the Muslims. The Christian Church was the main agency of social welfare in the Middle Ages, supplemented by the guilds. Later, national and local governmental agencies, as well as many private agencies, took over much of the charitable activity of the church.

First of the extensive state efforts was the Elizabethan poor law of 1601, which attempted to classify dependents and provide special treatment for each group on the local (parish) level. During the Industrial Revolution, many entrepreneurs believed that social welfare programs undertaken by the state violated the concepts of laissez faire and therefore opposed such measures. Exceptions were such men as Robert Owen, who believed that social welfare measures were essential but their implementation should be undertaken cooperatively rather than as a function of the state.

## Modern Welfare Programs

The first modern government-supported social welfare program for broad groups of people, not just the poor, was undertaken by the German government in 1883. Legislation in that year provided for health insurance for workers, while subsequent legislation introduced compulsory accident insurance and retirement pensions. In the next 50 years, spurred by socialist theory and the increasing power of organized labor, state-supported social welfare programs grew rapidly, so that by the 1930s most of the world's industrial nations had some type of social welfare program.

Not all governments have equally extensive social welfare systems. Great Britain and the Scandinavian countries, often termed "welfare states," have wide-ranging social welfare legislation. Britain's National Health Service, for example, was established (1948) to provide free medical treatment to all. Private philanthropies and charitable organizations, however, continue to operate in these countries in many areas of public welfare. International relief bodies, such as the Red Cross, and agencies of the United Nations, such as the World Health Organization (WHO) and the United Nations Children's Fund (UNICEF), provide social welfare services throughout the world, especially during times of distress and in poverty-stricken areas.

In the United States the Social Security Act of 1935 provided for federally funded financial assistance to the elderly, the blind, and dependent children. Subsequent amendments broadened the act in terms of coverage provided and eligibility; included was the provision for medical insurance to the aged (1965) under the Medicare program and to low-income families (1965) under the Medicaid program.

In the United States public assistance has increasingly come under state and federal control, although private philanthropy still plays a major role. By the early 1990s the Clinton administration approved changes in many states' welfare systems, including work requirements in exchange for benefits (so-called workfare) and time limits. In 1996 the president signed a bill enacting the most sweeping changes in social welfare policy since the New Deal. In general the bill, which sought to end long-term dependence on welfare programs, represented a reversal of previous welfare policy, shifting some of the federal government's role to the states and cutting many benefits. Among the bill's major provisions were the requirement that about a quarter of the population then on welfare be working or training for work by 1997 (a goal that was reached in most states) and that a half do so by 2002; the granting of lump sums to states to run their own welfare and work programs; an end to the federal guarantee of cash assistance for poor children; the limitation of lifetime welfare benefits to five years (with hardship exemptions for some); the requirement that the head of every welfare family work within two years of receiving benefits or lose them; and the establishment of stricter eligibility standards for the Supplemental Security Income program (which excluded many poor disabled children from benefits).

In terms of reducing the welfare rolls, the bill initially proved successful; in 1999 there were fewer welfare recipients then there had been in 30 years. Most states also reported a surplus of federal welfare funds. Those funds, which by law remained fixed for five years, provided an unforeseen benefit for the states, enabling some states to increase social welfare spending. Additional changes passed in 2005 forced states to increase the hours worked by recipients while tightening the regulations for those who are affected by the work requirements, raising concerns in a number of states with education and addiction-treatment programs for welfare recipients.

## Bibliography

See R. E. Asher, United Nations and the Promotion of the General Welfare (1957); H. Kraus, ed., International Cooperation for Social Welfare (1960); A. C. Marts, Man's Concern for His Fellow-man (1961); S. Mencher, Poor Law to Poverty Program (1967); J. F. Handler, Reforming the Poor (1972); E. W. Martin, Comparative Development in Social Welfare (1972); W. I. Trattner, From Poor Law to Welfare State (1974).

In economics a social welfare function can be defined as a real-valued function that ranks conceivable social states (alternative complete descriptions of the society) from lowest on up as to welfare of the society. 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 form. One use of a social welfare function is to represent prospective patterns of collective choice as to alternative social states. The social welfare function is analogous to an indifference-curve map for an individual, except that the social welfare function is a mapping of individual preferences or judgments of everyone in the society as to collective choices, which apply to all, whatever individual preferences are. One point of a social welfare function is to determine how close the analogy is to an ordinal utility function for an individual with at least minimal restrictions suggested by welfare economics. Kenneth Arrow proved a more basic point for a set of seemingly reasonable conditions.

## Bergson-Samuelson social welfare function

In a 1938 article Abram Bergson introduced the social welfare function. The object was "to state in precise form the value judgments required for the derivation of the conditions of maximum economic welfare" set out by earlier writers, including Marshall and Pigou, Pareto and Barone, and Lerner. The function was real-valued and differentiable. It was specified to describe the society as a whole. Arguments of the function included the quantities of different commodities produced and consumed and of resources used in producing different commodities, including labor.

Necessary general conditions are that at the maximum value of the function:

• The marginal "dollar's worth" of welfare is equal for each individual and for each commodity
• The marginal "diswelfare" of each "dollar's worth" of labor is equal for each commodity produced of each labor supplier
• The marginal "dollar" cost of each unit of resources is equal to the marginal value productivity for each commodity.

Bergson showed how welfare economics could describe a standard of economic efficiency despite dispensing with interpersonally-comparable cardinal utility, the hypothesizaton of which may merely conceal value judgments, and purely subjective ones at that.

 Earlier neoclassical welfare theory, heir to the classical utilitarianism of Bentham, had not infrequently treated the Law of Diminishing Marginal Utility as implying interpersonally comparable utility, a necessary condition to achieve the goal of maximizing total utility of the society. Irrespective of such comparability, income or wealth is measurable, and it was commonly inferred that redistributing income from a rich person to a poor person tends to increase total utility (however measured) in the society.* But Lionel Robbins (1935, ch. VI) argued that how or how much utilities, as mental events, would have changed relative to each other is not measurable by any empirical test. Nor are they inferable from the shapes of standard indifference curves. Hence, the advantage of being able to dispense with interpersonal comparability of utility without abstaining from welfare theory. A practical qualification to this was any reduction in output from the transfer.
Auxiliary specifications enable comparison of different social states by each member of society in preference satisfaction. These help define Pareto efficiency, which holds if all alternatives have been exhausted to put at least one person in a more preferred position with no one put in a less preferred position. Bergson described an "economic welfare increase" (later called a Pareto improvement) as at least one individual moving to a more preferred position with everyone else indifferent. The social welfare function could then be specified in a substantively individualistic sense to derive Pareto efficiency (optimality). Paul Samuelson (2004, p. 26) notes that Bergson's function "could derive Pareto optimality conditions as necessary but not sufficient for defining interpersonal normative equity." Still, Pareto efficiency could also characterize one dimension of a particular social welfare function with distribution of commodities among individuals characterizing another dimension. As Bergson noted, a welfare improvement from the social welfare function could come from the "position of some individuals" improving at the expense of others. That social welfare function could then be described as characterizing an equity dimension.

Samuelson (1947, p. 221) himself stressed the flexibility of the social welfare function to characterize any one ethical belief, Pareto-bound or not, consistent with:

• a complete and transitive ranking (an ethically "better", "worse", or "indifferent" ranking) of all social alternatives and
• one set out of an infinity of welfare indices and cardinal indicators to characterize the belief.

He also presented a lucid verbal and mathematical exposition of the social welfare function (1947, pp. 219-49) with minimal use of Lagrangean multipliers and without the difficult notation of differentials used by Bergson throughout. As Samuelson (1983, p. xxii) notes, Bergson clarified how production and consumption efficiency conditions are distinct from the interpersonal ethical values of the social welfare function.

Samuelson further sharpened that distinction by specifying the Welfare function and the Possibility function (1947, pp. 243-49). Each has as arguments the set of utility functions for everyone in the society. Each can (and commonly does) incorporate Pareto efficiency. The Possibility function also depends on technology and resource restraints. It is written in implicit form, reflecting the feasible locus of utility combinations imposed by the restraints and allowed by Pareto efficiency. At a given point on the Possibility function, if the utility of all but one person is determined, the remaining person's utility is determined. The Welfare function ranks different hypothetical sets of utility for everyone in the society from ethically lowest on up (with ties permitted), that is, it makes interpersonal comparisons of utility. Welfare maximization then consists of maximizing the Welfare function subject to the Possibility function as a constraint. The same welfare maximization conditions emerge as in Bergson's analysis.

 For a two-person society, there is a graphical depiction of such welfare maximization at the first figure of Bergson-Samuelson social welfare functions Relative to consumer theory for an individual as to two commodities consumed, there are the following parallels: The respective hypothetical utilities of the two persons in two-dimensional utility space is analogous to respective quantities of commodities for the two-dimensional commodity space of the indifference-curve surface The Welfare function is analogous to the indifference-curve map The Possibility function is analogous to the budget constraint Two-person welfare maximization at the tangency of the highest Welfare function curve on the Possibility function is analogous to tangency of the highest indifference curve on the budget constraint.

## Arrow social welfare function (constitution)

Kenneth Arrow (1963) generalizes the analysis. Along earlier lines, his version of a social welfare function, also called a 'constitution', maps a set of individual orderings (ordinal utility functions) for everyone in the society to a social ordering, a rule for ranking alternative social states (say passing an enforceable law or not, ceteris paribus). Arrow finds that nothing of behavioral significance is lost by dropping the requirement of social orderings that are real-valued (and thus cardinal) in favor of orderings, which are merely complete and transitive, such as a standard indifference-curve map. The earlier analysis mapped any set of individual orderings to one social ordering, whatever it was. This social ordering selected the top-ranked feasible alternative from the economic environment as to resource constraints. Arrow proposed to examine mapping different sets of individual orderings to possibly different social orderings. Here the social ordering would depend on the set of individual orderings, rather than being imposed (invariant to them). Stunningly (relative to a course of theory from Adam Smith and Jeremy Bentham on), Arrow proved the General Possibility Theorem that it is impossible to have a social welfare function that satisfies a certain set of "apparently reasonable" conditions.

## Cardinal social welfare functions

In the above contexts, a social welfare function provides a kind of social preference based on only individual utility functions, whereas in others it includes cardinal measures of social welfare not aggregated from individual utility functions. Examples of such measures are life expectancy and per capita income for the society. The rest of this article adopts the latter definition.

The form of the social welfare function is intended to express a statement of objectives of a society. For example, take this example of a social welfare function:

$W = Y_1 + Y_2 + cdots + Y_n$

where $W$ is social welfare and $Y_i$ is the income of individual i among n in the society. In this case, maximising the social welfare function means maximising the total income of the people in the society, without regard to how incomes are distributed in society. Alternatively, consider the Max-Min utility function (based on the philosophical work of John Rawls):

$W = min\left(Y_1, Y_2, cdots, Y_n\right)$

Here, the social welfare of society is taken to be related to the income of the poorest person in the society, and maximising welfare would mean maximising the income of the poorest person without regard for the incomes of the others.

These two social welfare functions express very different views about how a society would need to be organised in order to maximise welfare, with the first emphasizing total incomes and the second emphasising the needs of the poorest. The max-min welfare function can be seen as reflecting an extreme form of risk aversion on the part of society as a whole, since it is concerned only with the worst conditions that a member of society could face.

Amartya Sen proposed a welfare function in 1973:

$W_mathrm\left\{Gini\right\} = overline\left\{text\left\{Income\right\}\right\} cdot left\left(1-G right\right)$
The average per capita income of a measured group (e.g. nation) is multiplied with $\left(1-G\right)$m where $G$ is the Gini index, a relative inequality measure. James E. Foster (1996) proposed to use one of Atkinson's Indexes, which is an entropy measure. Due to the relation between Atkinsons entropy measure and the Theil index, Foster's welfare function also can be computed directly using the Theil-L Index.

$W_mathrm\left\{Theil-L\right\} = overline\left\{text\left\{Income\right\}\right\} cdot mathrm\left\{e\right\}^\left\{-T_L\right\}$

The value yielded by this function has a concrete meaning. There are several possible incomes which could be earned by a person, who randomly is selected from a population with an inequal distribution of incomes. This welfare function marks the income, which a randomly selected person is most likely to have. Similar to the median, this income will be smaller than the average per capita income.

$W^\left\{-1\right\}_mathrm\left\{Theil-T\right\} = overline\left\{text\left\{Income\right\}\right\} cdot mathrm\left\{e\right\}^\left\{T_T\right\}$

Here the Theil-T index is applied. The inverse value yielded by this function has a concrete meaning as well. There are several possible incomes to which an Euro may belong, which is randomly picked from the sum of all inequally distributed incomes. This welfare function marks the income, which a randomly selected Euro most likely belongs to. The inverse value of that function will be larger than the average per capita income.

The article on the Theil index provides further information about how this index is used in order to compute welfare functions.