Attempting to apply the principles of welfare economics gives rise to the field of public economics, the study of how government might intervene to improve social welfare. Welfare economics also provides the theoretical foundations for particular instruments of public economics, including cost–benefit analysis, while the combination of welfare economics and insights from behavioral economics has led to the creation of a new subfield, behavioral welfare economics. The field of welfare economics is associated with two fundamental theorems. Thus a social planner could use a social welfare function to pick the most equitable efficient outcome, then use lump sum transfers followed by competitive trade to bring it about. Because of welfare economics' close ties to social choice theory, Arrow's impossibility theorem is sometimes listed as a third fundamental theorem. A typical methodology begins with the derivation (or assumption) of a social welfare function, which can then be used to rank economically feasible allocations of resources in terms of the social welfare they entail. Such functions typically include measures of economic efficiency and equity, though more recent attempts to quantify social welfare have included a broader range of measures including economic freedom (as in the capability approach).
Additional consumption provides smaller and smaller increases in utility (diminishing marginal utility). All individuals have interpersonally commensurable 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. 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. Many economists use Pareto efficiency as their efficiency goal. Market failures and externalities; there is also social cost. There are many combinations of consumer utility, production mixes, and factor input combinations consistent with efficiency. Hence, Pareto efficiency is a necessary, but not a sufficient condition for social welfare. 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. 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. A social indifference curve drawn from an intermediate social welfare function is a curve that slopes downward to the right.
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).
The field of welfare economics is associated with two fundamental theorems. Because of welfare economics' close ties to social choice theory, Arrow's impossibility theorem 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 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 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 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.
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. Some even question the value of ordinal utility functions. Value assumptions explicit in the social welfare function used and implicit in the efficiency criterion chosen tend to make welfare economics a normative and perhaps subjective field. According to this line of argument, utility is not the only thing that matters and so a comprehensive approach to welfare economics should include other factors.
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