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Welfare economics

Welfare economics is a branch of economics that uses microeconomic techniques to simultaneously determine the allocational efficiency of a macroeconomy and the income distribution consequences associated with it. It attempts to maximize the level of social welfare by examining the economic activities of the individuals that comprise society.

Welfare economics is concerned with the welfare of individuals, as opposed to groups, communities, or societies because it assumes that the individual is the basic unit of measurement. It also assumes that individuals are the best judges of their own welfare, that people will prefer greater welfare to less welfare, and that welfare can be adequately measured either in dollars (or some other unit of currency) or as a relative preference.

Social welfare refers to the overall utilitarian state of society. It is often defined as the summation of the welfare of all the individuals in the society. Welfare can be measured either cardinally in terms of dollars or "utils", or measured ordinally in terms of relative utility. The cardinal method is seldom used today because of aggregation problems that make the accuracy of the method doubtful.

There are two sides to welfare economics: economic efficiency and income distribution. Economic efficiency is largely positive and deals with the "size of the pie". Income distribution is much more normative and deals with "dividing up the pie".


Two approaches

There are two approaches that can be taken to welfare economics: the Neo-classical approach and the New welfare economics approach.

The Neo-classical approach was developed by Pigou, Bentham, Sidgwich, Edgeworth, and Marshall. It assumes that utility is cardinal and that additional utils provide smaller and smaller increases in utility (diminishing marginal utility). It further assumes that all individuals have similar utility functions, therefore it is meaningful to compare one individuals utility to another's. Because of this assumption, 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 part of the discipline and the distribution part 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 need not require cardinal measures of utility: ordinal utility is adequate for this analysis.


Most 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 must be identical for all consumers (no consumer can be made better off without making others worse off)
  • The marginal rate of transformation in production must be identical for all products (it is impossible to increase the production of any good without reducing the production of other goods)
  • The marginal resource cost must equal the marginal revenue product for all production processes. (the marginal physical product of a factor must be the same for all firms producing a good)
  • The marginal rates of substitution in consumption must be equal to the marginal rates of transformation in production. (production processes must match consumer wants)

There are a number of conditions that, most economists agree, may lead to inefficiency. They include:

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.

Income distribution

There are many combinations of consumer utility, production mixes, and factor input combinations consistent with efficiency. In fact, there is an infinity of consumer and production equilibria that yield Pareto optimal results. There is 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 equation 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 welfare function) sums the utility of each individual in order to obtain society's overall welfare. Everyone is treated the same, no matter what their initial level of utility is. 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 that already has all the wealth he/she could ever spend. At the other extreme is the Max-Min function proposed by John Rawls. 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 procedure is to maximize social welfare, subject to various constraints such as the state of technology in production, available natural resources, national infrastructure, and behavoural 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 = 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 a little more complicated.

Efficiency between production and consumption

The relation between production and consumption in a simple seven equation model (2x2x2 model) can be shown graphicly. 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 inside the Edgeworth box (sometimes called a contract curve) 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 economies 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 (sometimes called the bliss point) 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.


Many doubt whether a cardinal utitity function (or cardinal social welfare function) is of any value. How do you aggregate the utilities of various people that have differing marginal utility of money (ie, the rich and the poor)?

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. These price based measures are seen as promoting consumerism and productivism by many. It should be noted that it is possible to do welfare economics without the use of prices, however this is not always done.

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 controvertial. If these value assumptions are hidden or uncritically accepted, welfare economics could be dangerous.

Welfare economics techniques are held hostage to their initial starting point. Welfare maximization is optimum relative to the initial starting position.

Marginal rates of substitution ignores Veblenesque effects.

See also

Last updated: 10-24-2004 05:10:45