Welfare economics

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 prefer greater welfare to less welfare, and that welfare can be adequately measured either in monetary terms 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, as well as strong underlying assumptions.

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 Neoclassical approach and the New welfare economics approach.

The Neoclassical approach was developed by Edgeworth, Sidgwick, Marshall, and Pigou. It assumes that:

With these assumptions, it is possible to construct a social welfare function simply by summing all the individual utility functions.
 * Utility is cardinal, that is, scale-measurable by observation or judgment.
 * Preference is exogenously given and stable.
 * Additional consumption provides smaller and smaller increases in utility (diminishing marginal utility).
 * All individuals have interpersonally comparable utility functions (Edgeworth would disagree about this--see his Mathematical Psychics).

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 dispenses with cardinal measures of utility: 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, principle-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 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. 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 function. 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 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 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 (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.

Criticisms
Many 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.

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 controversial.

Online Articles and books
A socio-economic Evaluation of Western Social Models. (pdf 3Mb) - The free Institute for Economic Research. The authors investigate Western social models on their efficiency in realising prosperity, employment, solidarity and individual freedom.  See the table comparing the major social objectives here 
 * path to a sustainable Welfare State.'''