#4972 - Compensation Tests Vs Social Welfare Functions - Advanced Microeconomics

Introduction for Compensation Tests

• There are limitations of the Pareto principle, as it cannot rank all states. Also, most policies make some better off whilst others worse off. In real life there are always losers and gainers, and the pareto criterion cannot handle such circumstances.

• One approach of moving beyond the Pareto principle involves the use of “potential pareto improvements” via compensation tests.

• This expands the range of states that can be ranked to include those where some are made worse off, but without recourse to distributional judgements.

Compensation Tests Explained

• Kaldor and Hicks suggested the compensation principle in 1939. According to the Kaldor criterion, if the gainers from a project can fully compensate the losers, and still be better off themselves, then the change is a potential Pareto improvement in welfare and is therefore socially desirable.

• The Hicks Criterion suggests that a project should go ahead if losers cannot bribe the gainers to refrain from undertaking the considered project.

• The power of the compensation test lies with it being hypothetical, and that it is not actually paid. If the compensation was paid, then we would not have advanced beyond the Pareto principle. In practical applications it would also be impossible to compensate everyone anyway. By focusing on the potential compensation one focuses on the efficiency aspects of the policy change. For instance, through knowing that the winners could compensate the losers, we understand that the benefits outweigh the costs – this is the basis for social cost benefit analysis.

Graphical Illustration

The UPC draws the utility implications of the contract curve. Say some project can now be implemented that reaches a higher UPC curve. B is preferred to A because there is a potential Pareto improvement, even though it is not an improvement according to the Pareto criterion. But according to the Kaldor criterion, re-distribution could move to point C, where there is an improvement in welfare for both individuals - the winners could compensate the losers and still be better off.

If we expand the range of states for further investment projects, we can note social ordering. That is, each change results in a potential Pareto improvement. Continued application of the compensation test ensures we reach Pareto optimality at the highest ranked state.

Problems

• The Utility Possibility Frontier represents differing distributions of purchasing power between two individuals for a given level of efficiency. In order for someone to be better off, another must be made worse off. Given the compensation isn’t actually paid, and someone is made worse off in the test, then the compensation principle, rather like the Pareto principle, cannot rank between two states on the UPF, as they are Pareto non-comparable.

• So a separate judgement must be made as to whether the distribution of utility is desirable or not:

  • It is possible for successive Pareto improvements to widen disparities in utility?

  • The initial distribution may even affect whether the compensation test will be passed for the new project.

  • The compensation test also assumes that costless re-distribution is possible, but this is only true when achieved through some form of lump-sum taxation.

Scitovsky Paradox

• So compensation principle cannot say anything about relative desirability of a project. A more paradoxical concept is the Scitovsky Paradox. Suppose a project would in fact alter the utility possibility frontiers between two individuals, so that they now intersect.

The move from I to F passes the compensation test, as there is room for reallocation that would suggest Pareto improvement. But the same is true for point F to I, so we cannot order all states with this test.

It is necessary then to make stronger assumptions than those covered by the Pareto and Compensation principle.

Solutions?

[Scitovsky criterion]

One possibility is the Scitovsky criterion. If the move passes both the Kaldor and Hicks test, then the Scitovsky paradox cannot arise. However, this does not deal with the problem of intransitivity. With numerous projects that pass both Kaldor and Hicks tests, it is possible for states to be ranked cyclically. So again, it is still impossible to rank all states. Furthermore, establishing the necessary information for appropriate the redistribution is very impractical as well, as it is normally very difficult to perform a Kaldor or Hicks test.

[Little 3-part Criterion]

An alternative viewpoint involves the Little 3-part criterion.

• If we accept that a Pareto improvement in welfare is a good thing, and we can judge whether the change being proposed is good or bad in terms of distribution, then clearly a move will be good if it satisfies a compensation test and is judged to be good from a distributional perspective.

• The problem is that it cannot rank all states, and distributional judgments require some sort of interpersonal comparison of utility, which may not be possible. Ultimately, we need a social welfare function, as it gives complete knowledge of how society ranks all states.

Introduction

• Given the issues of utility conflict, we want a “social decision rule” that can consistently rank all points within and on the UPF.

• A social welfare function is a set of rules for ranking alternative states of society.

• Social welfare function is assumed to have three properties:

  • Welfarism (depends solely on utility of households)

  • Strong Pareto Criterion (increase in household utility increases welfare)

  • Intensity of trade off depends on the inequality between individuals, and the utility curves are convex to the origin.

• The social welfare function enables us to reduce a large number of possible equilibria to a single point – a bliss point.

Implications for the Measurability of SWF

Arrow’s Impossibility Theorem

Though there are some considerations when determining the measurability of welfare, such as Arrow’s Impossibility Theorem. Let’s take a simple utilitarian social welfare function (Benthamite), where social welfare is the unweighted sum of household utilities. Individuals are equipped with an ordinal utility function to determine their own preferences. Therefore, the ranking of states in the social welfare function depends which individual’s utility function we choose to use. So if utility functions are ordinal and non-comparable, then the only possible consistent social welfare function is a dictatorship. Then a social welfare function is impossible to determine via majority voting, as some individuals’ preferences are disregarded.

Single-peaked preferences

• One way out of Arrow’s theorem is single-peaked preferences. The further he departs from this, the greater his loss in utility. I.e. if X>Z then if Y is in between, it is unlikely that Z>Y (should take that X>Y>Z). Thus each individual selects his first preference.

• In this scenario, intransitivity disappears as individual preference is represented by a single choice. The issue here is that single peaked preferences disregard free orderings, which is actually more of a reasonable assumption that can be applied.

Cardinal measurements

• Alternatively, cardinal measurements could be adopted.

• Issue of majority voting is to disregard for strength of preference. A 51% vote for a project may not achieve a desirable welfare improvement, as 49% may be at a loss.

• If utility could be measured on a cardinal scale and compared across all households however, then the problem would be solved.

• Cardinal utility, as opposed to ordinal utility, allows additional utility curves to express intensity of preferences and partial comparability via affine transformations of utility functions.

• The following function can specify a more comparable social welfare function:

W = k_iU_i

Where U_i = cardinal utility of person i

k_i = equity weight attached to it

Implications?

How do we measure utility? And how do we choose equity weighting?

• Monetary measures of willingness to pay or willingness to accept compensation – i.e. following the same principles of the compensation tests.

• Yet a monetary measure of income has no consideration of relative utility weighting. i.e. a marginal increase of 1 means more to a poor person than a rich person. In addition, we are faced with similar problems of distribution as with the compensation tests.

• We can use monetary measures multiplied by weights reflecting the relative marginal utility of income (MU_y).

• For a constant elasticity function: U=aY^b, money has been converted into utility, so that we can just add these utilities or apply equity weights.

• But how can we measure the value of b (b-1 = elasticity of MU_y with respect to Y) - does it have to be a subjective judgement of fact?

  • Some estimates suggest an elasticity of -2

  • So if income doubles then the marginal utility of income halves.

    • i.e. accounts for relative weighting of utility of marginal increments in income.

• Problems with equity weighting:

  • Different people choose different social welfare functions

  • People seek to maximise their expected utility so they chose the Benthamite function (which maximises sum of utilities)

  • Rawls argues that people adopt a maxi-min approach, so choose a function that maximises the utility of the poorest

  • So we are stuck at arrow’s theorem all over again. Who will choose the appropriate social welfare function to be adopted?

Ultimately, there is no universally accepted principle for making interpersonal utility ...