Justin Morton
Junior Sophister

Welfare economics is the branch of economics which applies theory laid down by the rest of the subject, mainly microeconomics. Basic theory is applied to the area of social choice in a bid to assist policy decisions in this area. Hence, the objective of welfare economics is a fruitful one. However, a certain ambiguity remains over the question of whether it has been successful in its aim. In this essay, I will show how welfare economics has succeeded in its original task, and has not failed into academic obscurity that is, it is not for light.

The literature in welfare economics can be divided into two areas: efficiency and distribution. The marriage of these two concepts is welfare economics and is what directs policy choice. Section I will deal with efficiency criteria, Section II with distribution criteria and Section III with the marriage of the two and what results.

Section I

To measure welfare, and hence welfare changes, we appeal to the microeconomic notion of utility. A societys utility is dependent on the utilities of all its INdividuals

W = f(U1,U2,.....Un).

As a proxy for utility, we employ the notion of willingness to pay.[1] The higher the willingness to pay, the greater utility he or she must obtain.

With a proxy of welfare in mind, we now turn our attention to maximising the economic cake. Vilfredo Pareto introduced the efficiency criteria which now form the basis of welfare economics. Pareto defines an improvement in social welfare to have taken place when at least one individuals utility has risen, and nobody elses utility has fallen. This is known as the Pareto criterion and is based on certain assumptions. According to Andrew John[2] these are:

(i) social welfare depends positively on the welfare of individuals

(ii) welfare of individuals depends on the goods and services they consume

(iii) individuals are the best judge of their own welfare, and act in their own self interest.

Although these are accepted, they are open to criticism. Granted they may not hold in certain instances but these cases are the exception rather than the rule. The key criticism of Paretos criterion for social improvement is that it does not allow for losers. (Responses to this will be discussed later.)

Writing after Pareto, the Irish economist Edgeworth furthered this work by constructing his boxes of consumption and production based on a two-person, two-good, two-firm economy. The first order conditions for Pareto optimality, a case where no-one can be made better off without someone losing, are:

(i) marginal rate of substitution (MRS), the rate at which a person would exchange one good for another while keeping utility constant, must be equal for both people in society. If this condition holds, efficiency in exchange is guaranteed and utility is maximised.

(ii) marginal rate of technical substitution (MRTS), the rate at which a firm can exchange the factors of production between two goods, while at the same time keeping quantity constant, must be equal for both firms. If this condition holds, efficiency in production is guaranteed and profits are maximised.

(iii)MRS is equal to marginal rate of transformation, the slope of the production possibility frontier. This ensures that the rate at which firms can reallocate to produce good 1 instead of good 2 is equal to the rate at which consumers want to exchange good 1 for good 2. The outcome is harmonious across all markets.

This analysis leads to the utility possibility frontier (UPF) which maps all combinations of utility which result from this general equilibrium (i.e. the locus of all Pareto optimal points). Consider the point A inside the UPF. This is not a Pareto optimum, since the movement to point D means that both individuals gain and there are no losers.

Diagram 1

As mentioned earlier Pareto gives a non-complete ordering of possible allocations. The point D has the property that there is no feasible Pareto superior point. It is therefore Pareto non-comparable to C. How then do we choose between two points that lie on the UPF?[3]

In an attempt to overcome this, Kaldor[4]developed his ingenious compensation tests. This test deems a project desirable if the gainers can hypothetically compensate the losers. That is, the policy should be implemented if there is a net monetary gain to society. In this case, the point K is more desirable than A. Notably the actual redistribution is not required, it is merely hypothetical.

However, Kaldor introduces another value judgement in order to validate his test. He asserts that there must be equi-marginal utility of money. Thus ten pounds to a millionaire yields the equivalent utility to a less well off person. While this may not necessarily hold, in the main, comparisons will be away from the extremities of the UPF, validating the Kaldor criterion.

Unfortunately for Kaldor, Scitovsky noted a paradox in the test. This arises when UPFs cross, with the present allocation on the first UPF, and the allocation after a potential policy implementation on the other. The paradox, that given the policy is not implemented it is preferred, and given the policy is implemented the former state is preferred! Hence Scitovsky introduced his reversal criterion to overcome this paradox.

The first order conditions for Pareto optimality will only be fulfilled in an entirely perfectly competitive market structure. Due to market failures such as public goods, externalities and monopolies, reality does not result in such a structure. Although this does not nullify the analysis it does have serious implications which are addressed in Section III.

Section II

Although both Pareto and Kaldor remained neutral about actual redistribution of welfare it is a key issue in modern life. According to Pigou:

The misery and squalor that surround us, the injurious luxury of some wealthy families..., these are evils too plain to be ignored.[5]

Hence, we attempt to compile a social welfare function (swf), a map of different levels of utility for each individual that gives rise to a given level of social welfare. The swf allows us to reveal the bliss point where it is tangental to the UPF. To find this point, we need to find the form of the swf. Appealing once again to the concrete foundations of microeconomics, we can think of an indifference curve as showing combinations of two goods which leaves the consumer at the same level of utility. A swf is an aggregate of n individual indifference curves and thus shows the combinations of n peoples utility which leaves society at the same level of social welfare.

However, a major difficulty arises when attempting to reveal social preference. Inconsistencies arise and paradoxes occur when using majority voting. In fact Arrow, in his Impossibility Theorem, claims that there is no way of deriving preferences consistent with social preferences.[6]

As an immediate result of this problem, there is debate over the shape of the swf. John Rawls posits that societys welfare only increases when the utility of the poorest person increases. A swf based on this viewpoint is L-shaped. Conversely, Jeremy Bentham believes that an increase in utility is equivalent and desirable regardless of the wealth of the individual. This leads to a straight-line downward sloping swf, a third swf was outlined by Bergson and Samuelson. In this case, extra negative weights are given to cases where the distributions of utility are highly skewed. The shape of this curve is convex to the origin. The very existence of at least three alternatives highlights the political nature of the swf.

Section III

Combining the efficiency and distribution criteria laid out in Sections I and II, in a perfect market where social preferences could easily be revealed, leads to a complete ranking of all social states, and hence we end up at the bliss point.

However, noted above are certain practical problems relating to both the efficiency and distribution areas. In the former we come across market failures and in the latter we encounter preference revelation difficulties.

The market failures imply a role for the government. However, due to complex market interrelationships, it appears implausible for the government to come up with a set of rules to apply uniformly across the economy to lead to optimum efficiency. Hence the government is limited to individual proposals to change welfare, such as a new public park or a new bypass. Thus their role cannot be to rank all social states but rather to rank certain proposals open to them at a given time to move the economy towards efficiency. This means that the governments role is discretionary. To rank these individual changes the government appeals to welfare economics, changing the actual role of the subject from ranking all social states to ranking a few. Kaldor-Scitiovsky criteria fulfil the task of choosing between proposed projects by estimating if there is a net monetary gain to society. This work is the foundation of Cost Benefit Analysis (CBA), welfare economics most powerful tool. CBA assesses all the costs and all the benefits of a given project in quantitative money terms.

So, with an (imperfect) proxy for the efficiency criteria, how then do we get over the problem of preference revelation? This is done, again imperfectly, by the voting system. The elected government give weights to different projects depending on their effects on distribution. Whereas a labour government may value a distribution friendly project highly, a conservative government may value an efficiency friendly project highly. These weights reflect public opinion (through the voting process) and are cleverly encompass in CBA. Depending on the regime, the Benefits/Costs ratio for a given project will vary as the relative benefits of the distribution or efficiency are calculated. Hence, CBA combines both the efficiency and distribution elements in one tool.

Is the notion of the swf redundant and the search for the bliss point vacuous? Yes would be the answer from certain naive economic killjoys. What these authors fail to realise is how absurd the alternative to the economic approach to social choice theory is. Whereas economics provides firm systematic analysis, the alternative is a rag-bag of ad hoc techniques and value judgements.[7] In fact while economics is able to quantify notions as abstract as social welfare in actual monetary terms, the alternative approach is engulfed in qualitative nonsense. Granted, welfare economics is an incomplete subject. For example massive problems arise in social preference revelation and the imperfect world in which we live does not result in Pareto optimality. As Culyer (1973) puts it

The economic approach to social policy is, in general, more comprehensive than any other, and though it has many half filled boxes, it has no empty ones.


Welfare economics is fruitful in two ways. Firstly it provides us with CBA, a vital policy instrument. Secondly, and more essentially, it has brought us a long way down the road to being able to rank all social states and globally say whether or not a policy is desirable. Considering the importance of this, I propose we accept welfare economics in its entirety, and strive to further ourselves along this road to being able to rank all social states successfully.


Culyer, A (1973) The Economics of Social Policy

Johannson, P (1991) Introduction to Welfare Economics

Ng, Yew-Kwang (1979) Welfare Economics

OHagan, J (ed. 1991) The Economy of Ireland 6th ed.

Price, C (1977) Welfare Economics in Theory and Practice

Rowley & Peacock (1975) Welfare Economics - a liberal restatement

Varian, H (1992) Microeconomics