Chapter 7: Welfare theory III





1st Two preliminary notes

2nd The value premises of the welfare theory

3rd The two Gossen's laws

4th Welfare maximisation at income equality?

5th The paretian welfare theory

6th The compensation criteria

7th The pension concept

8th The theory of the second best

9th The significance of the competition for the welfare

              10th  Externalities

              11th  The Cost-Benefit analysis

              12th  Pareto-optimal redistribution


6. The compensation criteria


Above, we have already touched a further objection to the criterion developed by Pareto, namely the question: How large is the amount of policy measures of which it can be said that they bring benefit to at least one individual, but do not harm any individual. In reality, we have to assume almost always (or even without exception?) that almost every (or even every) measure causes damage at least to a small group of individuals. Thus, the Pareto criterion would be doomed to failure in reality; a large majority of individuals could agree with the criterion provided that measures are found that meet this criterion, but in reality there is no such measure that does not harm any individual.


Just in order to overcome this weakness of the Pareto criterion, a discussion was fuelled within the framework of the new welfare theory on how to overcome this weakness, how the Pareto criterion could be applied to concrete measures by a certain reformulation without leaving the actual statement of this criterion.


This discussion begins with a proposal from Nicholas Kaldor and John Richard Hicks, that one could also see such policy measures as clearly welfare increasing in which some individuals are experiencing utility losses, provided that the winners of this measure are able to fully compensate the losers and nevertheless a net profit would be still left for the winners.


In order to clarify this proposal, we apply the concept of the utility possibilities curves. On the abscissa, we draw the respective utility of the individual 2 (n2) and on the ordinate the utility of the individual 1 (n1) and in this diagram we draw the utility possibilities curve, whereat this utility possibilities curve shows how a particular bundle of goods grants different utilities to the individuals at different divisions. It is assumed that this utility possibilities curve has a negative course. For the sake of simplicity we have drawn this curve as a straight line in the graphic below; the results do not change in a decisive manner when we consider this utility possibilities curve as a curved graph, as it is usually the case in reality.



The starting point is point 1 on the yet valid utility possibilities curve w1. There would be a policy measure up to discussion which would lead to a new utility possibilities curve w2, where the hereby resulting new distribution of utilities corresponds to point 2. This result clearly contradicts the Pareto criterion, since individual 1 now gains a lesser utility than before. However, by movement along the new utility possibilities curve, that means by compensating the loser (person 1), a new utility distribution can be achieved at point 3 in which both individuals obtain a higher utility than in the starting point 1.


This measure therefore can be classified as a welfare increasing measure according to the Kaldor-Hicks criterion. The field of application for the assessment of policy measures has been clearly extended in comparison to the original Pareto criterion. While under the exclusive validity of the Pareto criterion virtually no concrete policy measure could be assessed clearly, there are now numerous measures which allow a clear assessment. The hatched field in the graphic below shows the now new field of application for political measures.   



But if the new utility possibilities curve had a flatter course than the previous curve there would be no possibility of compensation. This measure could not be classified as welfare increasing even according to Kaldor-Hicks. A movement along the new utility possibilities curve does not lead to any solution. There is no point on this new utility possibilities curve that promises any utility increase to both (all) individuals.





The starting point is the utility possibilities curve w1 and the point 1. The new utility curve w2 results from a policy measure. This measure leads to a utility distribution which would correspond to point 2. Here, it is possible to head for a point 3 by movement along the new utility possibilities curve w2 in which both individuals are better off than before (point 1). Thus, this measure corresponds to the Kaldor-Hicks criterion.


Now, let us try to undo this measure.  This means that we are again returning from the utility possibilities curve w2 to the previous utility possibilities curve w1 and to the starting point 1. By a movement along the now again valid utility possibilities curve w1 we can control a new point 4, which in turn sets both persons better than in the condition point 2. Thus, the undoing of this measure also corresponds to the Kaldor-Hicks criterion. But this is not possible for logical reasons.


The execution of a measure and its former condition can not be regarded as both welfare increasing. If the implementation of a measure is classified as welfare increasing, then for logical reasons, the previous state (the undoing of this measure) must be described necessarily as welfare-reducing. According to Scitovsky, can a measure therefore only be classified as welfare increasing if it firstly corresponds to the Kaldor-Hicks criterion, and if secondly the reversal of this measure would not have to be viewed as welfare increasing.


By this contribution the scope of the evaluation of policy measures is significantly restricted once again, since many of the measures meet the Kaldor-Hicks criterion, but do not pass the Scitovsky test. At all measures that lead to a lower utility possibilities curve than before, the Scitovsky test fails.


Ian Malcolm David Little has now also criticised the welfare test of Kaldor-Hicks and Scitovsky, since changes in the distribution would remain unconsidered in this test. Little therefore proposes a multistage selection criterion:


1. Is the Kaldor-Hicks criterion fulfilled?

2. Is the Scitovsky criterion also fulfilled?

3. Is the redistribution associated with the measure desirable?

4. Is compensation possible at all? 


The third question could only be decided politically, if politicians approve the change in the distribution connected with the intended measure, then any measure that satisfies the double test of Kaldor-Hicks and Scitovsky can be described as welfare increasing. However, if this change in the distribution is viewed as undesirable by the politicians then it has to be examined on the part of science as to whether the necessary compensation can be carried out politically at all. The utility possibilities curve only indicates whether such compensation can be carried out technically, it does not say anything about whether such compensation is politically opportune and can therefore also be carried out actually. But only in this case could the measure ultimately be regarded as welfare increasing in the case of initially undesirable changes in the distribution. 


At these four criteria, which can each be fulfilled or not fulfilled, there can be distinguished 16 cases in a casuistry, where there are cases where a welfare increase can clearly be affirmed or denied, but there can also be cases where no clear decision is possible.


As a first example, let us take a case in which both the Kaldor-Hicks criterion is fulfilled and the Scitovsky test does not lead to any contradictions, but the change in the utility distribution is regarded as undesirable, but there would still be no chance for compensation. The following graphic would correspond to this case:





Point 1 on the utility possibilities curve w1 corresponds to the initial state. The proposed measure leads to the new utility possibilities curve w2 and the utility distribution of point 2. The new solution, which corresponds to point 2, is considered undesirable from the perspective of distribution policy. Point 3 and Point 4 were technically possible, but not politically feasible solutions. Therefore leads point 2 to an undesirable redistribution, it is thus welfare decreasing;  but on the other hand is the solution of the point 2 clearly superior to the solution of the point 4, that is to say, partially welfare increasing. According to Little, there is no way to decide whether the planned measure increases welfare or not, since the partial welfare changes can not be compared with each other.


Let us consider now a second case in which the Kaldor-Hicks criterion is not fulfilled, the Scitovsky test does not lead to contradictions, the change in the utility distribution is undesirable and can not be corrected by compensatory payments either. The following graphic illustrates the situation:



In this case, a welfare increase can be denied clearly. On the one hand, solution 4 is clearly inferior to solution 1 (the starting point); Solution 1 offers indeed a higher utility for both persons. But on the other hand is solution 2 subject to solution 4 for reasons of distribution policy. Thus is valid W (2) <W (4) <W (1), whereat W (n) indicates always the welfare of solution n. Consequently, W (2) is also inferior to the solution W (1).


Finally, let us take a third example in which a welfare increase can be affirmed clearly. The Kaldor-Hicks criterion is met, the Scitovsky test leads to contradictions, the occurred redistribution is not desired, but compensation would be possible also politically. Again, this situation is illustrated by the following graphic:



The political measure initially leads to point 2, which though is politically undesirable for reasons of distribution policy. But since compensation according to point 3 is also politically possible and this point 3 is clearly superior to starting point 1, can this measure be regarded clearly as welfare increasing under these conditions.


The advantage of the Little criteria lies in the fact that now the scope of the policy measures for which a clear assessment is possible was again increased compared to the double test of Kaldor-Hicks and Scitovsky. It was possible to carry out a clear assessment in the last example, although the Scitovsky test was not passed. It is now also possible to assess cases which do not allow compensation.


S. K. Nath has incidentally shown that by the Scitovsky test or the Little criterion not all conceivable contradictions could be eliminated. As soon as the advantage of a solution is measured on the principle of equality (near proximity to equality) one would come to different results, depending on which distribution of utility is assumed. However, this extension shall here not be discussed further.


Rather, we want to deal conclusively with a further narrowing of the scope proposed by Paul A. Samuelson. In the context of the Scitovsky test two solution pairs are compared as shown: The starting point (P1) with the solution which is reached due to compensation (P3), and - when the measure is withdrawn - the solution (P2) with the solution (P4). It is therefore accepted that evaluations are made on the basis of different utility distributions.


However, if one reasons ongoing from two different utility distributions, why, as Samuelson asks, is one not willing to base all possible utility distributions and to ask whether under all possible utility distributions there are no policy measures that can be classified as welfare increasing. However, such a solution presupposes that the original and the potential utility possibilities curve arising from the political measure do not intersect at any point.


Such an approach would have the advantage that a decision on whether a policy measure would lead to a welfare increase could be made without the help of political assessments. On the other hand, such a solution has the disadvantage that the scope of this welfare criterion shrinks almost to the level of the original Pareto criterion.


A similar limitation of the scope of application was found by W. M. Gorman, who assumes that even if the Scitovsky test is included, contradictions can still arise when more than two measures are discussed. The following graphic is intended to make this idea clear:



One proceeds from the solution (P1), then, by means of political measures, one proceeds to the solution (P2), then (P3), and finally (P4). According to Kaldor-Hicks and Scitovsky the following ranking order of the individual solutions applies: W (1) <W (2) <W (3) <W (4), nevertheless is the renewed transition to W (1) superior to the solution (4), which again is a logical contradiction to the first ranking order. Also here it can only be spoken of a consistent evaluation with absolute certainty if none of the utility possibilities curves intersects another; but this was already the result of the reflections of Samuelson. 


7th The surplus concept


With the surplus concept, Alfred Marshall has developed a new instrument for the evaluation of current conditions as well as political measures. This instrument differs from the previously discussed welfare criteria for one thing therein that the welfare is not measured in utility units, but in monetary terms and is thus much easier to apply than utility terms. For another thing, the surplus concept refers however only to individual markets and can not be applied to the entire national economy unlike the theory of choice.


The starting point of Marshall's considerations is a diagram on which abscissa the quantity of goods are drawn and on the ordinate are drawn the goods price as well as the marginal costs and marginal utilities. First, we draw a normal supply curve in this diagram. As is well known, this can be derived from the course of the marginal cost curve. We assume that entrepreneurs are striving to maximize their profit, but have no direct influence on the goods price, and thus behave as quantity adjusters.


The supply curve shall then indicate the amount of supply at which the entrepreneurs maximise their profit. We start from any amount of supply and ask ourselves if it is worthwhile for the enterprise to expand the supply. It is worthwhile as long as the proceeds from the last sold unit of goods (the marginal revenue) are higher than the cost increases of the last produced unit of goods (marginal costs). The profit is thus maximised exactly when marginal costs and price coincide. The supply curve then coincides (only at the assumption that the marginal costs increase with increasing production) with the marginal costs curve. The intersection of the marginal cost curve with the ordinate measures the amount of the fix costs (KF). 


We can now determine the amount of entrepreneurial profit for each given price. The profit is defined as the difference between sales revenues and total costs of production. We can now see the size of the profit in the diagram below: 



The red line represents the supply curve, the area shown in red indicates how much profit the enterprise achieves at a price p0 given from the outside. The total sales revenue corresponds to the area (p0, 0, x0, a’), the total costs correspond to the area (KF, 0, x0, a’); the difference between revenue and costs finally yields the profit, the area (p0, KF, a’). This profit is now declared by Marshall as a producer surplus, the term surplus is understood here as an excess (of the proceeds over the costs).


We now draw the demand curve in our diagram which indicates the quantity of goods that is demanded at alternative prices. The supply curve has a positive course, whereas the demand curve has a negative course; it is assumed that a rising price leads to a decrease in demand. In analogy to the supply curve, we can derive the demand curve from the course of the marginal utility curve. The marginal utility of a good decreases, as well known, with increasing consumption quantity.


If we assume that the household is trying to maximise its utility with its consumer goods demand, than it will extend its consumer demand until utility increases can be expected no longer. If we start from any quantity of consumer goods and ask what utility changes are to be expected when the household is asking for a further unit of goods. On the one hand, he has to pay the goods price (the utility is thus diminished by this amount); on the other hand, he receives a utility increase in the amount of the marginal utility dependent on the quantity of goods.


As long as this marginal utility is higher than the utility loss which arises from the fact that he has to pay a price, that he can not buy other goods for these income parts, and that he thereby misses benefits, increases the total utility. The utility maximum is therefore reached exactly when price and marginal utility coincide and this means that the point of intersection of the price line with the marginal utility curve (demand curve) yields the quantity of goods which grants a utility maximum to the household.


We can now declare the (blue) surface, which forms the price line with the demand curve, as a consumer surplus; this indicates the total utility that the household achieves at a certain price p0. This area represents the maximal amount of money that the household could pay, at which just no additional utility would result.




The sum of consumer and producer surplus then results in the total utility of the market participants from the production and consumption of the respective good.


This surplus concept can now be applied to determine how a particular policy measure affects the welfare of the whole society. Let us insinuate that the state is planning to introduce a consumption tax which the enterprises have to pay to the state. The marginal costs curve, and with it the supply curve, is then shifted upwards parallel to the tax amount if we assume that the entrepreneur has to transfer a certain absolute amount (t) as tax to the state for each sold quantity of goods. How does this measure change the total welfare now? Consider the following graphic:



The introduction of the sales tax now results in a decline in the consumer surplus, which corresponds to the light blue area (the remaining consumer surplus is determined by the dark blue surface), furthermore a decline in the producer surplus (= bright red area, the remaining producer surplus is now dark red). The government, though, receives tax revenues corresponding to the gold-framed, transparent area. The graphic shows that in balance a reduction in the total welfare is obtained, which corresponds to the two triangular surfaces (1, 2, a ') and (2, 3, a') and is declared as Harberger’s triangle in honour of Arnold C. Harberger, who has described this welfare reduction as the first.


Several criticisms were objected against the surplus concept. So has Ezra J. Mishan raised the accusation of double counting when the utility of the producer is added to that of the consumer, even though the use of the producer is merely derived. However, Mishan considers it possible to separate the utility that the individual is experiencing on the goods markets from the utility that the individual receives on the factor markets.


We have to assume that a household does not only experience utility in its capacity as a consumer, but also as a provider of production factors, such as work. Just as in the calculation of the consumer surplus, the utility growth of the additional purchased goods is compared with the utility loss which is caused by the fact that the purchase sum can not be spent on another good. The same way, the household has to compare, when it offers, for example, one additional hour of work, the utility gain from the additional income with the utility loss due to reduced leisure time. Thus, additional surpluses are also created from the supply of production factors.


A second criticism of the pension concept refers to the fact that the shown welfare gains have always been developed under the ceteris paribus condition, namely that all other markets remain unaffected by transactions in the considered market. This assumption is generally not possible. However, it can be said that with minimal changes on the one market the resulting changes in other markets are so minimal that they can be neglected.



Continuation follows!