Chapter 7: Welfare theory III
Outline:
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
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!