Chapter 7: Welfare theory





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



1st Two preliminary notes


The traditional welfare theory deals with the determinants of the welfare of a community. It wants to clarify above all, how economic systems, data changes and policy measures affect the welfare of a community. The Welfare theory, however, is not confined to factual connections, but asks for the evaluation of measures and conditions. It is therefore a science that is also looking for normative statements.


Here, the question arises whether such a claim does not come into conflict with the principle of freedom from value judgment formulated by Max Weber. With the reply of this question deals a first preliminary note.


Max Weber had famously put forward the thesis that ultimate values can neither be proved nor disproved with the methods of empirical science. Therefore, the scientists had to refrain from any value judgment in the sense that he issues political value judgments as a result of his scientific work.


The principle of freedom from value judgment, however, does not mean that a scientist must refrain completely from any political assessment. As every citizen, also the scientist is entitled to value judgments, he only shall not issue them as a result of scientific work and thus claim for his assessment a higher truth claim than applies for the assessments of all other persons involved in the political discussion.


If one accepts this principle of freedom from value judgment, there are basically only three different positions of a scientific examination of normative statements.


Firstly, one can hold, together with Hans Albert, the opinion that a scientist had to confine himself to examine facts connections in terms of a factual analysis. The scientist could therefore e.g. study and explain how a Keynesian fiscal policy would affect on inflation, but he was unable to judge on the desirability of such measures by means of scientific methods as a scientist. Thus, he had - in his capacity as a scientist - to refrain from any normative statements about the desirability of policy measures or conditions.


A second position took Gerhard Weisser (Hans Albert's teacher) on this question. The scientist could - without coming into conflict with the principle of freedom from value judgment - very well advance to normative statements on policy measures and conditions when he previously reveals the value premises due to which he came to these statements.


A scientific analysis in accordance with this scientific normativism formulated by Gerhard Weisser always begins hence with the disclosure of the value premises, followed by the then correct derivation of normative statements from these disclosed value premises for concrete policy measures.


Such an approach is to be preferred to the way proposed by Hans Albert therefore, that the scientist was much better than a normal, economic scientifically unskilled citizen will be able to draw conclusions from value premises and factual connections.


However, here would be noted critically that these conclusions in this case have always only validity for those citizens, who are sharing the value judgments of the scientist. There is the danger that the group of scientists falls into ideologically structured subgroups and that therefore the claim is lost that scientific statements should be valid regardless of the ideological position of the individual scientist.


A third position took the traditional welfare theory. In a first step, it tried to check which ultimate value premises are accepted by the vast majority of citizens, and then to clear in a second step, which concrete measures and economic systems are necessary in order to realise these generally accepted basic aims. This third position does neither contravene the principle of freedom from value judgment formulated by Max Weber.


We now come to a second preliminary note. The traditional welfare theory measures the societal welfare at the benefits that the single individuals derive from specific conditions or policy measures. This statement can be easily misunderstood in the sense that the welfare of a society is ultimately measured at the feeling of pleasure which perceive the individuals.


In fact, this was more or less the idea of hedonism, just as it has been advanced in connection with the development of the Early Classic in the late 18th century. Hedonism claimed not only that single individuals align all their activities the way that they achieve a maximum of pleasure - and this is an objective statement - but beyond, that in obtaining pleasure lays also the highest welfare of a population - and this is a normative statement.


Early on - in the framework of the subjective value theory, later mainly by Joseph Alois Schumpeter - was noted, however, that the most important statements of a utility and welfare theory by no means must relate to the pleasure principle, they can, but do not have to be interpreted in this way. The utility theory can then also be understood certainly as a theory that analyses a formal relationship between any aims and the necessity of scarce material goods to meet these aims.


One can divide the aims pursued by a human according to whether material goods are required to meet these aims or not. Wherever material goods for the realization of aims are necessary, it requires a calculus, which indicates how a maximum of aim realization of a given stock of material resources or in other words, how a minimum of material efforts can be achieved for a given aim. This is known as economic principle.


This calculus is necessary because on the one hand material goods in general are scarce and therefore do not last to realize all aims, on the other hand the extent of achievement of aims depends very well on the manner in which the aim realization is approached.


The question of whether and how much material resources are needed for the realization of an aim is independent to the value which is ascribed to an aim. It is in no case that aims with a high material effort for this reason have a lower value than the aims that can be realized without or with only little material efforts.


There are on the one hand aims with a very high moral value, which require a lot of material resources for the realization. We think, for example, about the aim to make a redistribution of goods in order to achieve in this way a more equitable distribution.


There are on the other side further aims that are generally rated very negatively, such as, for example, the joy of to harass and torment fellow human beings, but these can be realized under certain circumstances even without the use of material goods. These aims are not getting better morally thereby that they can be realized with almost no use of material goods.


One can now reformulate the utility theory very well the way that it is not about the gain of pleasure, but only about the realization of any arbitrary aim that can be classified as either valuable or as wicked, and that the most important statement of this theory consists in revealing ways in which the economic principle is met best possible way.



2 The value premises of the welfare theory


We have pointed out above that the traditional welfare theory answers the question, of how people ever can derive normative statements scientifically according to Max Weber's principle of freedom from value judgment, thus, that it asks in a first step on which ultimate value premises it is preceded in general. Therefore, let us ask ourselves which are now the value premises which may apply as generally recognized in the opinion of the welfare theory.


These are mainly two premises. Premise no. 1: the individualistic approach. Thereafter, the welfare of a national community derives from the welfare of its individuals and only from such:


WG = f(WI1, WI2, .... WIn),



with WG: Welfare of the community; WIn: Welfare of the individual n.


Compared to the Middle Ages or even the time of absolutism has occurred an enormous change, here. The welfare of a nation is no longer equated with the welfare of the current ruler, but it is the citizens of this state formation, whose welfare determines the welfare of the community.


Moreover, it is crucial that every single individual of a national community is included in the welfare function. Insofar all citizens are ultimately equal. Also herein a change of views can quite be seen. We think of the first constitution of the United States of America, not until the 13th Amendment of the US Constitution, which entered into force on 18 December 1865, slavery in the United States was finally abolished and declared the former slave to free, equal citizens.


Expressed negatively, says the individualistic approach that in the welfare function of a community enters also only the welfare of their members. This finding certainly contradicts any statist ideas, according to which the welfare of a community is at least not only determined solely by the welfare of its members, and general cultural values of the nation are consciously prized above the welfare of the individuals.


Here, it has to be taken into account that of course it is very well assumed, even at a properly understood individualistic view, that community aims are of great importance for the general welfare, but just only insofar as the implementation of these community aims ultimately benefits the individuals again.


Accordingly, it may be admitted quite also that the implementation of a community aim can sometimes come into conflict with the welfare of individual members of the community, namely in the sense that the welfare of a citizen may come into conflict with the welfare of other citizens, but that never community aims can get in contrast to the welfare of all individuals; the community aims always fulfill only a means function with regard to the ultimate aim, that all community institutions have to serve the welfare of the members of a community.


The individualistic approach may come into conflict with religiously based value systems. So according to Christian conviction surely to the glorification of God a central importance is attributed for the final evaluation of a community, though, according to Christian conviction, the commandment of love of neighbour (Respect your fellow man, for he is like you!) has to be counted of equal importance.


Now we get to value premise no. 2: the self-determination criterion. This criterion will give an answer to the question of who then actually has to decide which conditions cause benefits and which conditions cause damages to the single individual. The self-determination criterion answers this question the way that every individual has the right to decide for himself what is of benefit for him and what not, if hence, the individual condition changes are to be considered as a welfare-enhancing or welfare-reducing for himself.


Thus, the self-determination criterion opposes any meritorious approach under which another one - e.g. even a benevolent wise dictator - should determine about what is of benefit or harmful for the individual because this e.g. would dispose over a greater insight than the mass of his citizens.


The self-determination criterion corresponds certainly to the constitutions of democratic and liberal states, and therefore the finding that this is a generally accepted value premise may certainly be approved if certain exceptions to this rule are accepted.


Certainly, it corresponds to general conviction that the self-determination of the single individuals may be granted only above a certain age. One can argue about when the age of majority, from which on the individual is allowed to decide for himself, has to begin, with the 18th or even the 16th year of age or whenever, but it can not be denied that an individual is incapable of decision and action at birth and grows only gradually into the self-accountability.


A second limitation of the self-determination criterion is necessary at the very moment in which we consider that today pending decisions often decide on the welfare in the future and hence on the welfare of citizens, who are not even born at the time of the decision, or although born, but not having the majority age yet. Here, there is even no other choice than to provide for these people a foreign determination, whereat disagreements are present whether the parents have to take these decisions for their children or respectively the state as the representative of all individuals.


Of course, in individual cases, for adults may an external determination become necessary if the individual loses its decisions-making ability due to accidents and diseases.


Sometimes, it is spoken of a third value premise of the traditional welfare theory, namely the statement that the welfare of individuals depends on the provisions of resources (goods), that an increase in material goods enhances the welfare of individuals and thus the community.


I do not want to classify this statement as a value premise but rather as a factual premise. Indeed, if we proceed from the finding that the individuals themselves should determine when it can be spoken of changes in their individual welfare, then we can not see more than an additional value premise in the relationship between welfare and provision of resources.


When we therefore ascertain that the individuals speak of greater welfare if they are equipped with additional goods, then results this connection solely from the decision of individuals, there is no more room to evaluate this connection additionally - independently of the assessment of each individuals - from the perspective of society as a whole.



3rd The two Gossen's laws


From Hermann Heinrich Gossen stem the two Gossen's laws which are named after him. The first Gossen's law is called the law of diminishing marginal utility and contains the statement that the incremental utility (the so-called marginal utility) of a good drops, if of this good one unit more is consumed. The utility which brings about the first unit of a good is high; increases the consumption of this good, indeed increases the total utility of the good, though, the incremental utility gets each time lesser. Usually, it is assumed that from a certain amount of goods on occurs a saturation in the sense that an increase in consumption brings no additional incremental utility, the marginal utility then drops to zero, yes sometimes even it has to be expected that with further expansion of consumption the total  utility declines, thus, the marginal utility becomes negative.


Let us try to explain this law by way of an example. Let us suppose that an individual was near dying of thirst due to excessive heat, here the first glass of water brings him an infinitely large relief, the 2nd and 3rd glass of water may still be perceived as pleasant, but from a certain amount of consumption on the thirst is quenched, the consumption of another glass of water could not cause pleasant sensations any longer, though, perhaps even induce nausea.


We can illustrate these considerations in a chart. We draw on the abscissa the amount of goods consumed, on the ordinate the marginal utility, thus the incremental utility due to the last consumed amount. The marginal utility curve, that indicates how high the marginal utility is at different consumption levels, has a negative run, it is relatively high in the first consumption unit and decreases continuously with growing consumption quantity; the marginal utility becomes zero where the marginal utility curve intersects the abscissa, it extends further in the negative area of the chart if the marginal utility at expansion of consumption becomes negative. 



For simplicity, we have drawn the marginal utility graph linear. In reality, we have to assume that the marginal utility graph is crooked, whereas at varying goods both convex developments as well as concave developments are conceivable. At a convex development occurs by definition no absolute saturation.


The total utility depending on the consumed amount of goods can then be determined as the integral of the consumed area.






According to the subjective value theory we speak of utility and of marginal utility, which are caused by individual goods. However, the consideration should thereby not be limited to the achievement of desire and other sensations. According to the second preliminary note of this article one will also be able to detect similar laws, when one examines the question to which extent a particular aim realization is achievable by use of goods. Instead of utility and marginal utility one could therefore speak of welfare and marginal welfare.


According to the original intention of the subjective theory of value, the first Gossen's law refers to the consumption of material goods. However, there is no reason why one should not extend this law to non-tangible goods. So might e.g. proofs of friendship, which receives an individual from another individual, initially have a high utility and decline in their utility growth very well while this behavior extends.


Gossen and the representatives of the subjective value theory assumed initially that the marginal utility already decreases even at very small quantities of consumption (thus e.g. from the second consumer unit on). However, quite other marginal utility developments are conceivable. So we know that there are parallels in the theory of production to the law of diminishing marginal utility in the so-called law of diminishing marginal returns (growth of earnings of a production factor by one unit).


The classic development of the law of diminishing returns, however, assumes that the marginal return initially rises and declines not until a critical production volume. Behind this is the idea that the technology of the production process provides a certain optimal input of production factors and that therefore the marginal revenue decreases in each case, irrelevant of whether one departs from this optimum by an increase or decrease of the production factor.


It is natural to wonder whether such a development can not be assumed also for the marginal utility graph of certain goods. Let us think, for example, about the enjoyment we may experience when we listen to a piece of classical music. It is quite conceivable that initially upon renewed listening of this piece of music the incremental utility even increases because only with repeated listening one recognizes certain nuances. Of course, one will also have to assume that from a certain repetition on the marginal utility decreases also here. We receive here following marginal utility graph:





The first Gossen`s law was initially developed for individual consumer goods. The decreasing development of marginal utility always applies implicitly on the assumption that the consumption of all other goods consumed remains constant (= ceteris paribus condition). The development of the graph will change when more or less is consumed of the other goods.


Whether hereby the marginal utility graph for a particular good is shifted up or down depends on whether this changed good is in a substitutional or in a complementary relationship with the considered good. Take the case that we are investigating the marginal utility development of butter and assume that the bread consumption would have increased (the consumption of a complementary good). In this case, the marginal utility of butter would certainly become somewhat greater for each quantity consumed; the marginal utility graph of butter had been shifted upwards due to an increased consumption of bread.


Now let us take the case of substitutive goods: We investigate the marginal utility development of margarine and insinuate that the consumption of alimentary oils e.g. had declined due to a temporary shortage of oils. As the household disposes here over less oil, it has to use increasingly margarine for frying, the value of margarine has increased, the development of the marginal utility graph of margarine is now shifted upwards in this example due to a reduction in the amount consumed of a substitution good.


Now, of course, we are not only interested in the utility development at a change in consumption of specific products, rather we have to ask also how the utility of a household changes, when the total consumption of consumer goods increases due to an increased income. Here the law of diminishing marginal utility is no longer related to the consumed amount of a single good, but on the level of the overall disposable income.


Also here, one has assumed a law of diminishing marginal utility of income. If the income increases by one unit, then also here the incremental utility would decrease. This relationship is obvious. When a diminishing marginal utility is assumed for each good this must obviously also apply to the income, as an increase in income will cause that it is basically consumed more of all (or almost all) goods; and since at all goods the marginal utility diminishes in accordance with the assumption, it is expected that each additional unit of income causes an ever diminishing incremental utility.


Now, above we had already pointed out the parallels to the production theory. And here we ascertain that although the traditional production theory generally assumes that the partial marginal revenues of the individual production factors decline at an increased use, but that the marginal level product would nevertheless be constant, thus a simultaneous increase of all factors of production at a constant factor input ratio holds the marginal revenue constant very well.


Again, there are attempts to transfer this law on the budgetary theory and to say that the marginal utility - based on the total income - remains constant with increasing income. Here, the increase in total utility remains only constant at an increase of income since all demanded consumer goods remain in an ideal ratio.


The second Gossen's law examines the question at which allocation of income a household maximizes its utility (its aim achievement). Let us assume a particular allocation of the income on the individual consumer goods, whereby we only want to consider two competing consumer goods for the sake of simplicity. Every amount of the consumer goods corresponds to a very specific marginal utility.


Let us assume now that the marginal utility of a good - we call it the good A - referred to an income unit is lower than the marginal utility of another good (the good B). In this case the household can obviously increase its total utility if it can consume one income unit less of good A and therefore can consume more units of good B in accordance with the saved income parts. Ex definitione is the missed marginal utility due to the reduced consumption at good A indeed less than the incremental utility by the increased consumption of good B: The total utility has increased.


By means of this regrouping of consumption, the marginal utilities of both goods approximate to one another, the marginal utility of the good A is increased due to reduced consumption, the marginal utility of the good B has decreased. It is readily apparent that a household can experience utility increases through regrouping of consumption as long as the marginal utilities of both goods have different levels.


But this also means that the household has maximized the utility of his income exactly when the marginal utility of both goods have the same level. Transferred to n goods, says the 2nd Gossen's law therefore, that an utility maximum is reached exactly when the marginal utility of all goods have an equal level based on the income.


To be continued!