Chapter 7: Welfare theory

contd. 3





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 surplus concept

8th The theory of the second best

9th The significance of the business rivalry for the welfare

10th Externalities

11th The Cost-Benefit Analysis

12th Pareto-optimal redistribution




8th The theory of the second best


In the discussion on the welfare criteria introduced by Ian Malcolm David Little in connection with the compensation criteria we had seen: It can not always be assumed that the technically possible solutions can also be regarded as politically feasible. Precisely this problem is the subject matter of the theory of the second best.


The welfare theory has initially attempted to show at which quantities of goods a society can achieve, technically speaking, its highest possible benefit. The theory of the second best, especially developed by Richard G. Lipsey and Kelvin J. Lancaster, assumes though that in reality it is not always possible to realise the - technically speaking - best solutions, in the real world often only the second or third best solution can be headed for. In our welfare models now appears in addition to the transformation curve, which informs of the technical limitations, another politically caused limiting curve:





From a technical point of view, it would be desirable to realise an ophelimity according to the indifference curve O2, but for political reasons it is only possible to achieve an ophelimity which corresponds to the indifference curve O1.


Admittedly, this correction does not bring about any significant new insights. The curve of the politically caused limitations now takes the place of the transformation curve. The theory of the second best though concluded furthermore that the optimal conditions derived from the assumption of a first choice solution are no longer always valid if only a second best solution can be achieved.


Let us illustrate this statement using an example. Therefore, let us divide the national economy into two market segments: Market A and market B, on both markets goods were traded. Under conditions of the first best it can be demonstrated (as we shall see later) that the welfare of the society is then the greatest when there is complete competition in both markets. Now let us assume at first that in both markets in the initial state complete competition would have prevailed actually. We would also like to assume that on market A would now emerge the market form of a supply monopoly and that this monopoly could not be converted into a competitive market by political means. Is it now welfare optimal if the competition conditions are maintained on market B, or is it desirable to bring about monopoly conditions on market B?


According to the general welfare theory, one might be tempted to affirm the preservation of competition on market B; if competition could already not be achieved on both markets, then it would be desirable that competition was dominant at least on the markets on which this was politically possible. Although there would be a lower welfare increase than if competition conditions were present on all markets, but with a partial introduction of a monopoly there would be in any case an additional welfare reduction in all markets.


This statement contradicts now the theory of the second best. It tries to show that the welfare is greater under conditions of the second best if monopoly conditions prevail in both markets. Let us make this idea clear by means of a graphic:






In the starting condition there was competition on both markets, and the balance was on both markets at the intersection of supply curve and demand curve (light and dark red dot!). Now occurs a monopolisation at market A, the balance point would be shifted to the intersection of the supply curve with the (green) marginal revenue curve (green point!). In this way, production factors are released on market A, which migrate to market B under the conditions of full employment.


If under the conditions of complete competition an optimal allocation of the production factors to both markets took place, then the migration from production factors to market B leads to suboptimal results due to the monopolisation of market A. If now the monopolisation of market A can not be undone, then would, at a monopolisation of also the market B, occur a return migration of the production factors to the market A, which would be equivalent to the fact that we are approaching again the condition of the optimal distribution of the production factors on both markets. In this example, a monopolisation on both markets guarantees thus a higher welfare than if on market B the competition remained.


However, this conclusion can be criticised, since it starts from the assumption that monopolisation has no influence on production technology. In reality, however, we must expect that from the competition strong impulses emanate to reduce the costs and improve the quality of the goods by modifying production technology. In this case, though, a monopolisation of the market B is likely to diminish the welfare, since the dynamic competitive effects are higher than the static and negative allocation effects of a monopolisation.



9th The significance of the business rivalry for the welfare


In the scope of the discussion of the Paretian welfare theory, we have seen that if, and only if, the marginal rate of substitution corresponds to the marginal rate of the transformation, an optimal division of the production factors on the individual goods can take place.





It can now be shown that this optimal condition is in general only fulfilled if the market form of complete competition is realised on all markets. As it is well known, in the case of complete competition corresponds the price to the marginal costs, as the entrepreneurs maximise their profit just under these conditions. Here, an increase in production is no longer profitable since the marginal costs would then be higher than the sales revenue (the price of goods).


If we consider the two supposed goods x1 and x2, it must also apply that in balance the price ratio (p1/p2) corresponds to the ratio of the marginal costs of good 1 and good 2. The marginal rate of transformation refers now to the ratio of the quantities of goods that can be produced at given technique at the tangential point: (dx1/dx2). This term can though be obtained from the reformulation of the marginal cost ratio:


(dK1/dX1) : (dK2/dX2) = (dx2/dx1) * (dK1/dK2)


However, since the marginal costs of the two goods correspond to each other at the tangential point (as long as the marginal costs of the two goods are not equal, a shift of the production to the good which has the lower marginal cost is worthwhile) we can shorten the term (dK1/dK2) so as to the marginal cost ratio in the tangential point corresponds just to the marginal rate of transformation. In this case applies the following: in balance, both the marginal rate of the substitution and the marginal rate of the transformation correspond to the price ratio and thus also to itself (principle: if two sizes are equal to a third, they are also equal among themselves) so that under the conditions of complete competition an optimal welfare is guaranteed.


It can be argued against these considerations that here the dynamic productivity enhancing effects of competition are ignored and that only the static allocation effects are considered. But if additional welfare increasing dynamic effects emanate from competition and not from monopolistic conditions, then naturally applies a fortiori that under competitive conditions a higher welfare is achieved than like under monopoly conditions.


These considerations do not apply indeed when there is a bilateral monopoly present, if the partners continue to proceed according to the strategy of successive approximation and when finally the profit and benefit curves run homogeneously linear. Within the scope of the theory of the bilateral monopoly it has been shown that under these conditions the distribution can be changed in comparison with the competitive situation without therewith causing any change in the allocation.


There are, indeed, many areas where the market form of the bilateral monopoly is present and where the negotiating partners apply the strategy of successive approximation; but it is generally assumed that at least the marginal utility functions do not run homogeneously linear, so that in reality it is only very rarely possible to achieve optimal market results at not-presence of competition.



10th Externalities


In addition to the competition, there is also another condition for the market to head for a welfare optimum by itself. All costs (benefit losses) of a national economy which incur due to production must be included in the cost accountings of the entrepreneurs. But in reality, there are numerous costs associated with the production in a national economy, which though are not charged to the companies and therefore are not included in the cost accounting. This is referred to as external costs.


External costs arise wherever actually free goods (such as air) are polluted at the production and thus cause economic damage. It can also be said that clean air becomes a scarce resource and that production efforts are getting necessary to keep the air clean. For example, if an enterprise discharges environmental pollutants into the air via the chimney, then certain health injuries can appear cumulative to the population around the production site, the risk of disease increases. This is an example of a regionally limited environmental pollution.


A global environmental pollution - occurring in almost every country of the earth - is present, for example, when CO2 emissions are given off into the air so that the earth heats up and thus a strong climate change occurs, with the consequence that storms, floods etc. appear more frequently. At the same time, it has to be expected that due to the warming of the earth the glaciers melt, that in this way the sea level rises and many regions on the earth are flooded.


The real cause for the occurrence of external costs is a lack of property regime Only if property rights on the scarce goods required for production exist, it can be assumed that, under normal conditions, consumers of goods have to pay in the price also the costs which arise during production and only in this case it has to be expected that the goods bundle is produced which best meets the needs of the population.


The presence of external costs implies that the welfare optimum is missed by the fact that private costs differ more or less from the overall costs of the economy. Since the overall economic optimum is determined by the intersection of the marginal costs of the overall economy with the demand curve, but since the enterprises head for a production quantity in which private marginal costs correspond to the price of goods, a production is striven which differs more or less from the welfare optimum. Let us make these relationships clear to us by the following graphic:






The graphic shows that the overall economic optimum lies at the quantity xopt, but that the companies offer the quantity x0. They can sell this quantity only because they do not demand the economically necessary price popt, but reduce the price to p0. Since buyers now have to spend less on this pollution-intensive product, they are increasingly asking for these goods and can therefore ask for less of the other goods which are less polluting the environment, with the result that just too much of the goods with a high environmental impact are demanded and the demand for goods with low environmental impact is too little. The "too much" and "too little" is measured by the allocation (goods division), which would have been realised under optimal conditions.


There are essentially three attempts to eliminate or reduce the damage associated with external costs by political means. The first instrument provides prohibitions of goods which are particularly detrimental to the environment or restrictions on production or requirements which must be met when these goods are produced. The requirements include, for example, the provision of certain filter systems so that no environmental toxins beyond the permitted limits are emitted into the environment (air, water).


In the scope of a second instrument, the state imposes an environmental tax, which in the ideal state corresponds exactly to the amount of the external costs, with the consequence that the private costs now also correspond to the overall economic cost and thus the external costs are internalised.


A third instrument is that the state creates pollution rights and allows the individual enterprises to produce the products which are polluting the environment only then and only to the extent to which these enterprises have sufficiently purchased such environmental certificates. A possible introduction of this instrument is that the state assumes the current extent of production of these goods and makes environmental certificates available to the individual enterprises to the extent of the current production.


The enterprises are entitled to sell a part of these environmental certificates on the stock exchange to enterprises which have a greater need for environmental certificates due to an expansion of the production. Enterprises are thus encouraged to develop new technologies with lower environmental impacts and to achieve thereby additional revenues by the sale of certificates. To the extent that new technologies are developed in this way, the state has the possibility to repurchase some of the environmental certificates and thereby to reduce the environmental pollution without the risk of a decline of employment as a result of higher environmental requirements.


These three instruments are able to solve the problem of external costs and the resulting environmental pollution to very different extents. The lowest success will be achieved with the instrument of prohibitions and restrictions. An appropriate solution to this problem requires that the benefit increases generated by the production of goods and the benefit losses (damages) are set off against each other due to the external costs that occur. However, only a market is able to do this, whereas the state has no means of determining and comparing benefit sizes, so that prohibitions always bring uncertainty as to whether the state is doing too little or too much on this issue.


If the state in addition stipulates the use of very specific filter systems, it also hinders progress in the development of environmentally friendly technologies at the same time It is better if the state only stipulates which emission levels of pollutants are not allowed to be exceeded, letting the enterprises themselves choose the most appropriate and cheapest methods to reduce pollutant emissions to the permitted level.


Similar reservations apply to the introduction of an environmental tax, which was already proposed by Arthur Cecil Pigou at the beginning of the 20th century. If the state would be aware of the size of the external costs, then the tax solution would be ideal as it would lead to a complete internalisation of the external costs. As already mentioned, in this case the private sector marginal cost curve would coincide with the overall economic curve and the guarantee would be given that an optimal production expansion would take place. However, since there is no market for external costs, the amount of the resulting benefit losses is unknown and there is a risk that the state will charge an environmental tax either too high or too low.


The instrument of environmental certificates is the most appropriate among the three measures discussed. This instrument was proposed by the group of the property rights movement (Harold Demsetz, James M. Buchanan, Ronald Coase and others) in the time after the Second World War. With the creation of these pollution rights, the real cause of the externality is eliminated, namely the fact that no property rights exist for the use of these free goods, although from the overall economic perspective the use of these free goods is just as likely to cause benefit losses (damages) as the use of scarce goods.


However, a final welfare increase is only achieved when the state uses the revenues from the sale of these environmental certificates to repurchase some of these certificates. Only in this case, the level of environmental damages declines permanently.


For the welfare increase by creation of pollution rights count two factors: Firstly, enterprises have an incentive here to develop new welfare increasing technologies and only in this case a reduction in pollution can be achieved without hereby causing the reduction of employment. Secondly, welfare increase takes place only when the state gradually repurchases the pollution rights as a result of these technically possible improvements.



11th The Cost-Benefit Analysis


The Cost-Benefit Analysis was developed in order to be able to carry out an efficiency analysis comparable to the entrepreneurial profitability calculation in governmental and public projects. Thus could a municipality or another local authority try to find out in the scope of a Cost-Benefit-Analysis, whether an industrial settlement, for example, in consideration of potential environmental damages, is advantageous to the municipality.


The aim of the Cost-Benefit Analysis is here to adopt or at least simulate a profitability calculation, as it is always carried out in the case of commercial enterprises, also in the case of public legal bodies (e.g. municipalities). The actual problem here is that, unlike enterprises, not all the benefits and costs can be determined in terms of monetary units, since there is no market for collective goods and thus no market values exist, and since intangible objectives such as safety requirements are also important and should therefore be included in the evaluation.


The way of such a Cost-Benefit Analysis is carried out in five steps.


First step: The expected relevant effects of the intended measure for the municipality are to be listed: for example, increased tax revenue, increased accrual of sulphur dioxide with the consequence of a higher incidence of illness and thus an increased demand for hospital capacities, greater need for traffic routes, and so on and so forth.


Second step: Furthermore, it is necessary to check for the individual listed facts, whether they can be categorised as welfare increasing or welfare reducing. Environmental impacts may almost always be classified negative.


Third step: It is further important to quantify the listed facts as far as possible. Relatively unproblematic are the facts, whose effects can be summarised in monetary terms. This applies, for example, to the expected additional tax revenue or to the additional costs resulting from the need to acquire, for example, new trams and additional tram staff.


This problem appears a little more difficult for all the other facts which can not be measured directly or at least not only in monetary terms. For example, if cases of illnesses accumulate as a result of industrial settlements, it is crucial to develop auxiliary criteria which are able to quantify the problems that arise. So it could be clarified, for example, how many per cent of cancer cases are likely to increase, or whether and how many accidents with personal injury have to be expected additionally. In the most general sense, measured values must be defined for the emission of dangerous environmental toxins.


Fourth step: All the items that could be recorded in monetary terms can now be summarised, whereby a sum of the revenue sizes and a sum of the expense sizes are to be formed and finally the income and cost sums are to be netted.


Fifth step: Now the expected net incomes or net costs must be compared with the facts that are not measurable in monetary terms. For example, if material net income is generated on the one hand, but intangible charges (health hazards) are expected on the other hand, it is necessary to clarify whether the price in form of burdens is not considered too high to achieve the expected net income. In the same way, a political decision must be taken if on one side additional costs arise, but on the other side positively assessed facts can be realised. Are the newly emerging costs for the realisation of these intangible aims perhaps too high?


A Cost-Benefit Analysis is not rendering a progress in all incidental questions at the level of a regional authority. Such an analysis raises four problems:


Problem no. 1: In the development of public projects is a Cost-Benefit Analysis only useful if the majority of the facts to be determined can be recorded in monetary terms. If, though, the monetary factors play only a minor part, a Cost-Benefit Analysis is not suitable, since it merely pretends an objectivity that is not given.


Facts that are recorded in monetary terms can be offset without additional evaluation. The advantage and objectivity of a profitability calculation lie just in the uniform scale. If, however, there are a large number of monetarily not measurable facts, and if the balance of the monetary impacts is relatively low, then even at formal application of a Cost-Benefit Analysis occurs fundamentally nothing different as already at political decisions. The non-monetary facts must be compared judgemental with each other, and the Cost-Benefit Analysis does not bring any change at all for this task. Each individual politician participating in the vote must decide this evaluation for himself.


There is, however, the risk that by the application of this analysis a greater degree of objectivity will be awarded to the decision, and that at the defence of the decisions in the political environment is side lined what constitutes the actual decision: A political and personal evaluation of different aims, which can not be replaced by any analysis no matter how very objective that pretends to be.


Problem no. 2: Problems also arise when the benefits and costs of the projects under discussion appear at different times. Primarily industrial projects are characterised by a relatively long useful life. In contrast to investment projects of commercial enterprises, where it can be assumed that costs and revenues are compared with present values and enterprises also have a relatively long life, at political organisations it has to be taken into account that the officials are elected only for a relatively short lifetime and that therefore the long-term effects are not redounded to them at all and that therefore they will assess the impact in the distant future much less than the impact in the coming years.


Hence, it is to be feared that political bodies will prefer projects that have high yields and low costs in the near immediate future, while the costs incurred in the distant future will only experience little attention, even if the investments have to be regarded actually as unprofitable because of these costs.


Similarly, it is to be feared that in the case of public institutions, the one time costs are predominantly taken into account, while the material follow-up costs are often not considered at all. The material follow-up costs naturally include also costs that are caused by the construction of a public facility, but which must be paid by private households (households and enterprises). Thereby, however, a further problem is addressed already.


Problem no. 3: We have to assume namely, that both the costs and the revenues of public projects are not arising only in the municipalities or other public bodies which have decided on these projects, but also extend to other regions depending on the nature of the projects. Let us bring an example for an export of costs. For example, if on a grand scale industrial plants are promoted, which emit large-scale amounts of CO2 into the air, not only the region itself but practically all countries on this earth are adversely affected by the climate change caused by this. Here, it must be feared that the costs and damages incurred in other regional authorities will not be taken into account at the consultation on these projects.


Conversely, it must also be assumed that certain objects also bring additional revenues to other regional authorities, for example, if neighbouring communities benefit from an expansion of the transport network. Although it would actually be desirable that the neighbouring communities benefiting from the project would participate in the costs, such a participation in the costs can generally not be expected. This circumstance contributes that these projects are addressed to an insufficient extend, since the respective regional authorities do not include all the revenues in their calculation.


Problem no. 4: It is furthermore to be feared that political decision-makers have the tendency to underestimate the expected costs for the future and reversely to overestimate the expected revenues for the future. The political profit of the politicians does not lie in the material yield of the projects, which generally does not benefit the decision-making politicians at all. The profit of a politician lies rather in the fact that his popularity and his chances of re-election are improving. If politicians are able to convincingly assert that the expected costs are lower than they are actually, and vice versa, that the expected revenues are higher than they are actually, the politician has the chance to improve - of course unauthorised - his re-election and his prestige .



12th Pareto-optimal redistribution


The revolution introduced by Pareto seemed to suggest initially that the welfare theory could not take an evaluative position on distribution issues at all. If we are not able to compare benefit expectations with each other, we also can not, of course, answer the question of whether certain redistribution has a welfare increasing effect or a welfare diminishing effect. But even if one, together with Pareto, rejects the possibility of interpersonal benefit comparisons, the desirability of redistribution can be explained with the newer welfare theory, provided that external consumption effects are considered.


External consumption effects are present when a household experiences satisfaction not only from its own consumption, but also from the consumption of other persons. This is firstly the case at an altruistic attitude, when the individual feels obliged to help others if these need help. Such an attitude arises, for example, from the Christian commandment of charity. But also pure compassion with the suffering of others or the need to do good to friends belongs to this altruistic attitude.


The external consumption effects are not exhausted therewith, however. An individual can indeed use income for other individuals also according to purely selfish aims. This is the case, for example, if by granting aid to the poorest countries of the world he hopes to avert the danger that the peoples of these countries, or even individual persons, will behave warlike (for example by terrorist acts) against the highly developed countries. Or this is also the case when a rich donates money to a hostel for homeless in order to be annoyed to a lesser extent by homeless people prowling the streets.


Three forms of external consumer effects can be distinguished. Firstly, the individual can achieve satisfaction of his external consumer effects by granting a very specific donation amount regardless of how these donations are used in detail by the recipient. Here it is the height of the donation which brings satisfaction:


Wext = f (Sp),


With Wext: Welfare from external consumer effects; Sp: Donation sum.


Secondly, it is conceivable that with the donations to others the donator is concerned above all that the recipient has a subsistence minimum of income. In this case, it is indifferent to the donator how the recipient uses his income. Further, for the satisfaction by external consumption effects it is actually indifferent whether and how much the potential donator has contributed to this income.


Wext = f (EB),


With EB: income level of the recipient.


Thirdly, it is conceivable that the donator is interested in the fact that the recipient makes use of very specific goods or services and that the donator grants his donation in form of material goods. For example, a rich man may be disturbed by the fact that ragged figures are running in his street and cause him disgust:


Wext = f (X1B, X2B ...,)


With XnB: quantity of good (n) consumed by B


The following graphic may now illustrate the circumstances on which depends how much the individual donates due to external consumer effects:





In the right quadrant of the diagram above, the internal benefit is drawn that the donator experiences at alternative levels of net income (gross income minus donation sum), in the left quadrant is illustrated how the external benefit varies with the amount of donation. Both for internal as well as for external benefit, the law of the diminishing marginal utility is assumed.


The potential donator has a gross income of E0 and reaches a marginal utility corresponding to the course of the internal marginal utility curve. If he now uses an income unit for donations, he has on one side a reduction in the internal benefit, but at the same time an increase in the external benefit. As long as the external benefit increase is greater than the internal benefit reduction, the potential donator can increase his overall welfare by expanding the donation sum. The welfare maximum of this person is reached if the external marginal utility corresponds just to the internal marginal utility.


This post-Pareto approach initially explains only voluntary forms of the redistribution. The individual has certainly his own interest in granting a certain donation sum. A compulsion can though become necessary if the success of the redistribution has the character of collective goods. The amount of the external benefit in this case depends solely on the fact that the income or also the consumption reaches a certain level or at least gains an increase in the group of beneficiaries. The extent to which the donator has contributed to the achievement of this external aim is of lesser importance, here.


In this case, there is a risk of freeloader behaviour. Individuals are better off if the external aims are achieved by donations of others, e.g. certain development assistance is granted. Here, a state compulsion to participate in the donation volume could lessen this risk. This compulsion is also in the own interest of the persons concerned, since in this case the individual can assume that the other persons also participate in the redistribution activities and that the success of the donation campaign is thus greater than as if no compulsion would be exercised.