Review of Population and Social Policy, No. 8, 1999, 139 –154.

The Public Economics of Redistribution andthe Welfare State
Agnar SANDMO*

Abstract
This article gives a broad survey of the arguments why governments
should engage in large-scale redistribution, as they do, e.g., in the Scandinavian
countries. Official data for redistribution via government budgets tend tooverstate its magnitude, since much of the aggregate volume is due to incomesmoothing, which is really a substitute for private saving and insurance. The
arguments in support of socialized saving and insurance must basically be aboutmarket failure, while the amount of net interpersonal redistribution must be
based on a calculation of the trade-off between efficiency and equity. The
optimal degree of income equalization depends on the efficiency cost of the tax
system.

1. Introduction
How far should we go in the equalization of incomes? This is perhaps thefundamental question that faces policy makers with a commitment to egalitarianvalues. A fervent egalitarian would perhaps argue that the right thing would be toproceed all the way to complete equality. On second thought, however, mostpeople would probably admit that such a policy would have strongly adverse
effects on economic incentives, which should act as a brake on redistribution
policy. How far we should go then becomes a question partly of ethics, partly of
economics. I would like to emphasize that I certainly do not claim—neither on myown part nor on the part of the economics profession—to know the precise
answer to the question. But I note as a fact that there is a lot of popular andpolitical support for the redistribution schemes of the welfare state. This is revealed
in many sources, as in the programs of the political parties and in public opinion
polls. Taking this support for a fact, my analysis in the following consists in trying
to think systematically about redistribution policy and its relationship to otherobjectives of public policy. It does not imply a strong commitment to any specificethical or philosophical view, although I shall occasionally use formulations
derived from such views to illustrate my general points.
Starting from this basis. I would like to consider the question of how far it is* Professor of Economics, Department of Economics, Norwegian School of Economics andBusiness Administration, Norway.
I am grateful to Mats Persson for his comments on an earlier version of this article.

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reasonable to go in the direction of income equality. To do this, I try and assemble
bits and pieces of economic theory that together may lead to a hopefully coherent
view of the role of redistribution and provision of social insurance in the welfare state.
What that role is, has been the subject of a lively debate over the years, so that
it is by no means a trivial matter to arrive at a balanced view. The title of afamous book by Arthur Okun (1975), Equality or Efficiency: The Big Trade-off,probably summarizes the widely held conviction that more equality can only bebought at the price of less efficiency, roughly in the form of a reduction of GDP
or GDP growth. However, not all economists agree with this; several writers, e.g.
Nicholas Barr (1987), have emphasized that the welfare state can also beinterpreted as a device to overcome some basic market failures in the private
sector. From this perspective, therefore, there may be grounds for doubting
whether every aspect of welfare state policy really involves any trade-off.

2. How Much Redistribution Is There?
I am not going to dispute the view that the welfare state policies of the
Scandinavian countries (which are the ones that I know best) really achieve
substantial redistribution. If you use annual data to compute Lorenz curves forfactor incomes on the one hand and for disposable incomes on the other, they
typically look like the picture shown in Fig. 1. Not only does the Lorenz curve forfactor incomes lie below the curve showing the inequality in disposable income;
especially for Sweden it lies in fact substantially below, as demonstrated by Fritzell(1991). Fritzell shows in particular that the Gini inequality index in 1980 was only
half as large for disposable incomes as it was for factor incomes, and he refers tothis difference as the redistribution effect. I want to begin my analysis bydiscussing whether that is really a good measure of the actual redistribution thatthe welfare state achieves. This is not meant to detract from the value of studies
like that of Fritzell and others. Empirical research is necessarily constrained bywhich data are available, and I really want to argue that we should also beinterested in data that—at least in large measure—are unobservable.
Let us imagine that we start from data about the distribution of labour
incomes. This, of course, shows great inequality. Not only is there considerable
inequality in the distribution of income among those who are actually in thelabour force, but even more importantly, there is a large number of people(approximately half the population) who do not work at all. This group includes
children and young people who are being educated, the old, the sick and thedisabled. It also includes a number of people who have voluntarily chosen not towork, such as mothers with young children.

The Public Economics of Redistribution and the Welfare State141

disposable income
factor income

Figure 1 Lorenz curves
The reason why a large number of the people who do not have any labour
incomes, still have a reasonable standard of living, is not only that the welfare state
redistributes income in their favour. Some individuals live on income from capital.
Another (related) reason is that consumption is not only determined by current
income, but also by past and future income. A study of the distribution of lifetime
income would almost by definition show less inequality than that of annual income;for an empirical analysis see Lindbeck (1983). A further reason is that some people
are taken care of through the voluntary support of their families and friends.
At a more general level it seems clear that if we are concerned with inequality,
what really matters is not the distribution of income per se, but the distribution of
the standard of living between persons. That is not an easy concept to makeempirically operational. It clearly depends on the level of consumption of private
goods, but also on the supply of public goods (public safety, the physical andcultural environment) and publicly provided private goods, such as health andeducation. It also depends on the amount of voluntary transfers received fromothers, above all through the family. In the following I shall concentrate on
private goods consumption, so let me first say a few words about the componentsof the standard of living that are not captured by data on private consumption.
It is clear that the public provision of certain goods and services makes the
distribution of the standard of living less dependent on income. Although there may

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in fact be a positive relationship between the access to and use of certain public
services on the one hand and income on the other, it still seems safe to assume thatthe value of such services is more equally distributed than labour incomes. From
this point of view, since Sweden—the prime example of a highly developed welfare
state—has more public provision of both public and private goods than most othercountries, one might perhaps expect that the equalization of incomes would beof less importance in Sweden. In fact, to the extent that inequality measures arereally internationally comparable, there is more redistribution of income in
Sweden than in the rest of the OECD area. I leave this as a puzzle to be reflected
upon while emphasizing the general point that the deeper study of inequality
should also take account of the redistributive impact of public expenditure.
The distribution of factor incomes is in principle observable. Now let us imagine
that we were able to observe what the distribution of private income andconsumption would have been, had the public sector not engaged inredistribution. This is nonobservable, but we can make some pretty good guesses
at what it would look like. In terms of financial resources, the old people without
labour incomes would live off their savings. The young people at universities
would live on private loans. Disabled people would live on income provided
through disability insurance. Within all of these groups we would in addition
observe a considerable amount of private redistribution, partly through organizedcharity, partly through intrafamily transfers. Thus, in this hypothetical situation theold and disabled would to a larger extent than now live with their families, andstudents’ expenses would more likely be paid by their parents.1 To summarize, themarket’s allocation of consumption, i.e., the private component of the standard ofliving, would be considerably less unequal than the distribution of labour income.
Note that both private and public redistribution are of two kinds. When people
save for their old age or insure against work disability, they engage inintrapersonal redistribution or income smoothing, i.e., they transfer income
between periods and states of nature2 in their own lives. The transfer of income
from rich to poor could on the other hand be characterized as interpersonal
redistribution. The latter kind is what we usually think of when we talk about
1

2

In judging the realism of this scenario, one must of course keep in mind that the working partof the population would have much higher disposable incomes, since the government would
no longer need tax revenue for redistribution.
I use the concept of the state of nature in the sense made familiar by the work on generalequilibrium theory by Arrow (1953) and Debreu (1959). To illustrate, imagine that in somefuture period, my standard of living depends crucially on whether or not I am able to work.
This defines two states of nature as “healthy” and “disabled”. The optimum amount to save forthe future depends on which state actually occurs. In this situation a rational course of action
for me would be to channel some of my present saving into a form where the return is
contingent on the state “disabled” occurring, i.e., a disability insurance policy.

The Public Economics of Redistribution and the Welfare State143

redistribution, but it is important to be aware that much of welfare state
redistribution is really of the first kind. In the case of old age pensions, one
could compute the actuarial value that would correspond to the premium paid
over the years spent in the labour force and compare that with the actual valueof the benefits. Particularly in the universal systems that we have in the
Scandinavian countries, a comparison of the differences so obtained would show
the extent of redistribution of the old age pension system, but it would also showthat the actuarial part of the pension is very considerable.3
In order to correctly assess the redistributional effect of the welfare state, ourstandard of comparison should not be the distribution of factor incomes that we
actually observe, but the distribution of consumption if the state had not engaged
in redistribution. Even if we cannot observe this, we should note that this in allprobability would lead us to a much lower estimate of the effect. The point isthat public redistribution tends to crowd out both income smoothing andvoluntary transfers. While the latter will be discussed below, a stylized exampleof the former is shown in Fig. 2. This shows the case of an individual who lives
and consumes in two periods, working in the first and being retired in thesecond. His first-period income is Y1, and in the absence of any government
pension schemes he saves an amount which enables him to achieve his desired
lifetime consumption profile, C*=(C1*, C2*). Now suppose that the government
introduces a pension scheme under which the consumer pays a certain
contribution in the first period in return for a pension in the second period. If thepension scheme is actuarially fair, this scheme moves the initial income point of
the consumer—in terms of disposable income—to (say) Y'. The point to note isthat the pension in this case does not change the present value of the consumer’s
lifetime income. Therefore, his preferred consumption profile remains the same.
What changes is his private saving, which is reduced by the exact amount of the
public pension premium. (If the amount of the premium had been sufficiently
high, the consumer would have responded by personal dissaving, so that hewould actually have borrowed against his future pension. This raises somequestions about the nature of capital markets that I do not go into here.)Suppose now that we were able simultaneously to observe two persons who
were identical in terms of preferences and lifetime private incomes, except that
we observed one of them in the first and the other in the second period of his
3Mats Persson (1998) has calculated that for the Swedish working population as a whole, about
75 % of the pension charge must be considered a tax while the remaining 25 % is an insurance
premium. However, these numbers do not necessarily reflect the redistributional impact of thepension system, since they refer to the marginal effect of the pension charge. In order to assess
the balance between intra- and interpersonal redistribution in the system, one would have to
study the differences between the actuarial value of the total benefits and contributions.

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C2

C*2

C*

Y'

C*1

Y1

C1

Figure 2 A public pension crowds out private saving

life. A study of labour market inequality would show this to be very large interms of wage income, since one person would have all of the income. The
distribution of consumption would show much less inequality, since theconsumption of the old person would now be equal to his pension, while theincome of the young would be reduced by the amount of his contribution; infact, as the diagram has been drawn, the individuals have a strong preference for
consumption equality over their own lifetime, so that consumption is virtually thesame. In this case, therefore, the pension scheme would not have changed thereal amount of inequality, since the distribution of consumption among the twogroups is exactly the same as in its absence.
I conclude by observing that data about the amount of redistribution must be
interpreted with a good deal of care. There is no doubt that the welfare state
carries out much redistribution, but also that much of it is what we have called
intrapersonal redistribution, so the interpersonal redistribution of income is lessthan what might appear from a superficial inspection of the statistics. I now turnto a consideration of the arguments for the two kinds of redistribution.

3. Government Interference in Intrapersonal Redistribution
Why would the government engage in intrapersonal redistribution (income

The Public Economics of Redistribution and the Welfare State145

smoothing)? Figure 2 showed a case where there was no point in this, since the
distribution of the standard of living was independent of government policy. The
argument could even be extended to cover some insurance markets where
similar crowding out arguments would apply. However, it should be kept inmind that the reasoning was based on some very strong assumptions that need
to be examined carefully.
The basic assumption is that markets are perfect. There must exist a perfectcapital market for ordinary borrowing and lending, as well as a complete set of
insurance markets in which individuals may obtain any desired degree of coverageagainst events that may affect their standard of living. This would include such
events as sickness, disability and unemployment. The model of general competitive
equilibrium developed by Arrow (1953) and Debreu (1959) has the property that acompetitive equilibrium is a Pareto optimum, so that a rational policy ofredistribution would seem to be limited to the interpersonal kind.
However, the Arrow-Debreu model is a very special case. Let us consider theassumption of a complete set of insurance markets. In the more recent literaturemuch attention has been paid to problems that arise out of the existence ofasymmetric information, viz. moral hazard and adverse selection. Moral hazard
exists when the behaviour of the insured person is influenced by the insurance.
The theoretical hypothesis is that automobile insurance makes car owners drive
less carefully, unemployment insurance makes people less keen to hold on totheir jobs, and sickness insurance makes people less careful in the choice of theirprivate lifestyles. Adverse selection is the case made famous by Akerlof (1970). If
individuals differ with respect to their risk exposure, but the insurance company
only knows the average risk in the population or the risks characteristics ofbroad groups, then the bad risks will drive out the good risks, possibly resulting
in the insurance market for the risk in question vanishing altogether. Examples
are easy to find: Insurance against unemployment would be especially attractive
to those which a high risk of being laid off, while insurance against becoming alone parent would attract people with a lifestyle that involved a particularly highrisk that this event would occur. These reasons for failure of private insurance
markets have been extensively discussed and are by now well understood. It isalso generally accepted that social insurance—in the sense of mandatory
universal membership — can overcome the adverse selection problem, but not
the problem of moral hazard. A major part of the reason for market failure carries
over to the case where insurance has been socialized, and the incentive
problems associated with extensive social insurance coverage constitute thepotentially most significant cost of the system.
As has been pointed out by Atkinson (1991), it is difficult to interpret thegrowth of the social security system without considering the development of the

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labour markets in modern industrial societies. As a result of the development ofmodern industrial societies, labour has become ever more specialized, often as
the result of large investments in human capital through specialized education or
on-the-job training. These are investments that cannot easily be diversified
through private markets, and they are also—both because of moral hazard andadverse selection problems—difficult to ensure against on a voluntary basis. The
social security system provides protection against these risks, and the progressive
income tax may also be seen in part as an insurance device, by which the stateshares in the risk of income fluctuations; see Varian (1980).
The market failure justifications for social insurance have been extensively
discussed in the literature. However, there are also other arguments, whichshould perhaps be given more attention than they have so far received in thewelfare economics of social security and certainly in positive studies of the actual
development of the welfare state. Let me briefly mention three such arguments.
The first of these is the free rider problem. Someone who realizes that he lives
in a society which is committed to certain standards of equality and protection
against poverty, might be tempted, if all saving and insurance were private andvoluntary, to refrain from providing for himself in the expectation that society
would take care of him anyway by selective social assistance programs. These
programs would have to be financed by general tax revenue, but the benefits
would to a large extent accrue to the free riders. Mandatory membership in thesocial insurance system does not completely solve this problem, since it would
still be possible for someone with inadequate saving and insurance coverage to
exploit the welfare system. But it no doubt relieves it considerably.
The second argument is a truly classical one, being associated with names like
Böhm-Bawerk and Pigou. These and other authors argued that individuals werelikely to underestimate their own future needs, discounting future utilities at a
subjective discount rate that was too high; this led to a rate of saving that was
too low in the sense that later in life they would come to wish that they had
saved more.4 A public pension would—according to this argument—force people
to save more that they would have done voluntarily. There is little doubt that this4

Whether the rate of saving would also be too low from a social point of view is a complex
issue precisely because of the non-constancy of individual preferences. - A modern version of
the argument stems from the article by Strotz (1955–56), who introduced the problem of time
inconsistency. A rational individual who plans his future time profile of consumption at time t,
will—unless his intertemporal preference ordering is of a very special form—wish to deviate
from the plan at time t+1. Realizing this, he may wish to precommit himself, e.g. in the form ofa mandatory pension scheme. His analysis led Strotz to question the meaning of the principleof consumer sovereignty for intertemporal resource allocation; “the individual over time is an
infinity of individuals”. See also the account of the related concept of “Allais optimality” inMalinvaud (1972, ch. 10).

The Public Economics of Redistribution and the Welfare State147

argument historically has been very important for the development of thepension part of the social security system. Although the analysis in Fig. 2 casts
some doubt on the effectiveness of the pension in increasing future
consumption, alternative assumptions about the operation of capital markets
might lead to a more positive view of this. A related line of reasoning suggeststhat the government might not always accept people’s subjective probabilities of
events like unemployment and disability. If people tend to take a too optimistic
view of the occurrence of such events, one could build a case for forcing them tohave a better insurance coverage; see Lundholm (1998).
The third argument concerns transactions costs. In our formal theories,
building a savings and insurance portfolio is costless. But we all know thatbuilding a savings portfolio which yields both a desirable time profile ofconsumption and a satisfactory risk coverage is a difficult task. It may be madeeasier by securing expert advice, but this does not come for free. Also, the returnon the portfolio depends on one’s own effort and ability—in fact, just as labour
income does. Mandatory saving and insurance can therefore be regarded as an
attempt to economize on transactions costs, exploiting economies of scale. In
this, there is also an element of redistribution, since it makes the benefits lessdependent on ability and income—just as progressive taxation of wage income
makes disposable income less dependent on an individual’s productivity.

4. Interpersonal Redistribution
So far we have mainly been concerned with governmental interference withdecisions concerning intrapersonal redistribution through saving and insurance
decisions. From this point of view the aim of welfare state policies is to maketime and risk markets function more efficiently. The welfare state can therefore
be seen as attempt to improve upon the market system in efficiency terms.
However, this is clearly not the whole story. The welfare state also involves,both through social security and the tax system, a substantial volume ofinterpersonal redistribution. E.g., a more realistic picture of the pension system isthe one shown in Fig. 3. Here the high-income person gets a benefit which isless than actuarially fair, while the low-income person gets more than his
actuarial expectation. There is accordingly a redistribution from high-income to
low-income individuals through the social security system, and this comes in
addition to what is achieved through the progressive tax system.
In our account of public interference with intrapersonal redistribution thefundamental justification for public policies lay in some basic assumption about
the nature of preferences, particularly with regard to risk aversion, in combination

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C2C2High income earner

Low income earner

Y'

Y'

Y1

C1

Y1

C1

Figure 3 A redistributive pension schemewith an assumption about incomplete markets. The existence of gamblingnotwithstanding, it is fair to say that the prevalence of risk aversion is well
documented through actual behaviour, so that helping to diversify risk more
efficiently can be interpreted as helping to satisfy people’s preferences. In thecase of interpersonal redistribution it is less clear that one can appeal to suchrevealed preference arguments. The amount of voluntary income transfers that
we actually observe is clearly not insignificant, but we do not know what thatamount would have been, had not the transfers been made one of the main
responsibilities of the state. Do the transfers generated by the welfare state crowdout private philanthropy?
Consider a model where individuals have preferences for transferring income
to others. Assume first that person A is altruistic in the sense that his utility
depends both on his own consumption and on that of B. Assume that A is richand B is poor, and that A decides to give some of his income to B. Now the state
decides on a policy that increases the income of B by taxing A. If the tax paid by
A equals the transfer received by B, the model implies that A will reduce theamount of his voluntary giving by exactly the amount of the transfer. The welfare
state does indeed crowd out private philanthropy and achieves in fact noredistribution at all.5 This confronts us with a puzzle: If this analysis is even justan approximation to reality, why is there public redistribution? The puzzle may
be resolved by reformulating the model to look at the problem from the point ofview of a single A as before, but assuming that there is a large number of Bs, so
5

It is doubtful whether this type of model can satisfactorily explain the observable facts aboutcharitable giving. For criticism and further discussion see Sugden (1982) and Andreoni (1990).
Both these authors point out that a gain in realism may be obtained by assuming that donors
also derive utility from the act of giving.

The Public Economics of Redistribution and the Welfare State

149

that we try to explain the behaviour of a single rich donor who is confronted
with many poor recipients. If A’s donation is divided equally among the Bs, it
makes little difference to any single B. If, at the same time, A realizes that there
are many like him, the problem assumes a public good character, whereby eachA has incentives that imply that too little is offered as private donations.6 The
problem might be overcome by a social contract whereby the rich As commit
themselves to contribute jointly to the welfare of the poor. This contract has an
obvious interpretation as the welfare state.
Another justification and explanation for redistribution policy, represented
most prominently by the work of Vickrey (1945), Harsanyi (1955) and Rawls(1971), consists in deriving the desire for income equalization from the theory ofrisk aversion. The basic idea of Vickrey and Harsanyi is the following: Imagine
that you were asked to choose between participating in a number of lotteries,
where each lottery gives you an equal chance of becoming any one person in aparticular country. How would you evaluate the utility of each lottery? Appealing
to the axioms of the von Neumann-Morgenstern expected utility theorem, theyshow that the value to you of each of the lotteries would be given by the
expected utility associated with it, or, since the probability of becoming any one
person is the same for all, by the sum of utilities, which is the utilitarian social
welfare function. If you are risk averse, you would also, in the choice between
two lotteries/countries whose average income level is the same, choose the one
with the least unequal distribution of income. In other words, risk aversion
implies inequality aversion. Rawls’ argument is similar, although his notion of risk
aversion leads to the welfare criterion of the wellbeing of the least advantaged
person in each society. Thus, the general argument is that risk aversion implies
aversion against inequality, provided that you evaluate society from behind a veilof ignorance concerning your own position in it. There is a difficulty in making
this idea operational, since as a rule you do in fact know your own position insociety. Perhaps you could come close to the Rawlsian “original position” bythinking about the organization of society from the point of view of yourchildren and children’s children and so on, some of whom are not yet born andwhose preferences and abilities cannot therefore be known, but whom you stillcare about. From this point of view, it is quite reasonable to assume that you
would like to see a society with some system of redistribution from the more to
the less fortunate members of society.
Given that such a social preference for equality could be established, how far
would it be rational to go? The general answer to this question is that it depends
firstly on the precise formulation of the preference for equality (the social welfare
6This is a version of Sen’s “isolation paradox”; see Sen (1967).

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function), and secondly on the policy instruments that are available forredistribution. Let us suppose that the policy objective can be represented as the
maximization of the utilitarian sum of utilities. Suppose also that the government
can redistribute income through lump sum transfers, i.e. taxes and subsidies thatare related directly to personal characteristics and that do not affect any relative
prices as individuals see them. As a utilitarian you would also like to assume thatthe marginal utility of income is decreasing, reflecting the judgement that a dollarof extra income is worth less to a rich than to a poor person. The optimal
amount of redistribution will then be given by the condition that the marginalutility of income is the same for all. Let us think about this in the simplified
setting in which there are two homogeneous groups of individuals, the workers
and the disabled, and that disability pensions can be financed through a lumpsum tax on workers. Let m be the marginal utility of income, and let superscripts
1 and 2 refer to the workers and the disabled, respectively. We can then write
the condition for optimal redistribution as
m1 = m2(1)

Note that this would not necessarily imply equal incomes. Because of differencesin needs or tastes, the functional relationship between income and utility might
differ between the workers and the disabled, but full equality is in any case a
useful benchmark case.
Note that in this case there is no trade-off between equality and efficiency. If
the market system were such as to lead to an efficient use of resources in theabsence of taxes and transfers, this would still be the case after incomes had
been redistributed. The point is that no prices are being distorted, so that the tax
system does not create any efficiency loss. This does not mean that nothing haschanged. The redistribution of income has shifted the competitive economy toanother equilibrium, but this is efficient just as the initial equilibrium was.
Lump sum taxes are not very realistic as a description of real life policy
instruments. One reason is, as emphasized by Mirrlees (1971), that the
government does not have the information necessary to implement such taxes inan optimal fashion.7 We therefore move our analysis a step forward in terms ofrealism by assuming that taxation of workers takes the form of an income tax. In
contrast to the lump sum tax the income tax has both income and substitution
7

Although Mirrlees (1971) is the classic reference in this area, the explicit reference to theinformational problem came later, both in his work and others’. Several years earlier the
problem of optimal income taxation had been formulated very clearly by Vickrey (1945) in anarticle that in several respects was much ahead of its time. For an informal discussion of thework of Mirrlees and Vickrey see Sandmo (1999).

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effects; like the lump sum tax it reduces disposable income, but in addition it
also distorts relative prices in favour of leisure and household work and against
market labour supply. It is the latter effect which leads to a loss in terms ofefficient use of resources, because a wedge has been driven between theworker’s marginal productivity and his subjective evaluation of leisure. Thisefficiency loss is the marginal cost of redistribution, and because of this cost it
will now be rational to carry redistribution less far than under the hypotheticallump sum tax. It turns out that the marginal efficiency cost can be expressed as
the product of the marginal tax wedge and the reduction in labour supply, sothat the condition for optimal redistribution becomes
m1 = m2 (1–θ e)(2)

where θ is the tax wedge8 and e is the workers’ compensated elasticity of labour
supply with respect to the after-tax wage, which is positive. Thus, redistribution
stops short of the point of equality of marginal utilities of income and is limitedby the magnitude of the elasticity of labour supply. If the two marginal utility ofincome schedules are the same, the optimum will occur at a point where m1<m2,
so that workers have the higher income. From (2) we also see that the higher theelasticity, the less is the optimal degree of redistribution. If the compensatedelasticity were to be zero, the income tax is equivalent to a lump sum tax (having
only income effects), and the optimal degree of redistribution in the two cases is
the same.9
The marginal cost of redistribution has a wider interpretation as the marginal costof public funds and is of importance not only for the redistributive policies of thegovernment, but also for its supply of public goods like communications infrastructure
and public safety and private goods like child care and higher education.
Although I have here expressed the efficiency loss from tax finance and thecosts of redistribution as stemming from the personal income tax and the labour
supply response, the point is of course a much more general one. All the major
types of taxes, with the exception of taxes on goods that are harmful to theenvironment, involve price distortions and efficiency losses. Just as the efficiency
loss from taxes limits the degree of redistribution, it also limits the efficient
89

The tax wedge is the percentage difference between the consumer and producer wage. If t is
the marginal tax rate, the two are related by the equation θ =t/(1-t)
This analysis has been presented in more detail in Sandmo (1991). Note that by solving
equation (2) for the tax rate, one obtains an optimal tax formula which is a special case of thefamous inverse elasticity rule, whereby the tax rate should be higher, the lower is thecompensated price elasticity. Note also that for the formula to make sense, it must be the casethat (1-θ e)>0. This condition is satisfied if tax revenue is an increasing function of the tax rate,
so that we are on the upward-sloping part of the “Laffer curve”.

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supply of public goods. However, the efficiency loss from taxation stems in large
measure from its redistributive function. Although marginal tax rates involve asocial cost, they also reflect a possible gain in the form of a more equitable
distribution of income. Both aspects should be taken into account in calculationsof the optimal size of the public sector.10

5. Concluding Remarks
In this brief survey I have argued first that it is by no means a trivial matter todecide how much redistribution the welfare state actually achieves, since thisinvolves comparison with the unobservable situation where the state does notengage in redistribution. I have also pointed out that much of the public
redistribution scheme consists in redistribution between periods and states in aperson’s life that might conceivably have been achieved through private markets;nevertheless, there are several arguments for having the state carry out some ofthis income smoothing on behalf of individuals. Finally, I have argued that theamount of redistribution between persons should, in a rational calculation of costs
and benefits, be limited by the efficiency losses arising from the tax distortions.
There are some problems that I have not touched upon. Let me just mention afew. As Assar Lindbeck (1995) has recently pointed out, conventional economic
analysis assumes that incentives can be changed without any effect on
preferences, whereas it would be more realistic to assume that in the long run,the economic system will have an effect on the preferences of the members ofsociety. Thus, a weakening of the economic incentives to work might over timestrengthen people’s preferences for not working, through a softening of thesocial sanctions against idleness. On the other hand, a society with a low degreeof economic and social stratification might be less prone to social conflicts andtherefore more productive. Clearly, the assumption that preferences are
independent of the economic system is a strong one, and further research isneeded to explore more general models.
I have also neglected a whole set of problems suggested by political economy
considerations. The individuals in society do not simply adapt passively to theeconomic system. As political agents they also try to change the system to theirown advantage. In a society where one’s disposable income to a large extent isdetermined by government policy, much private effort will be directed towards
changing the rules of the redistributive game. This effort has an alternative costin terms of productive work and should clearly be counted as one of the
10 I have discussed this in more detail in Sandmo (1998).

The Public Economics of Redistribution and the Welfare State

153

additional costs of running a redistributive society.
While in the present paper I have mainly taken a normative approach to the
problems of the welfare state, there is also a lot to be said for the more positive
approach, whereby the goal is to explain the policies actually chosen, rather thanpoint out the optimal ones. A positive study of the development of the welfare
state would have to consider both the choice of institutional framework and the
choice of policies, given the institutions. A fertile meeting ground for positive
and normative analysis will be in the study of how institutions influence
outcomes and the degree to which actual outcomes conform to the optimality
conditions of normative economic theory.

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