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New Sources of Development Finance$

A. B. Atkinson

Print publication date: 2004

Print ISBN-13: 9780199278558

Published to Oxford Scholarship Online: January 2005

DOI: 10.1093/0199278555.001.0001

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Global Public Economics

Global Public Economics

(p.200) 10 Global Public Economics
New Sources of Development Finance

James A. Mirrlees

Oxford University Press

Abstract and Keywords

This chapter, together with chs. 2 and 11, approaches the question of development funding in a theoretical way, rather than by examining individual proposals for sources. One purpose of the book is to bring to bear on this accumulated knowledge in the field of national public finance, and more generally public economics. Consequently, a discussion of global public finance/economics is presented here that considers the lessons from optimal tax design when applied at a global level. The different sections of the chapter look at: global taxation; taxation for aid; the possibility of an international agreement whereby income taxation is applied to nationals (rather than residents) and countries report people's income to their country of nationality (international allocation of tax bases); supranational taxation; subsidies and transfers; voluntary contributions and taxation; and development assistance expansion. An appendix considers the conditions for marginal tax rates to be independent of the revenue requirement.

Keywords:   development assistance expansion, development funding, global public economics, global public finance, global taxation, international allocation of tax bases, marginal tax rates, public economics, public finance, subsidies, supranational taxation, tax design, taxation for aid, transfers, voluntary contributions and taxation


Transfers by governments to low-income countries, whether to their governments or their citizens, through agencies such as the UN, or directly, are part of the global fiscal system of taxes and subsidies. We can think about optimal global taxes and subsidies, as they might be instituted by a world government. There is no possibility that such a system will be implemented, but it might provide a reference point to illuminate or suggest more realistic policy options; or a moral challenge that will merely leave us deeply uncomfortable.

Here is a specific, too simple model, of a kind many of us have used to think about optimal national tax systems. It is a timeless model, where income and consumption are the same, and people's labour is the only input into production of goods that will be used for private or government consumption. People have utility u(c, ℓ ), where c is income, net of taxes and subsidies, and ℓ is labour supplied. u is, as we usually assume, concave, increasing in the first argument, decreasing in the second. The difference between people is that they have different productivities w. Assuming competitive conditions, a person's income before taxes and subsidies is wℓ. This income is the base for determining transfers, whether to or from the individual.

If an optimal system of transfers is one that maximizes the sum of individual utilities, it is to be expected that it would involve substantial positive taxes on almost everyone in the richer countries and substantial transfers to the majority of households in lower-income countries. There would also be transfers to governments in low-income countries to pay for public consumption. One would imagine that the optimal provision of public facilities like police and security, water supply, roads, schools, and health care would be rather similar in real (PPP, purchasing power parity) per capita terms among countries, and indeed that might be the most dramatic difference between an optimal world economy and a system of optimal national economies with only small transfers between nations.

Because of incentive considerations, marginal tax rates would not necessarily be any higher in an optimal world than in optimal nations, even if average tax rates would (p.201) be higher in rich countries, and lower (even sometimes negative) in poorer ones. It is interesting to consider this further. Unfortunately, there is a terrible lack of good general propositions in optimal tax theory: we must rely on qualitative differences that can be seen in numerical examples, or differences that are clear between extreme cases, and are likely to apply to most intermediate cases in a similar way.

It seems that world inequality in relative incomes is somewhat greater than inequality within most (but certainly not all) countries. We may take it that something similar is true of inequality in wage rates, though that is not easy to observe directly. Differences between countries in lifetime hours of work, though certainly quite marked, are clearly not at all as large as differences of income, and therefore inequality of wage rates should be somewhat similar to inequality of incomes. The question then is how inequality of wage rates affects optimal tax rates, most particularly marginal tax rates. The answer we expect is that greater inequality will be associated with higher marginal tax rates.

At the extreme of perfect equality, taxation can be lumpsum, with everyone paying the same amount of tax, and a marginal tax rate of zero. Thus, at least at small degrees of inequality, marginal tax rates should increase with inequality. (At the same time, we should remember that two-class models have been constructed in which the optimal marginal tax rates are negative (Allen 1982), though they are probably not too close to reality.) At the opposite extreme, when there are only very high-productivity people and very low-productivity people, the optimal schedule c = x(wℓ) must be close to one of the high-w people's indifference curves. According to a familiar argument, we would want the high-w person to choose a point on that schedule where the slope was equal to the wage. Her marginal tax rate would be zero (just as in the no-inequality case), but she would still pay a substantial total tax, to be compared with the subsidy received by low-w individuals. The zero marginal tax rate feature is an artefact of the unrealistic assumption that it is perfectly known what the highest w (though the w of any particular individual is unknown to the taxing authority); but we can still derive instruction from this crude model.

One measure of progressivity in the tax system (though not one that has been used to my knowledge) is the difference in tax paid by richest and poorest divided by the difference in incomes. Call this the incremental tax rate. It is an average of marginal tax rates across the whole income range. As a particularly simple case, take a two-class economy with pure redistribution, that is to say, no public consumption. Compare across models with the same average product per person, but low and high wages diverging. When the divergence is large, all the work is done by those with high w. In a wide range of cases (with utility additively separable in the two arguments) it is found that the incremental tax rate converges to one as the high wage tends to infinity. There is a sense, therefore, in which as inequality increases, the progressivity of the system increases, and indeed with this measure becomes as great as possible, despite the fact that the marginal tax rate at the highest income levels is zero.

We do not have to rely on extreme examples of this kind for evidence that, on average, marginal tax rates increase as inequality increases. Numerical calculations have supported this conjecture. But, particularly at higher income levels, the rate at which marginal tax rates increase as inequality increases turns out to be quite slow.

(p.202) The simplest tax system is a linear one, creating a universal budget constraint

c = ( 1 t ) w + b

with constant marginal tax rate t applying at all income levels and a fixed lumpsum payment b. b is roughly equivalent to personal allowances in the income tax, along with welfare benefits and education and publicly provided health expenditures. Considering that greater inequality seems to imply greater marginal tax rates, but that world inequality is, in proportional terms, not much greater than inequality within most countries, we would expect a world optimal system to have a slightly larger level of t than is optimal for single nations without significant international transfers, whereas b would be much smaller than is appropriate for high-income countries, and larger, no doubt considerably larger, than would be appropriate for low-income countries (if they were to implement such a safety net). The different level of b is primarily dictated by the different level of average product in the different countries and the world.

As a consequence, people whose productivity is high even within a rich country would have a budget constraint not very different from that they currently experience, since the lumpsum element of the tax system is (and should be) small relative to their after-tax labour income. Paradoxically, the introduction of a world optimal tax/subsidy system would have the greatest negative impact (in relative terms) on middle-income people, while the greatest positive impact would, of course, be for people with the lowest productivity. In a sense, an optimal tax system will go far to extract as much revenue as possible from the richest in society, so that any further revenue requirement, as a result of joining a redistributive world tax system (or, more moderately, for increased foreign aid) will have to be drawn, to a considerable extent, from those in the middle of the income distribution.


It is natural, then, to consider nations whose governments choose some fixed level of development assistance, presumably not the level that would be implicit in a world-optimal tax and transfer system, but where, within each country, national welfare is maximized. The arguments already developed can be modified to address the question how taxes should change if there is to be an increase in the development assistance grant.

When doing calculations of optimal linear income taxation, Nicholas Stern noticed that an increase in the revenue requirement for public consumption had little effect on the marginal tax rate: additional expenditure was to be financed to a considerable extent by a reduction on the lumpsum subsidy which we have denoted by b. This observation corresponds closely to the argument developed in the previous section.

It is difficult to tell how general or relevant this result is. One way of throwing some light on the question is to look at the inverse problem and ask for what utility functions the result would be exactly true in the simple model we are using. The answer is that the optimal marginal tax rate is independent of the government expenditure requirement (p.203) when (and, in a certain sense, only when)

u ( c , ) = ( k c ) m m , k > 0 , m > 0.

It is shown in an appendix that this utility function implies the stated result: the necessity theorem is more involved and less interesting and is omitted. This is certainly a somewhat peculiar utility function, with a maximum level of desirable consumption, and no upper bound to the labour that a person can supply. Yet it may not be a bad approximation to people's consumption/labour preferences. It shows that in acceptable models, it is optimal to finance increased government consumption entirely by reduction of the uniform subsidy. Indeed it shows, implicitly, that there must be acceptable models in which the marginal tax rate would actually fall when the government expenditure requirement increased.

The conclusion is that, broadly, increased aid should come from everyone. That is to say, if it is generally recognized that development assistance does more good than had previously been appreciated, it is implied that the tax structure should be modified in such a way as to generate more revenue in an optimal manner, and that may involve only small increases in taxes on labour (and commodities).

A dual question to this is whether, when it is recognized that new revenue raising taxes are desirable, for example, to reduce smoking, or consumption of cholesterol, or environmentally damaging goods, it follows that more should be spent on foreign aid (and desirable public goods). No, it does not follow.

The simplest example uses the same model as before. Suppose it is newly recognized that production brings about global warming. In the model, we cannot allow for some kinds of production doing that and others not, nor for the damage occurring at a later date than the production. These would just complicate the analysis and lead to broadly the same conclusions. For simplicity, suppose that the damaging effect of global warming is just a reduction in production (actually at a different time, but all periods are combined together here). In the model, everyone's productivity is reduced from w to kw, where k is a positive number less than one. Since individual producers do not recognize the external impact of production, the competitive level of wages is still w. One further simplification gives a neat, clean result: it will be assumed that utility is a homogeneous function of consumption c.

The optimal budget constraint, with a given level of foreign aid, is then

c = ( 1 t ) k w + b k ,

where the optimal levels of t and b are independent of k.

This conclusion follows from the fact that one feasible tax system is preferred to another in the economy with k = 1, then both these tax systems remain feasible for the economy with externality, if modified by the introduction of the factor k as above. And, furthermore, everyone's utility is multiplied by a factor that is a power of k. Thus the order of preference between the two tax systems remains the same. Consequently, the optimal tax system is deduced from the original optimal system simply by introducing the factor k.

(p.204) The actual marginal tax rate is changed, of course. Denoting it by t′, we have

t = 1 ( 1 t ) k = 1 k + k t ,

which is greater than t, and grows as k diminishes. It is true then that taxation (of labour or, equivalently, goods) should be increased because of the environmental externality; but the uniform subsidy b should be reduced to kb. People will be worse off than they would have been if there were no externality, and their marginal utility of income (of b) will be reduced. Consequently, the domestic welfare cost of giving foreign aid, or of any revenue for public spending, is reduced. It follows that the case for foreign aid is less strong.

It may be argued that it is a different matter if new taxes are introduced because of a previously existing externality that had not been recognized. For this to modify the conclusion, one must accept the idea that people recognized the reduced marginal utility of income implied by environmental effects, but did not recognize the need for and desirability of controlling policies. Then the optimal-tax account is not really appropriate to the issue. In effect, I have argued that people's apparently simple-minded intuition that increased (environmental) taxes make them worse off is essentially correct, and that governments should not be told that they are in some sense better off and can afford to be more generous when they find that they ought to introduce these new taxes.


In the previous section, it was taken for granted that there was well-defined membership of the welfare function, which is to say that there is no doubt as to whose utility counts in determining the optimal tax system. In fact, there is considerable movement of people, both long term and short term. In reality, tax laws are applied in a bewildering mixture to residents, migrants, absentees, and nationals. It would be hard to construct a rationale for the way they are applied. Some few countries apply income taxation to nationals (or those with rights to reside and work) even when they have been resident abroad for some time. Surprisingly, it is unusual for the tax law to discriminate substantially against visitors or residents who are not entitled to vote.

The citizens of low-income countries often receive substantial remittances from nationals or relatives abroad. It is a major source of foreign assistance. It is an attractive proposal, then, that countries should tax their nationals (Bhagwati and Wilson 1989). Nationals of low-income countries abroad are generally much more prosperous than the average domestic resident. Such a move would surely benefit residents. The proposal envisaged double taxation, with nationals abroad paying taxes both to country of residence and country of nationality. It would be tidier and more natural to have an international agreement whereby income taxation applied to nationals, not to residents, with countries reporting people's income to their country of nationality.

The practical difficulties are considerable. Price levels vary considerably among countries. While there is no way of measuring PPP ‘correctly’—it is impossible to give a rigorous definition of the concept—clearly some adjustment would have to be made. (p.205) A much more serious difficulty is that different countries use commodity taxation and factor-income taxation in different proportions. It is hard, too, to see how dual nationality (which is often a desirable status) should be handled, and how family taxation (dependent allowances and joint taxation) should operate when different members of the household have different nationalities. Probably the most serious objection is that many people would be sufficiently unaltruistic or unpatriotic that they would adopt a national flag of convenience. It is a matter of regret, but the idea of reconstructing the international allocation of tax bases is not worth pursuing.


A world agency might be given some taxation power, but probably not simply for development assistance. There are many cases where countries should negotiate to ensure that taxation on some commodity is at more or less the same rate in different countries. The European Union has been trying to achieve ‘harmonization’ of many taxes, without committing itself to anything like an equal tax-rate principle. It has not created any supranational taxes. On the other hand, the Common Agricultural Policy constitutes a system of supranational subsidies. Also there are rules for transfers of parts of tax revenues to central funds, which come close to creating supranational taxes.

There are cases where efficient and reliable administration seems to suggest a supranational agency. Taxes on the combustion of hydrocarbons might well have been done that way (except that we know it would not be accepted by many governments). At least a tax on aircraft fuel, which is much to be desired, could be administered supranationally. The Tobin tax, on foreign exchange transactions, could also be done that way. The main point is to ensure common tax rates for tax rates in different locations.

If there were such supranational taxes, should the revenue be used for aid? There is no particular reason why the international nature of the revenue flow constitutes an argument for using the revenue for an international cause. Presumably, international causes would include financing UN administration, refugees, and UN military operations as well as development aid. But the connection is merely terminological. The existence of international revenue, if any, does not strengthen the claims of development assistance (and these other international expenditures), and it is hard to see why governments or voters would think it. The best one can say is that it might be politically possible for a novel revenue source to be used for purposes that international civil servants and members of NGOs find attractive, because its novelty might mean that other claimants, such as national governments, would not be quick to secure it for themselves.

It is also possible for a supranational agency to undertake profit-making activities, the proceeds from which could be available for aid. In effect, the World Bank is such an agency, using borrowing and lending as its instruments. It is hard to think of other opportunities. Production should require little skill, and yet the operation should be profitable. The proposal of a global lottery is an interesting and promising one, since lotteries appear to constitute an industry where entrants can still make substantial profits, presumably because of national regulation. It is only socially optimal to have (p.206) a high cost of gambling (which is what these profitable lotteries provide), if gambling ought to be discouraged. It is then rather dubious to try to increase supply. It is a bit like increasing the production of tobacco or other drugs as a way of getting revenue.


Subsidies are as much a part of public finance as taxes. We should, therefore, look at the expenditure side of development assistance as well as at the generation of revenue for it.

The general tax model we started with does not at first sight appear to describe very well the way that development assistance operates. Provision of schools and health care is rather close to the idea of a general uniform subsidy, if everyone is entitled to the same facilities, or at least does not pay or have entitlement related to income. The distribution of food aid can locally be of similar character. Grants to governments seem rather different. But where the recipient government is efficient and not corrupt, these grants do also fit the model fairly well, with the government using the funds as part of its revenues, influencing the level of subsidies to individual households as well as taxes. When aid is given in the form of finance for public projects, whether as pure aid or loans with concessionary terms, that should mean that part of government expenditure is being paid for by aid, so that required tax revenue within the recipient country is reduced.

It is clear that the form of the tax/subsidy system within the recipient countries is of great importance. Generally, in the lower-income countries, these systems are not very progressive as tax systems. It is supposed to be difficult to redistribute in poor, particularly in agricultural, countries. No doubt, the leakages from a general system of subsidies to farming households, both through administrative costs and corruption, are great. That reduces the marginal social value of subsidies (represented by b in the model), and means that the optimal tax system should be less progressive than would otherwise have been desirable. There are also leakages in the collection of taxes and in the disbursement of funds for public or private investment. The latter makes public spending (g) less desirable than otherwise. The former consideration has ambiguous implications: the adverse incentive effects of higher marginal tax rates may be less when there is considerable evasion. Though one must allow for unfair variation in effective (as opposed to legislated) tax rates, higher legislated rates may be needed to raise the actual tax revenue.

The main issue is what form the tax system should take when there are substantial errors in the observation of income, or, equivalently, in the transfers (whether taxes or subsidies). Little work has been done on the problem. A preliminary conclusion, from a model with no explicit incentive effects, is that the formal (i.e. legislated) progressivity of the system should not necessarily be less because of measurement errors.

On balance, subsidy leakages probably imply that the tax system should be somewhat less progressive than in high-income countries. But there is nevertheless a strong case for bringing pressure on recipient countries to make their systems more redistributive, pressure that might well take the form of aid conditionality. Certain forms of aid (p.207) are much less at the mercy of corruption and ineffiency than others, particularly aid programmes that are directly administered by international agencies, or at least that is what one hopes. One should perhaps question the common assumption that aid is always best given in the form of capital investment, rather than for consumption. Perhaps gifts of money (like the model) are best?


Private voluntary contributions to development assistance are not negligible. When one remembers that much official aid has been in the form of concessionary loans, and the official figures have included many expenditures that are really only aid to manufacturers in the donor country and of little net benefit (after loan repayments) to the recipient, one realizes that private aid has been a quite substantial proportion of total aid to developing countries. It is worth modelling, so that we can consider whether and how it is to be increased.

Suppose people make voluntary contributions to aid because the income that recipients get contributes to their utility. (This assumption is not consistent with experimental evidence that people would not give more to larger groups.) Denote contributions by xi. According to the hypothesis,

x i maximizes u ( y i x i ) + a i v ( j x j ) .

This way of modelling has different people with different income yi, and places different weight on the value of aid receipts. The amount people give provides some information about the value placed on aid, but of course is also influenced by their income.

Consider what would maximize the sum of utilities. Maximizing

i u ( y i x i ) + a i v ( j x j )

yields a very different outcome: much larger values of contributions to aid are implied. A similar result is obtained if we seek to maximize the median voter's utility. To do this calculation, of course we need to know incomes and the value placed on recipient utility. Income we may observe directly. ai should be deduced from the amount an individual would choose to give. We can arrange for the value placed on aid to be revealed by individual choice if we introduce matching grants, so that a voluntary contribution x is expanded to Mx. (A more general function could be used.) The matching element comes from compulsory contributions, that is, taxation. We can let it be a proportional tax on income.

This will not in equilibrium bring about the welfare maximum, but a second-best. The second-best would be the welfare maximum if everyone were identical. In that case the optimal value of M is the number of people. More generally, we get a moderately (p.208) complicated expression approximately equal to the number of people. When people all have the same income, and quadratic utility, optimal M is (∑a)2/(∑a 2).

This is an absurdly large number, of course, and would mean people made extremely small individual contributions that get multiplied up to aid that would be a substantial part of total incomes. People could not calculate correctly. One cannot really take the result seriously, and yet it suggests a case for much more generous matching than is provided by tax systems in which voluntary contributions to charitable causes are simply tax exempt.


On the whole a public finance approach to development assistance is not sympathetic to some of the main proposals for expansion, using revenue from environmental taxes or a Tobin tax. Yet it acknowledges a strong case for increasing aid by government and by individuals. Two proposals that are rather utopian suggest themselves from a public finance perspective:

  1. 1. Introduce a voluntary additional income tax to be used for development assistance, this tax to be matched by a substantial multiplier from general revenues. The individual would choose what percentage rate should be applied to income. Matching by a double contribution from general revenues would not be unjustified.

  2. 2. High-income countries with particularly low tax systems, which are to a considerable extent tax havens, might be induced by international pressure to institute a supplementary income tax on income arising in their territories, the income from which should be used for development aid.


It will be verified that when the sum of utilities is maximized, utility functions take the form

u ( c , ) = ( k c ) m m , k > 0 , m > 0 ,

the budget constraint is

c = ( 1 t ) w + b

and the overall resource constraint is

E [ c w ] = g

(where we use the operator E for averaging over the population), then, regardless of the distribution of marginal products w, optimal t is independent of g.

(p.209) Utility maximization by the consumer implies that for someone with wage w, ℓ maximizes − [k − (1 − t)wℓ − b]m − ℓm, so that

( 1 t ) w [ k ( 1 t ) w b ] m 1 = m 1 .

Solving this equation for ℓ, and introducing the temporary notation v = (1 − t)w, we have

= ( v 1 / ( 1 m ) + v ) 1 ( k b )

and from this we deduce that

c = k ( v m / ( 1 m ) + 1 ) 1 ( k b )

Substituting these expressions into the utility function, we find that a w-person's utility is

( v m / ( 1 m ) + 1 ) 1 m ( k b ) m .

We want to maximize the average value of utility,

E ( v m / ( 1 m ) + 1 ) 1 m ( k b ) m

subject to the resource constraint, which we can now calculate: it is

t 1 t E [ v ( v + v 1 / ( 1 m ) ) 1 ] ( k b ) = b + g ,

which can be rewritten to give a formula for kb:

k b = { 1 + t 1 t E [ v ( v + v 1 / ( 1 m ) ) 1 ] } 1 ( g + k ) .

Substituting this into our expression for average utility, we get

E [ u ] = E [ ( v m / ( 1 m ) + 1 ) 1 m ] { 1 + t 1 t E [ v ( v + v 1 / ( 1 m ) ) 1 ] } m ( g + k ) m .

This has to be maximized with respect to t (remember that v = (1 − t)w). g appears in the maximand only in the final factor, which does not involve t. Therefore the level of g does not affect the maximizing value of t. The result claimed is proved.


Bibliography references:

Allen, F. (1982). ‘Optimal Linear Income Taxation with General Equilibrium Effects on Wages’. Journal of Public Economics, 17: 135–43.

Bhagwati, J. N. and J. D. Wilson (1989). Income Taxation and International Mobility. Cambridge, MA: MIT Press.