friedman's theory of income redistribution up after being down for the count

Friedman's Theory of Income Redistribution up after Being Down for the CountAuthor(s): Michael BrooksSource: Public Choice, Vol. 99, No. 1/2 (1999), pp. 177-184Published by: SpringerStable URL: http://www.jstor.org/stable/30024515 .

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Public Choice 99: 177-184, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands.

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Friedman's theory of income redistribution up after being down for the count*

MICHAEL BROOKS Department of Economics, University of Tasmania, GPO Box 252-85, Hobart Tasmania 7001, Australia; e-mail: Michael. Brooks@ econ. utas. edu. au

Accepted 29 March 1997

Abstract. Many years ago McKenzie set out to expose the hidden assumptions underlying the orthodox case for the collectivization of charity as put forward by Friedman. In doing so he argued that collectivization may reduce the degree of transfers and this will necessarily make the poor worse off. I demonstrate that McKenzie's analysis contains hidden assumptions of its own and that even if there is a reduction in the level of transfers it does not necessarily follow that this will result in a Pareto inferior redistribution.

1. Introduction

For many years there has been widespread acknowledgment of Friedman's (1962) ingenious argument that the 'private charity' market may not provide sufficient transfers to the deserving poor. An exception is instanced by McKenzie's (1981) note published in this journal some years ago. In his discussion McKenzie sets out to show that Friedman's discussion is flawed: that once the hidden assumptions have been exposed it is readily seen that collectivization of charitable giving can result in a Pareto inferior realloca- tion. McKenzie's argument is also interesting in its own right as his line of attack on government intervention does not rely on any of the 'standard' public choice lines of argument.' McKenzie relies instead on the novel idea that collectivization can result in less rather than more transfers and that this reduction will make the poor worse off. In such a case public intervention into the charity market must be therefore regarded as an instance of a Pareto inferior change. McKenzie's argument represents one of the few critical arguments on the validity of Friedman's argument, at least with the framework of conventional public economics. And, McKenzie's paper has withstood the test of time: there have not been any critical comments on his paper. One

* Thanks to John Head and Richard McKenzie for helpful comments. Neither of them are responsible, however, for the content of the paper.



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might be inclined to draw the conclusion from the absence of any counter-

arguments that McKenzie has carried the day - that Friedman's argument is

seriously marred. The purpose of this note is to indicate some deficiencies in McKenzie's

argument. In doing so I attempt to set the record straight: despite being down for a long count, a strong defence can be made of Friedman's general line of argument for government intervention, at least within the terms of conventional public economics.

Specifically, I seek to show that: (i) even when all of the assumptions of McKenzie's model strictly hold,

collectivization of charity can equally result in more as opposed to less transfers, and

(ii) even if collectivization results in fewer transfers, McKenzie's argument that this necessarily represents a Pareto inferior change is not correct.

2. McKenzie's model

In order to see what is at stake, consider Figure 1 which is a modified version of McKenzie's first figure.2 The potential donors, I and II are assumed to have an identical market demand for poverty relief, D and the marginal cost of poverty relief is MC. It is important to note that in keeping with Fried- man's formulation, the motivation for giving is the satisfaction each individual receives from the reduction in poverty. McKenzie observes correctly that as the benefits of poverty relief are potentially consumable by all, the demand curves need to be summed vertically and the efficient level of giving here is

X*. In this conventional setting, McKenzie raises the novel possibility that the

private charity market may well result in more transfers than X*. This result follows from McKenzie's assumption that each donor may be unaware of the amount of transfers made to the recipient, R. Donor I or II may not wish to draw attention to R's plight and thereby embarrass him. Accordingly, each donor may take steps to conceal the level of transfers made to R. Similarly, R in an attempt to hide his embarrassment may also take steps to conceal the amount he has received. In this specific setting, each donor will transfer income up to the point where his demand curve intersects the marginal cost of giving. The total level of transfers in the private charity market is therefore

equal to XM (= 2X2). Although McKenzie does not put the matter quite in these terms, it is clear that poverty relief here does not yield public benefits as each donor is completely unaware of the other donor' s activity. A transfer is therefore a private good to each and every donor. Since the transfers are a private good, it follows that the donors' demand curves have to be summed



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$

S

V

F

T

ZvD

D

Dm

-r W

K E

P

A

B

MC'

MC ChD

0 X0 X1 X2 X3 X H X= 2X2 Poverty Relief

Figure 1.

horizontally, yielding the aggregate demand curve Eh D. Under McKenzie's specific scenario the total level of transfers can be read off the point at which the horizontally summed demand curve intersects the marginal cost curve, yielding a level of transfers of XM.

In this setting, McKenzie claims that collectivization of charity can be undesirable. This follows from the simple proposition that collectivization may provide information about the extent of poverty relief made by each and every donor. Each donor can adjust the amount he gives as he can consume the poverty relief offered by the other donor. Despite the potential problem of arriving at just what will be the level of transfers under some political institution, McKenzie asserts the level of transfers will be reduced to the level which is consistent with a Pareto optimal level of poverty relief. Col- lectivization is undesirable here, not because it fails to provide the optimal quantity, but because it results in a reduction in the level of transfers to R. Collectivization of charity therefore represents a Pareto inferior movement as the recipient will end up receiving less transfers and, according to McKenzie, will be worse off. McKenzie thereby presents a case in which the government fails.3



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3. Some critical remarks on McKenzie's case against collectivization

There are a number of difficulties and ambiguities, however, with his argument. First, McKenzie analysis contains, despite his objective to expose the hidden assumptions underlying the traditional analysis, a hidden assumption of its own. In his introductory remarks, McKenzie (1981: 337) claims that he will show that ".. . non-collective provision of a public good may (my emphasis) at times lead to over-consumption and production and that, therefore, collectivization of the provision can lead to a reduction in the amount of the public good available". What is not clear from McKenzie's discussion is the reason for his equivocation; there is simply no discussion why he was willing to suggest only that collectivization might result in fewer transfers. From his discussion, one is left to draw the conclusion that his equivocal result depends on whether or not the hidden knowledge assumption holds. For example, suppose that only one of the two donors is aware of the transfers made to the recipient. The level of transfers made by the 'ignorant' donor would be X2 which would be fully and equally consumed by the other donor. Here, collectivization would involve an increase in the level of transfers going to the recipient as the Pareto optimal amount involves an increase in the degree of giving, X* is greater than X2. If, however, both donors are unaware of the transfers made by the other, then, as McKenzie's analysis suggests, collectivization here will result in less rather than more transfers. This interpretation is certainly consistent with the tenor of his discussion in which he notes that the donors and the recipient may undertake steps to hide the transfers. Whether or not collectivization results in fewer transfers would appear to rest therefore on how many individual donors and recipients undertake some measure to be secretive and the extent to which they are successful.

This interpretation is, however, misleading. Even if McKenzie's assumption strictly holds - that there is universal ignorance on the part of the donors of the level of giving - whether collectivization results in fewer or more transfers depends on the relationship between the aggregate demand curves, EVD and EhD, and the marginal cost of poverty relief. If, for example, the value of marginal cost is raised to MCI, then collectivization will result in more not less transfers than the private charity market, i.e., X1 is greater than Xo.4 McKenzie case against collectivization of charity, which is based on the notion that the market outcome involves relatively more rather than less transfers, appears to rest on a hidden assumption about the relationship between the aggregate demand curves and the marginal cost curve.

Second, even if collectivization results in a reduction in the level of poverty relief, there is no reason to follow McKenzie in his belief that the reduction in poverty relief must necessarily imply that the recipient is worse off. Suppose,



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for example, that under the private charity scenario the recipient feels a good deal of social discomfort at having to rely on the hand-outs of the donors and that this discomfort rises as the degree of poverty relief increases. In terms of the geometrical framework here, this effect can be depicted straightforwardly. In the absence of any discomfort the most the recipient would be willing to pay for a dollar transfer is a dollar. If the initial marginal cost curve measures the cost of transferring a dollar, then the recipient's demand curve would be coincident with the cost curve. Now introduce a recipient's demand curve for poverty relief, such as D', which captures indirectly the social discomfort of receiving charity. The vertical difference between that demand curve and D' reflects the marginal discomfort the recipient incurs from receiving hand-outs. In this case, McKenzie seems to be correct in suggesting that collectivization will make the recipient worse off. A reduction in transfers would seem to involve a loss of surplus as measured by area AX*Xm.

It is by no means clear, however, that the recipient's behavioral response should be assumed to be invariant across differing institutional settings. Although the individual may suffer discomfort from accepting the hand-outs of the relatively well-to-do, there is no reason to believe that the recipient will similarly express discomfort when the government is directly responsible for poverty relief. The change in attitude is captured by the following conversa- tion between two poor individuals: "Well, I'm glad that the government has taken on its social responsibility of looking after us poor". "I agree", as the other fellow nodded approvingly, "I had fought in the war when the country needed me and now I'm getting what I deserve. It was downright degrading to have to depend on hand-outs from the well-heeled but now I can hold me head up with some pride". In this event, although collectivization may result in a reduction in the level of poverty relief, the individuals can be nevertheless better off! Suppose the recipient's demand curve under the government scenario is coincident with the marginal cost curve, MC, indicating that he suffers no discomfort from receiving charity from the government but given by Dm under the private charity market. In this case the recipient is better off under public charity despite the reduction in the level of transfers. The gain from avoiding the social discomfort experienced under private charity outweighs the loss arising from the reduction in poverty relief, FEA is larger than AX*XM.

Suppose the amendments just made to McKenzie's model are put to one side: that we obey his seemingly hidden assumption that the recipient's preferences are invariant across institutions and that the recipient's demand curve is coincident with the marginal cost curve. This seems to be the case McKen- zie has in mind when he draws the conclusion that collectivization will result



182

in a Pareto inferior change. The reduction in the level of poverty relief will make the recipient worse off by area X*EBXM.

Although this is the formulation that McKenzie appears to have in mind, it will not suffice to rule out the possibility that there can be unanimous support for collectivization. It is possible to find a collective program that could secure the approval of all. This might seem an odd claim. After all, McKenzie's argument appears to rest on the proposition that collectivization will involve a movement from one Pareto optimal outcome to another. This line of reasoning follows from the observation that when the preferences of the recipient are included with those of the donors, the Pareto optimal set coincides with the points on the marginal cost curve from point E onwards. Accordingly, it does not appear to be the case that collectivization could win unanimous support as collectivization will involve a movement from one Pareto optimal position to another and will therefore invariably make someone worse off in the process. The argument is, however, seriously misleading because it fails to take account of the change in technologies associated with the movement to collectivization.

Under the private charity market a transfer by any particular donor to the recipient is effectively a private good. For epistemological reasons, a transfer does not yield utility to any other donor. The movement to collectivization brings about a radical change in the degree of information about the level of transfers made to the recipient. Collectivization involves a change from a private to a public goods technology. The change in technology provides the opportunity for a Pareto-superior move.5 Consider, for example, a potential collective program in which the recipient is made no worse-off but the donors are made better off. The rectangular hyperbola r, describes all the combinations of transfers which would maintain the recipient's income at the level XM. If each donor, for example, agrees to be taxed an amount equal to area OX3PT, then the total amount to be distributed to R is represented by area OX3WV [=2(OX3PT)]. Since this amount falls on the rectangular hyperbola the recipient's income can be maintained at XM which means that the recipient is neither better nor worse off than under the private charity market. Under this alternative arrangement to the one presumed by McKenzie, each of the donors accrues a gain in consumer's surplus represented by area FKPT.

Manifestly, collectivization of charity can represent a Pareto-superior move. In short, it appears as if McKenzie's emphasis on demonstrating that collectivization can be Pareto undesirable has caused him to overlook the point that his discussion of the potential change in technology contained the seeds of a novel defence of collectivization.



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4. Conclusions

In the analysis I have been obedient to McKenzie's framework that government acts as if it were a benevolent despot. If this assumption is relaxed, then it would be possible to show that the private charity market may be the preferred institutional setting. But that would move us to another story and too far afield from the conventional framework McKenzie used to criticize Friedman's argument. The objective here has been the more limited one of demonstrating that one significant aspect of McKenzie's case against collectivization of charity is not well taken: a fall in the level of transfers going to the recipient does not necessarily imply that the poor will be worse off. In doing so, some unfamiliar arguments about the potential role of government with respect to charitable giving have been unearthed. In particular, it raises a warning about pushing too far the point that private markets always make the best use of the knowledge of particular circumstances of time and place. Government provision can have a potential advantage over the market in that the very public nature of government activity can allow a dollar of transfers to be simultaneously and equally consumed by all. In doing so collectivization can represent a Pareto superior policy.

Notes

1. In his note, McKenzie raises two hidden assumptions that are alleged to weaken the thrust of the traditional case for government intervention in the charity market. In this note, I concern myself only with the first of his arguments, since it is only the knowledge assumption that is relevant to Friedman's case for collectivization of charity. Perhaps a word or two of explanation is warranted on why I have chosen to put aside his discussion of the possibility of negative marginal evaluations. McKenzie views that one of the strengths of his argument is to demonstrate that some people's demands can ". .. extend downward into the negative quadrant or originate in the negative quadrant" (1981: 343) and that the lack of any analysis of this possibility represents a hidden assumption of the traditional public goods analysis and, in particular, the orthodoxy's case for collectivism of charity.

Despite the impression created by McKenzie's discussion, the possibility that a public good may be an economic bad to some individuals is part and parcel of the orthodox treatment of public goods theory. The possibility of negative marginal evaluation was recognized, at least in the modern treatment of public expenditure, as long ago as 1955 when Samuelson [1973 (1955): 192, footnote 1] in his second paper on public goods noted that if "... one man's circus is another man's poison ..." the indifference curves between a private and public good will take on a positive slope. Indeed, the possibility that a public good could be a bad to some individuals was fully incorporated into the public goods orthodoxy by giving it recognition in terms of the non-rejectability or impossibility of rejection characteristic (see, for example, Shoup, 1969: 93-94). McKenzie's claim that some individuals could have a negative marginal evaluation for a public good is therefore part of the public good orthodoxy.

Nevertheless, it is hard to see how this possibility relates to the orthodox case for collectivization of charity as put forward in Friedman's discussion. An examination of Friedman's argument reveals that he assumed that all of the donors had a positive marginal



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evaluation for transfer, viz ". .. we might all of us be willing to contribute to the relief of poverty ..." (Friedman, 1962: 191, my emphasis). Manifestly, Friedman is not guilty of making a hidden assumption about whether or not some of the donors' evaluations extend to the negative quadrant; he explicitly ruled the possibility out of the analysis. Accordingly, while McKenzie's analysis of the hidden assumption about marginal evaluations might be relevant to some orthodox analyses of redistribution, it is not germane to the orthodoxy as put forward by Friedman. The knowledge assumption does appear, however, to represent a hidden assumption of Friedman analysis and therefore I restrict my discussion to that assumption.

2. McKenzie's Figure 1 involves three voters who each have a different demand for transfers. The figure here contains two donors who are assumed, for simplicity, to have an identical preference for transfers. Nothing of substance is lost in the simplified figure constructed here.

3. Note that in his argument, McKenzie does not rely on any of the lines of argument conven- tionally found in public choice to support a case against government intervention. In his argument there is no majoritarian exploitation of a minority nor is there any manipulation of the majority at the hands of an agenda setter. Either line of argument would point to the possibility that there will be a divergence between the Pareto optimal outcome and the majority rule equilibrium. In stark contrast to this general line of argument, McKenzie presumes that the government program will provide an amount of poverty relief consistent with the Samuelsonion optimal amount of the public good. McKenzie case against government intervention into the charity market appears to rest on the claim that there could not be unanimous approval for a change to the public goods optimum at point E.

4. If the marginal cost of poverty relief cuts the two aggregate demand curves at their intersection point, then the private charity market equilibrium can coincide with the Pareto optimal outcome under collectivization.

5. It is, of course, true that information on the level of transfers made to R is a two-edged sword. The public nature of information enables each of the donors to free-ride on the contributions of the others. This free-riding may well mean that the level of transfers will fall short of the amount required for the Pareto-desirable move. In this regard it is worth recalling that McKenzie's discussion is predicated on the assumption that collectivization does not involve government failure in the standard sense.

References

Brennan, G. (1976). The distributional implications of public goods. Econometrica 44: 391- 399.

Friedman, M. (1962). Capitalism and freedom. Chicago: The University of Chicago Press. McKenzie, R. (1981). The construction of the demand for public goods and the theory of

income redistribution. Public Choice 36: 337-344. Samuelson, P.A. [1973 (1955)]. Diagrammatic exposition of a theory of public expenditure.

Review of Economics and Statistics 37: 350-356. Reprinted in R.W. Houghton (Ed.), Public finance: Selected readings, 190-204. Second edition. Harmondsworth: Penguin.

Shoup, C.S. (1969). Public finance. Chicago: Aldine.



friedman's theory of income redistribution up after being down for the count

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