Public Choice99: 177–184, 1999. 177c 1999Kluwer Academic Publishers. Printed in the Netherlands.

Friedman’s theory of income redistribution up after being downfor the count�

MICHAEL BROOKSDepartment of Economics, University of Tasmania, GPO Box 252-85, Hobart Tasmania7001, 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 theorthodox case for the collectivization of charity as put forward by Friedman. In doing so heargued that collectivization may reduce the degree of transfers and this will necessarily makethe poor worse off. I demonstrate that McKenzie’s analysis contains hidden assumptions of itsown and that even if there is a reduction in the level of transfers it does not necessarily followthat 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 pro-vide sufficient transfers to the deserving poor. An exception is instanced byMcKenzie’s (1981) note published in this journal some years ago. In hisdiscussion McKenzie sets out to show that Friedman’s discussion is flawed:that once the hidden assumptions have been exposed it is readily seen thatcollectivization of charitable giving can result in a Pareto inferior realloca-tion. McKenzie’s argument is also interesting in its own right as his line ofattack on government intervention does not rely on any of the ‘standard’public choice lines of argument.1 McKenzie relies instead on the novel ideathat collectivization can result inlessrather thanmoretransfers and that thisreduction will make the poor worse off. In such a case public interventioninto the charity market must be therefore regarded as an instance of a Paretoinferior change. McKenzie’s argument represents one of the few critical argu-ments on the validity of Friedman’s argument, at least with the frameworkof conventional public economics. And, McKenzie’s paper has withstood thetest 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 areresponsible, 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 isseriously marred.

The purpose of this note is to indicate some deficiencies in McKenzie’sargument. In doing so I attempt to set the record straight: despite beingdown for a long count, a strong defence can be made of Friedman’s generalline of argument for government intervention, at least within the terms ofconventional 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 inmoreas opposed to lesstransfers, and

(ii) even if collectivization results in fewer transfers, McKenzie’s argumentthat 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 versionof McKenzie’s first figure.2 The potential donors, I and II are assumed tohave an identical market demand for poverty relief, D and the marginal costof 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 individualreceives from the reduction in poverty. McKenzie observes correctly that asthe benefits of poverty relief are potentially consumable by all, the demandcurves need to be summed vertically and the efficient level of giving here isX�.

In this conventional setting, McKenzie raises the novel possibility that theprivate charity market may well result in more transfers than X�. This resultfollows from McKenzie’s assumption that each donor may be unaware of theamount of transfers made to the recipient, R. Donor I or II may not wish todraw attention to R’s plight and thereby embarrass him. Accordingly, eachdonor 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 concealthe amount he has received. In this specific setting, each donor will transferincome up to the point where his demand curve intersects the marginal costof giving. The total level of transfers in the private charity market is thereforeequal to XM (= 2X2). Although McKenzie does not put the matter quite inthese terms, it is clear that poverty relief here does not yield public benefitsas each donor is completely unaware of the other donor’ s activity. A transferis therefore a private good to each and every donor. Since the transfers are aprivate good, it follows that the donors’ demand curves have to be summed

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Figure 1.

horizontally, yielding the aggregate demand curvePh D. Under McKenzie’s

specific scenario the total level of transfers can be read off the point at whichthe 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 beundesirable. This follows from the simple proposition that collectivizationmay provide information about the extent of poverty relief made by each andevery donor. Each donor can adjust the amount he gives as he can consumethe poverty relief offered by the other donor. Despite the potential problemof arriving at just what will be the level of transfers under some politicalinstitution, McKenzie asserts the level of transfers will be reduced to thelevel which is consistent with a Pareto optimal level of poverty relief. Col-lectivization is undesirable here, not because it fails to provide the optimalquantity, but because it results in a reduction in the level of transfers to R.Collectivization of charity therefore represents a Pareto inferior movement asthe recipient will end up receiving less transfers and, according to McKenzie,will be worse off. McKenzie thereby presents a case in which the governmentfails.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 argu-ment. First, McKenzie analysis contains, despite his objective to expose thehidden assumptions underlying the traditional analysis, a hidden assumptionof its own. In his introductory remarks, McKenzie (1981: 337) claims thathe will show that “: : : non-collective provision of a public goodmay (myemphasis) at times lead toover-consumption and production and that, there-fore, collectivization of the provision can lead to a reduction in the amountof the public good available”. What is not clear from McKenzie’s discussionis the reason for his equivocation; there is simply no discussion why he waswilling to suggest only that collectivization might result in fewer transfers.From his discussion, one is left to draw the conclusion that his equivocalresult depends on whether or not the hidden knowledge assumption holds.For example, suppose that only one of the two donors is aware of the trans-fers 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 otherdonor. Here, collectivization would involve an increase in the level of trans-fers going to the recipient as the Pareto optimal amount involves an increasein the degree of giving, X� is greater than X2. If, however, both donors areunaware of the transfers made by the other, then, as McKenzie’s analysissuggests, collectivization here will result in less rather than more transfers.This interpretation is certainly consistent with the tenor of his discussionin which he notes that the donors and the recipient may undertake steps tohide the transfers. Whether or not collectivization results in fewer transferswould appear to rest therefore on how many individual donors and recipientsundertake some measure to be secretive and the extent to which they aresuccessful.

This interpretation is, however, misleading. Even if McKenzie’s assumptionstrictly holds – that there is universal ignorance on the part of the donors ofthe level of giving – whether collectivization results in fewer or more transfersdepends on the relationship between the aggregate demand curves,

PV D andPh D, and the marginal cost of poverty relief. If, for example, the value ofmarginal cost is raised to MCj, then collectivization will result inmorenotlesstransfers than the private charity market, i.e., X1is greater than X0.4 McKenziecase against collectivization of charity, which is based on the notion that themarket outcome involves relatively more rather than less transfers, appearsto rest on a hidden assumption about the relationship between the aggregatedemand curves and the marginal cost curve.

Second, even if collectivization results in a reduction in the level of povertyrelief, there is no reason to follow McKenzie in his belief that the reduction inpoverty 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 gooddeal of social discomfort at having to rely on the hand-outs of the donors andthat this discomfort rises as the degree of poverty relief increases. In terms ofthe geometrical framework here, this effect can be depicted straightforwardly.In the absence of any discomfort the most the recipient would be willing topay for a dollar transfer is a dollar. If the initial marginal cost curve measuresthe cost of transferring a dollar, then the recipient’s demand curve would becoincident with the cost curve. Now introduce a recipient’s demand curve forpoverty relief, such as DmR, which captures indirectly the social discomfort ofreceiving charity. The vertical difference between that demand curve and Dm

Rreflects the marginal discomfort the recipient incurs from receiving hand-outs.In this case, McKenzie seems to be correct in suggesting that collectivizationwill make the recipient worse off. A reduction in transfers would seem toinvolve a loss of surplus as measured by area AX�Xm.

It is by no means clear, however, that the recipient’sbehavioralresponseshould be assumed to be invariant across differing institutional settings.Although the individual may suffer discomfort from accepting the hand-outsof the relatively well-to-do, there is no reason to believe that the recipient willsimilarly express discomfort when the government is directly responsible forpoverty relief. The change in attitude is captured by the following conversa-tion between two poor individuals: “Well, I’m glad that the government hastaken on its social responsibility of looking after us poor”. “I agree”, as theother fellow nodded approvingly, “I had fought in the war when the countryneeded me and now I’m getting what I deserve. It was downright degradingto have to depend on hand-outs from the well-heeled but now I can hold mehead up with some pride”. In this event, although collectivization may resultin a reduction in the level of poverty relief, the individuals can be neverthe-less better off! Suppose the recipient’s demand curve under the governmentscenario is coincident with the marginal cost curve, MC, indicating that hesuffers no discomfort from receiving charity from the government but givenby Dm

R under the private charity market. In this case the recipient is betteroff under public charity despite the reduction in the level of transfers. Thegain from avoiding the social discomfort experienced underprivate charityoutweighs the loss arising from the reduction in poverty relief, FEA is largerthan AX�XM.

Suppose the amendments just made to McKenzie’s model are put to oneside: that we obey his seemingly hidden assumption that the recipient’s pref-erences are invariant across institutions and that the recipient’s demand curveis 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

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in a Pareto inferior change. The reduction in the level of poverty relief willmake 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 unanimoussupport for collectivization. It is possible to find a collective program thatcould secure the approval of all. This might seem an odd claim. After all,McKenzie’s argument appears to rest on the proposition that collectivizationwill involve a movement from one Pareto optimal outcome to another. Thisline of reasoning follows from the observation that when the preferences ofthe recipient are included with those of the donors, the Pareto optimal setcoincides with the points on the marginal cost curve from point E onwards.Accordingly, it does not appear to be the case that collectivization couldwin unanimous support as collectivization will involve a movement from onePareto optimal position to another and will therefore invariably make someoneworse off in the process. The argument is, however, seriously misleadingbecause it fails to take account of the change in technologies associated withthe movement to collectivization.

Under the private charity market a transfer by any particular donor to therecipient is effectively a private good. For epistemological reasons, a transferdoes not yield utility to any other donor. The movement to collectivizationbrings about a radical change in the degree of information about the levelof transfers made to the recipient. Collectivization involves a change froma private to a public goods technology. The change in technology providesthe opportunity for a Pareto-superior move.5 Consider, for example, a poten-tial collective program in which the recipient is made no worse-off but thedonors are made better off. The rectangular hyperbola r, describes all thecombinations of transfers which would maintain the recipient’s income at thelevel XM. If each donor, for example, agrees to be taxed an amount equal toarea OX3PT, then the total amount to be distributed to R is represented byarea OX3WV [=2(OX3PT)]. Since this amount falls on the rectangular hyper-bola the recipient’s income can be maintained at XM which means that therecipient is neither better nor worse off than under the private charity market.Under this alternative arrangement to the one presumed by McKenzie, eachof 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 collec-tivization can be Pareto undesirable has caused him to overlook the point thathis discussion of the potential change in technology contained the seeds of anovel defence of collectivization.

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4. Conclusions

In the analysis I have been obedient to McKenzie’s framework that govern-ment 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 thepreferred institutional setting. But that would move us to another story andtoo far afield from the conventional framework McKenzie used to criticizeFriedman’s argument. The objective here has been the more limited one ofdemonstrating that one significant aspect of McKenzie’s case against collec-tivization of charity is not well taken: a fall in the level of transfers going tothe recipient does not necessarily imply that the poor will be worse off. Indoing so, some unfamiliar arguments about the potential role of governmentwith respect to charitable giving have been unearthed. In particular, it raisesa warning about pushing too far the point that private markets always makethe best use of the knowledge of particular circumstances of time and place.Government provision can have a potential advantage over the market in thatthe very public nature of government activity can allow a dollar of transfers tobe simultaneously and equally consumed by all. In doing so collectivizationcan represent a Pareto superior policy.

Notes

1. In his note, McKenzie raises two hidden assumptions that are alleged to weaken the thrustof 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 knowledgeassumption that is relevant to Friedman’s case for collectivization of charity. Perhaps aword or two of explanation is warranted on why I have chosen to put aside his discussion ofthe possibility of negative marginal evaluations. McKenzie views that one of the strengthsof his argument is to demonstrate that some people’s demands can “: : : extend downwardinto the negative quadrant or originate in the negative quadrant” (1981: 343) and that thelack of any analysis of this possibility represents a hidden assumption of the traditionalpublic 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 publicgood may be an economic bad to some individuals is part and parcel of the orthodoxtreatment of public goods theory. The possibility of negative marginal evaluation wasrecognized, at least in the modern treatment of public expenditure, as long ago as 1955when Samuelson [1973 (1955): 192, footnote 1] in his second paper on public goodsnoted that if “: : : one man’s circus is another man’s poison: : : ” the indifference curvesbetween a private and public good will take on a positive slope. Indeed, the possibility thata public good could be a bad to some individuals was fully incorporated into the publicgoods orthodoxy by giving it recognition in terms of the non-rejectability or impossibilityof rejection characteristic (see, for example, Shoup, 1969: 93-94). McKenzie’s claim thatsome individuals could have a negative marginal evaluation for a public good is thereforepart of the public good orthodoxy.

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

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evaluation for transfer, viz “: : : we mightall of us be willing to contribute to the relief ofpoverty: : : ” (Friedman, 1962: 191, my emphasis). Manifestly, Friedman is not guilty ofmaking ahiddenassumption about whether or not some of the donors’ evaluations extendto 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 berelevant to some orthodox analyses of redistribution, it is not germane to the orthodoxy asput forward by Friedman. The knowledge assumption does appear, however, to representa hidden assumption of Friedman analysis and therefore I restrict my discussion to thatassumption.

2. McKenzie’s Figure l 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 identicalpreference for transfers. Nothing of substance is lost in the simplified figure constructedhere.

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 hisargument there is no majoritarian exploitation of a minority nor is there any manipulationof the majority at the hands of an agenda setter. Either line of argument would point tothe possibility that there will be a divergence between the Pareto optimal outcome andthe majority rule equilibrium. In stark contrast to this general line of argument, McKenziepresumes that the government program will provide an amount of poverty relief consistentwith the Samuelsonion optimal amount of the public good. McKenzie case against gov-ernment intervention into the charity market appears to rest on the claim that there couldnot 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 theirintersection point, then the private charity market equilibrium can coincide with the Paretooptimal outcome under collectivization.

5. It is, of course, true that information on the level of transfers made to R is a two-edgedsword. The public nature of information enables each of the donors to free-ride on thecontributions of the others. This free-riding may well mean that the level of transfers willfall short of the amount required for the Pareto-desirable move. In this regard it is worthrecalling that McKenzie’s discussion is predicated on the assumption that collectivizationdoes not involve government failure in the standard sense.

References

Brennan, G. (1976). The distributional implications of public goods.Econometrica44: 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 Choice36: 337–344.Samuelson, P.A. [1973 (1955)]. Diagrammatic exposition of a theory of public expenditure.

Review of Economics and Statistics37: 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.