A Rational Theory of the Size of Government

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Carnegie Mellon University

Research Showcase

Tepper School of Business

10-1-1981

A Rational Teory of the Size of GovernmentAllan H. MeltzerCarnegie Mellon University, [email protected]

Sco F. RichardCarnegie Mellon University

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Recommended CitationMeltzer, Allan H. and Richard, Sco F., "A Rational eory of the Size of Government" (1981). Tepper School of Business. Paper 750.hp://repository.cmu.edu/tepper/750
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G R A D U A T E S C H O O LO F I N D U S T R I A L A D M I N I S T R A T I O NWILLIAM LARIMER MELLON, FOUNDER

REPRINT NO. 974

A Rational Theoryof the Size of Governmentb y

Allan H. Meltzer and Scott F. Richard

1981

Carneg ie-Mel Ion UniversityPITTSBURGH, PENNSYLVANIA 15213


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Graduate School of Industrial AdministrationWilliam Larimer Mellon, FounderCarnegie-Mellon UniversityPittsburgh, Pennsylvania 15213

SOME CURRENT REPRINTS845. Sequ ential Investment Decisions with Bayesian Learning. R. M. Cyert, M. H. DeGroot,and C. A. Holt.846. The Manage ment of Universities of Constant or Decreasing Size. Richard M. Cyert.847. An Arbitrage Mo del of the Term Structure of Interest Rates. Scott F. Richard.849. Toward an Optimal Design of a Network Database from Relational Descriptions. Pra-buddha De, William D. Haseman, and Charles H. Kriebel.850. Effects of Group Size, Problem Difficulty, and Sex on Group Performance and MemberReactions. Robert M. Bray, Norbert L. Kerr, and Robert S. Atkin.851. On a Class of Least-Element Complem entarity Problems. Jong-Shi Pang.852. Bivalent Programming by Implicit Enumeration. Egon Balas.853. Te mporary Taxes as Macro-Economic Stabilizers. W alter Dolde.854. A New Charac terization of Real H-M atrices with Positive Diagonals. Jong-Shi Pang.855. What Computers Mean for Man and Society. Herbert A. Simon.856. How American Executives Disagree About the Risks of Investing in Eastern Europe. IonAmariuta, David P. Rutenberg, and Richard Staelin.857. A Generalized Capital Asset Pricing Model. Scott F. Richard.858. On the Solution of Some (Parametric) Linear Complementarity Problems with Applica-tions to Portfolio Selection, Structural Engineering and Actuarial Graduation. J. S. P ang,I. Kaneko, and W. P. Hallman859. Leniency, Learning, and Evaluations. John Palmer, Geoffrey Carliner, and Th omasRomer.860. Facets of One-Dimensional and Multi-Dimensional Knapsack Polytopes. Egon Balas.861. Report of the Session on Branch and Bound/Implicit Enumeration. Egon Balas and M.Guignard.863. Price Change Expectations and the Phillips Curve. Timothy W. M cGuire.864. On Estimating the Effects of Controls. Timothy W. McGu ire.866. A Bilinear-Quadratic Differential Game in Advertising. K. Deal, S. P. Sethi, and G. LThompson.867. The Relationship Between Relative Prices and the General Price Level: A SuggestedInterpretation. Alex Cukierman.868. Judgment Based Marketing Decision Models: An Experimental Investigation of the Deci-sion Calculus Approach. Dipankar Chakravarti, Andrew Mitchell, and Richard Staelin.869. Heterogeneous Inflationary Expectations, Fisher's Theory of Interest and the AllocativeEfficiency of the Bond Market. Alex Cukierman.870. Product Reliability and Marke t Structure. Dennis Epple and Artur Raviv.872. The Redistributive Effects of Inflation and of the Introduction of a Real Tax System in theU. S. Bond Market. Assa Birati and Alex Cukierman.873. A Comparison of Rates of Return to Social Security Retirees Under Wage and PriceIndexing. Robert S. Kaplan.874. Epidemiology, Causality, and Public Policy. Lester B. Lave and Eugene P. Seskin.875. A Dynamic Dominant Firm Model of Industry Structure. Finn Kydland.876. Expectations and Money in a Dynamic Exchange Model. Milton Harris.877. Bayesian Estimation and Optimal Designs in Partially Accelerated Life Testing. MorrisDeGroot and Prem K. Goel.878. On the Monetary Analysis of Exchange Rates. A Comm ent. Robert J. Hodrick.879. The Elusive Median Voter. Thomas Romer and Howard Rosenthal.881. Institutionalization of Planned Organizational Change. Paul S. Goodman, Max Bazermanand Edward Conlon.884. Rational Expectations and the Role of Monetary Policy. A Generalization. Alex Cuk ier-man. (continued on inside back cover)


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A Rational Theory of the Size of Government

Allan H. Meitzer and Scott F. RichardCarnegie-Mellon University

In a general equilibrium model of a labor economy, the size ofgovernme nt, m easured by the share of income redistributedTs^ de-termined by majority rule. Voters rationally anticipate the liincen-t h e , a b 0 r - | e i s u r e of their feHowcitizens and take the effec t into account when voting. Th e share ofearned income redistributed depends on the voting fule and on thedm nb uao n of productivity in the economy. Under m^ority n Zequilibrium tax share balances the budget and pays for he voters'choices. The principal reasons for increased size of government

position of the f t h e f r a " c h i - ^ a f chaTge t h eposition of the decisive voter m the income distribution and c h a n g e sn r e , a t l v e p d d v k y A n ^ j n m e a n i n c o m e ^ d v e to fheincome of the decisive voter increases the size of government

I. Introduction

u m ! T b u t ' t h T h a l l O C u t e d b y g V e r n m e n t d i f f e r s fr^ cou ntry tocountry, but the share has increased in all countries of westernEurop e and Nor th Amer ica du r in g the pas t 25 yea rs N u t r SIn the United States, in Britain, and perhap s elsewhe re the rise n t Spaymen t s r e l a t ive to income has pe r s i s t ed fo r more thanTcen tu(Peacock and W iseman 1961; Meltzer an d Richard 1978) Th er e is as

forWL any S S d t S S S ^ ^ i * - " * a n dEconomics Workshop^n anoiwnous referee die rlTt "f T ^ ^ " 0 " P u b , i cfor constructive comments o n T ' r l f c r v ^ ^ ^ I n t e r ' a k e n S e m i n a rt ^ t E c m r * , 9 8 1 ' ">' 89. no. 5) 1981 by The University of Chicago. 0022-3808/81/8905-0008*01.50

9 1 4


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SIZE OF GOVERNMENT 9 1 5yet, no generally accepted explanation of the increase and no singleaccepted measure of the size of government.In this pape r, the bu dget is balanced.1 We use the share of incomeredistributed by gover nm ent, in cash and in services, as ou r mea sureof the relative size of government and develop a theory in which thegovernment's share is set by the rational choices of utility-maximizingindividuals who are fully informed about the state of the economy

and the consequences of taxation and income redistribution. 2/ i Z ^ i SS U eS W C a d d r e s s h a v e a l o n g intellectual history. Wicksell(1958) join ed the the ory of taxation to the theo ry of individual choiceHis conclusion, that individual maximization requires governmentspending and taxes to be set by unanimous consent, reflects theabsence of a mechanism for grouping individual choices to reach acollective decision. Following Downs (1957), economists turned theirattention to the determination of an equilibrium choice of publicgoods, redistribution, and other outcomes under voting rules that donot require unanimity.Several recent surveys of the voluminous literature on the size orgrowth of government are now available (see Brunner 1978; Peacocko l m 3

Ax ?

n S

n/ ?

d

r d e s h o o k 1 9 8 0= and Larkey, Stolp, and Winer1980). Many of the hypothes es advan ced in this literatu re em phasizethe incentives for bureaucrats, politicians, and interest groups toincrease their incomes and power by increasing spending and thecontrol of resources or rely on specific institutional details of thebudget, taxing, and legislative processes. Although such studies con-tribute to an understanding of the processes by which part icularprog ram s are chosen, they often neglect general equil ibrium aspects.Ot part icular importance is the frequent fai lure to close many of themodels by balancing the budget in real terms and considering theeffect on voters of the taxes that pay for spendin g and redistribution(see, e .g., Olson 1965; Niskanen 1971; and Hayek 1979). A recentempirical study by Cameron (1978) suggests that decisions about thesize of the budget are not the result of "fiscal illusion," so the neglectot budget balance cannot be dismissed readily.We differ from much of the recent l i terature in three main ways.

' Al l variables are real . There i s no inflation. Budget balance means that redisrrih, ,don uses real resources. Publ ic good s are neglected red.stn bu-r e n i t ^ * ^ ^ d e n i m p o s e d ( o r


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6 JOURN AL OF POLITICAL ECONOMYFirst, voters do not suffer from "fiscal illusion" and are not myopic.They know that the government must extract resources to pay forredistribution. Second, we concentrate on the demand for redistri-bution and neglect any "public goods" provided by government (seealso Peltzman 1979). Third, we return to the earl ier tradit ion ot deTocqueville ([1835] 1965) who associated the size of government,measured by taxes and spending, with two factors: the spread ofthe franchise and the distribution of wealth (property).4Ou r hypothesis implies that the size of governm ent de pend s on th erelation of mean income to the income of the decisive voter. Withuniversal suffr age and majori ty rule, the m edian voter is the decisivevoter as shown by Roberts (1977) in an extension of the well-knownwork of Hotelling (1929) and Downs (1957). Studies of the distribu-tion of income show that the distribution is skewed to the right, so themean income l ies above the median income. Any voting rule thatconcentrates votes below the mean provides an incentive for redis-tribution of income financed by (net) taxes on incomes that are (rela-tively) high. Extensions of the franchise to include more voters belowme an income increase votes for redistribution a nd, thus, increase thisme asur e of the size of gover nm ent. ,

The problem with this version of the de Tocqueville hypothesis isthat i t explains too muc h. No thing l imits the am oun t of re distributionor prevents the decisive voter from equalizing incomes or, at aminimum, el iminating any difference between his disposable incomeand the disposable income of those who earn higher incomes. Incen-t ives have been ignored. Higher taxes and redistribution reduce theincentive to work and thereby lower earned income. Once we takeaccount of incentives, there is a limit to the size of government. Tobring together the effect of incentives, the desire for redistributionand the absence of fiscal illusion or myopia, we develop a generalequil ibrium model. , . . ,Section II sets out a stat ic model. Individuals who di ffe r m prod uc-t ivity and th ere for e in earn ed income, choose their prefe rre d combi-nation of consumption and leisure. Not all individuals work, but thosewho do pay a port ion of their income in taxes. The choice betweenlabor and leisure, and the amount of earned income and taxes, de-pend on the tax rate and on the size of transfer payments.The tax rate and the amount of income redistributed depend onthe voting rule and the distribution of income. Section III shows howincome redistribution, taxes, and the size of the government budget

* We are indeb ted to Larkey et a l . (1980), for poin un g out the s imi la nty^ betw eerdeToca uevi l le and the conclusion we reach ed in an earl ier version and n Meltzer andR i X r d ( 197s" D e Tocquevi l le ' s distr ibution of property f inds an ech o m the concern sabout "mob rule" by the wri ters of the Consutution.


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SIZE OF GOVERNMENT 9*9 9*7cha nge with the voting rule and t he dis tr ibution of productivity Aconclusion summarizes the f indings and main implications.II . The Econom ic EnvironmentTh e economy we consider has re la tively s tandard fea tures . The re area large number of individuals . Each treats prices , wages, and tax ratesas givens, determined in the markets for goods and labor and by thepolitical process, respectively. Dif fere nce s in the choice of labo r lei-

C n s U m P t i o n a n d differences in wages arise solely becauseot d i f ferences m end owm ents which ref lect d i f ferences in p roduc-tivity. In this section, we extend this s tandard model to capture thesalient features of the process by which individuals choose to work orsubsis t on welfare payments and show the conditions under whichthese choices are uniquely determined by the tax rateThe util i ty function is assumed to be a s tr ictly concave function,u(c, I), for consumption , c , and le isure , I. Consumption and le isureare normal goods, and the marginal uti l i ty of consumption or lei-sure is infinite when the level of consumption or leisure is zero, re-spectively. There is no capital and no uncertainty.The individual 's endowment consis ts of abili ty to produce, or pro-ductivity, and a unit of time that he allocates to labor, n, or leisure / =1 - n. Individual incomes reflect the differences in individual pro-ductivity and the use of a common, constant-returns-to-scale technol-ogy to produce consumption goods. An individual with productivity *earns pre tax income, y: F y

y (p c)=xn(x) . ( j )Income is measured in uni ts of consumption .

Ta x revenu es f inance lum p-sum redis tr ib ution of r units of con-sumption per capita. Individual productivity cannot be observed di-recdy, so taxes are levied against ear ned inc ome. Th e tax rate, is ar t l ^ r i ; f C a r n e d i n / 0 r n e b u t a d e c l i n i n S f r aion of d ispos-J l l l c o I I i e - a ne traction of income paid in taxes net of transfershowever, nses with income. There is no saving; consumption equals '

5 e l ' a n C r n a K n e a r f o l l o w s a wel l -establ ished tradition. Romer (1975) analv^i ^ l S n H S S U S i " g 3 ' l n T ^ P - d e t e n n i n e dRoberts (1977), us ing a l inear tax and a pred eterm ined b udget, showe d that the m edianv o ter do mi na te s the so lut i o n if inco mes a re o rdered by pr ldA ct i v ky l i ne a r uT fU nc_ , j , , 2 ) ' 7 1 1 6 degree to which actual taxes di ffer from l inear taxes hasgener ated a large hterature. Pechma n and Okn er (1974) f ind that the t S rateTs anpro x ,ma te y c o n st a n t. K i g ( 1 9 8 0) w r it es t h at m o s t U i s t r i b u l n T n t h e ^ n i e d s J s "a nd the U mted Ki ng do m co mes fro m the tra ns fer sy s tem, no t fro m t h e ^ sv stemmrdeoegndnieJavHnSOn ^ ^ ^ about p r op o r no n^ f taxes y n a S S u m P t , o n s u s e d t o a^ate the burden of indirect business


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8 JOUR NAL OF POLITICAL ECONOMYdisposable income as shown in (2):

c(x ) = (1 - t)nx +r , c 0. (2)If there are individuals without any ability to produce, x = 0, theirconsum ption is r 3s 0.Each individual is a price taker in the labor market, takes t and r asgivens, and chooses n to maximize uti l ity. T he maximization problemis: m ax u(c, I) = m ax u[r + nx( 1 - t), 1 - ]. (3) [ 0 , 1 ] n e [ 0 , l ]The first-order condit ion,

0 = JO- = uj[r + we(l - t), 1 - n]x (l - t)dn (4)- u{r + ruc(l - t), 1 - n],

determines the optimal labor choice, n[r, x(l - t)], for those whochoose to work. The choice depends only on^the size of the welfarepaym ent, r, and the after- tax wage, x(l - i )-6Some people subsist on welfare payments. From (4) we know thatthe productivity level at which n = 0 is the optimal choice is = . (5)Mc(r, 1)(1 - t)

Individuals with productivity below x 0 subsist on welfare paymentsand choose not to work; n = 0 for x x0.Increases in redistribution increase consumption. For those whosubsist on welfare, c = r, so dcldr = 1. Th ose who work mu st considernot only the direct effect on consumption but also the et tect otredistribution on their labor-leisure choice. The assump tion that con-sumption is a normal good means that dcldr > 0. Differe ntiat ing (4)and using the second-order condit ion, D < 0, in footnote 6 restrictsM cl-

dc = urlx( 1 ~ t) ~ Ug > Q (6)dr ~DConsumption increases with r for both workers and nonworkers pro-vided consumption is a normal good.The posit ive response of c to r takes one step toward establishingcondit ions under which we find a unique value of r that determines

By assu mp tion , i s str ictly concave so the s e c o n d - o r d e r co ndi uo n i s neg a t i v e a nd(4 ) de f i nes a ma x i mum. The seco nd-o rder co ndi t i o n i s c^ / dn - D - u cj (I t)2 u d x ( l - t) + u < 0.


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SIZE OF GOV ER N M EN T 9 * 9the amount of earned income and amount of redistribution for eachtax rate. The next step is to show that normali ty of consumption issufficient to establish that earned income (income before taxes) in-creases with productivity.Pretax income is

y(r, t, x) = xn[r, x(l - *)] ( 7 )

People who do not work, x ^ x0, have y = 0 and dy/dx = 0. For allothers,= X ox

The first-order condition (eq. [4]) yieldsdn _ u c( 1 - t) + uccnx { 1 - t)2 - ucln{ 1 - t)~dx~ ~ -D (9)

The sign of dn/dx is indeterminate; as productivity increases, thesupply of labor can be backward bending . Pretax income, = nx , doesnot decline, however, even if n falls. Substituting (9) into (8) andrearranging terms shows that the bracketed term in (10) is thenumerator of dc/dr in (6). Hence, dy/dx is positive for all x > x0provided that consumption is a normal good:fly M l " 0 * + n[uclx(l - t) - uu] ^ Q ^dx D

The final step in establishing that there is a unique equilibriumsolution for any tax rate uses our assu mption that leisure is a n orm algood. The government budget is balanced and al l governmentspending is for redistribution of income. If per capita income is y,thenty=r. . (11)

LetFO) denote the distribution function for individual productivity,so thatF(jc) is the frac tion of the po pula tion w ith productivity less thanx. Per capita income is obtained by integrating:

J XQn[r, (1 -t)xW{x). (12)>Equation (12) shows that per capita income, and therefore totalearn ed incom e, is determ ined once we know x0, t, and r. From (5), weknow thatx 0 depen ds only on t and r, and fro m (11) we know that , forany tax rate, there is at least one value of r that balances the budget. 7

7 The left s ide of (11) i s nonnegative and is a continuous function of r tha t i s bo unde dby ix, w here x i s the average of x.


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9 2 0 JOURN AL OF POLITICAL ECONOMYIf leisure is a norm al go od, th e value of r tha t satisfies (11) fo r each t isunique. 8

O n c e r or t i s chosen , the o ther i s de term ined . Th e indiv idual 'schoices of consumption and the dis tr ibution of his t ime between laborand leisure are determined also. The choice of r or t uniquely deter -mines each individual 's welfare and sets the s ize of government.

III. Th e Size of Govern mentThe polit ical process determines the share of national income taxedand redis tr ibuted. The many ways to make this choice range fromdicta torsh ip to unanimous consent , and each produces a d i f feren toutcome. We call each polit ical process that determines the tax rate avoting rule.In this section, we consider any voting rule that allows a decisiveindividual to choose the tax rate. Two examples are dictatorship anduniversal suf fra ge with majority rule. A dictator is con cern ed abou tthe effe ct of his decis ions on the p opula tion's decis ions to work andconsume, but he alone makes the decis ion about the tax rate. Undermajority rule, the voter with median income is decis ive as we showbelow. We then show that changes in the voting rules and changes in

productivity change the tax rate and the s ize of government.T he decis ive voter chooses the tax rate tha t maximizes his uti l i ty. Inmaking his choice, he is aware that his choice affects everyone'sdecis ion to work and consume. Increases in the tax rate have twoeffects . Each dollar of ear ned inc ome raises m ore rev enu e but ear ne dincome declines; everyone chooses more leisure, and more peoplechoose to subsis t on redis tr ibution. "High" and "low" tax rates haveoppo site effects on the choice of labor or leisure and, th ere for e, onearned income.Formally, the individual is constrained to f ind a tax rate that bal-ances the government budget, equation (11), and maximizes uti l i tysubject to his own bud ge t constraint, equatio n (3). T he f irst-ordercondition for the decis ive voter is solved to f ind his pre fe rre d tax r ate:

wh ere is the incom e of the decis ive voter .8 The normal i ty of le i sure means that 61/dr > 0 and, theref ore , dn/dr = -dl/dr


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SIZE OF GOVERNMENT 9 2 1Roberts (1977) showed that if the ordering of individual incomes isindependent of the choice of r and t, individual choice of the tax rateis inversely ordered by income. This implies that with universal suf-frage the voter with median income is decisive, and the higher one'sincome, the lower the preferred tax rate. By making the addit ionalassumption that consumption is a normal good, we have shown thatincomes are ordered by productivity for al l r and t. CombiningRob erts s lemm a 1 (1977, p. 334) with ou r results, we can or de r thechoice of tax rate by the productivity of the decisive voter Thehighe r an individual 's productivity, the lower is his prefe rre d tax ra teFigu re 1 illustrates the pro position and shows the effe ct on the taxrate of changing the voting rule. The negatively sloped line is therelation between individual productivity, *, and the individual's pre-ferred tax rate. This l ine need not be l inear.

Th e maximum tax ra te , tma x, is chosen if the decisive voter does notwork . An exa mp le is * = In this case, * *0; the decisive voterconsumes only r, so he chooses the tax rate (max) that maximizes r.Any higher tax rate reduces aggrega te earne d income, tax collectionsand the am ount available for redistribution. From equation (5), we seethat the maximum tax rate must be less than t = 1As productivity rises fr om * to the tax rate declines fr om W tou . At * d - x, the decisive voter is end ow ed with average produc tivityand cannot gain from lump-sum redistribution, so he votes for noredis tnbu uon by choosing t = 0." From equation (5) and uc(0, ) = 00we see that everyone works when r = 0. If the decisive voter's produc-tivity exceeds x, t and r remain at zero and aggregate earned incomeremains at society 's maximum.Changes in the voting rule that spread the franchise up or down theproductivity distribution change the decisive voter and raise or lowerdie tax rate. Our hypothesis implies that changing the position of thedecisive voter m the distribution of productivity changes the size ofgovernment provided * 0 < * d < Major changes in have occurre din two ways. Wealth and income requirements for voting were re-duced o r el iminated, gradually broade ning the franc hise and lower-ing the incom e of the decisive voter. Social security retire m ent systemsgrew m most countries after the franchise was extended. By increas-

9 The formal statement of the resul t i s: Consider any two pairs (r L) a nd (r t \ lit


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12 JO U R N A L O F P O LI TI C A L EC O N O M Y

FIG . 1ing the number of retired persons, social security systems increase thenumber of voters who favor increased redistribution financed bytaxes on wages. Some of the ret ired who favor redistribution alsofavor low taxes on capital , property, and the income from capital .T he size of gover nm ent chang es also if there are changes in relat iveincome, as shown by equation (13), or relat ive producuv,^ Conclu-sions about the precise effect of changes of this kind are difficult todraw We cannot observe productivity directly and can only in terchanges in the distribution of productivity, F(-), by observing chang esin relat ive income. Recent l i terature makes clear that these effects aredisp uted (see Sahota 1978; King 1980; and others ). Fu rth er wecanno t deduc e the e ffect of changes in productivity on t directly fr omequation (13). T he reason is that y depends on t, so finding the eltectof changes in relative productivity requires the solution to a nonlinearequa tion in Inste ad, we rew rite (13) in a fo rm which involves the(partial) elasticities of pe r capita inco me (y) with respec t to re distrib u-tion (r) and th e wage rate (x[l - 0).

L e t T = x _ t b e the fraction of earned income retained. From (1 T) '


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S I ZE O F G O V E R N M E N T 9 2 3where m is the rat io of mean income to the income of the decisivevoter, y/yd, and the v's are partial elasticities. Using the commoneconomic assumption that the elasticities are constant, the tax raterises as mean income rises relative to the income of the decisive voterand taxes fall as m falls:dt = v(y, t)[1 - r)(y, r)]

dm [m - 1 + f,{y, r) + m,7)(y, r ) ] 2 > ( J 6 )Relaxing the assumption of constant elasticities weakens the conclu-sion, but we expect the sign of (16) to remain positive provided thechange in the elasticities is small.One of the oldest and most frequently tested explanations of thegrowth of government is known as Wagner's law. This law has beeninterpreted in two ways. The tradit ional interpretat ion is that gov-ern m ent is a luxury go od so that the re is a posit ive relat ion between

A . N t \ S 1 Z e f S v e r n m e n t a n d the level of real incom e. Recently/1 no n questioned this interpretat ion of Wagner's idea. Alt(1980, p. 4) notes that Wagner argued that there is "a proportionbetween public expenditure and national income which may not beperm anently overstep ped." T his suggests an equil ibrium relative sizeof gove rnm ent rath er than an ever-growing gove rnm ent sector.The t radi t ional s ta tement of Wagner 's law-that governmentgrows m ore rapid ly than income-has been tes ted many t imes, butwith mixed results. Peacock and Wiseman (1961), Cameron (1978),^ ? a L d980) discuss these tests. Our hypothesis suggesti iat the resuks are ambiguous because Wagner's law is incomplete.The effect of absolute income on the size of government is condi-tional on relative income. Average or absolute income affects theelasticities m equation (15), and the relative income effect is given by

vo l r T f 6 U r hyPthesis testable, we must identify the decisivef Z ' J ! f P h C a b , e V O t m S m l e i n t h e U n ed States is universal

r m a J m y r U l e" U n d C T t h i s r u l e> t h e ^ t e r w i th med ianncom e is decisive in single-issue elections, as we argu ed above. He ncethe median voter is decisive in elections to choose the tax rate, soZtme ratio or mean to median income. 11

i n l ^ i ^ n r r l t r T t h ^ r HS analyses arem ed ia n a nd a ny o t h e r T a c t i l T r f I ^ tests dG n o t discriminate between the

assum ptio n o n distribu tion o f ' a b i l i t y - v i n d ^ X e ^ d i T v o t e r T u ^ " ^ 5 ^


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14 J O U R N A L O F P O L I T I C A L E C O N O M Y

IV. ConclusionGovernment spending and taxes have grown re la t ive to output inmost countries with elected governments for the past 30 years orlonger. Increased relative s ize of government appears to be inde-pen den t of budg et and tax systems, federa l or nat ional go vernments ,the s ize of the bureaucracy , a nd o ther f req uent ly ment io ned ins ti tu -t ional ar rangem ents , a l tho ugh th e re lat ive ra tes of change in d i f f eren tcountr ies may depend on these ar rangements .Our explanation of the s ize of government emphasizes voter de-mand for red is t r ibu t ion . Us ing a pars imonious , genera l equi l ibr iummodel in which the only government activit ies are redis tr ibution andtaxat ion , the rea l budget i s ba lanced , and voters are fu l ly informed,we show that the s ize of gove rnm ent is det erm ine d by the weltare-maximizing choice of a decis ive individual. The decis ive individualmay be a d ic ta tor , absolu te mon arch , or ma rginal mem ber of a jun ta .With major i ty ru le the voter wi th median income among the en-

f r a n c h i s e d citizens is decisive. Voters with inco me below the in com e ofthe decis ive voter choose candid ates who favo r high er taxes and mo reredis tr ibution; voters with income above the d e c i s i v e voter desirelower taxes and less redis tr ibution. The decis ive voter chooses the taxshare. When the mean income rises relative to the income of thedecis ive voter , taxes r ise, and vice versa. The spread of the franchisein the n ineteenth and twent ie th centur ies increased the number o tvoters with relatively low income. The position of the decis ive votershif ted down the dis tr ibution of income, so tax rates rose. In recentvears the pro por tion of voters receiving social security has increased ,rais ing the number of voters favoring taxes on wage and salary in-come to f inance red is t r ibu t ion . A ra t ional socia l secur ity re a pi e nt w ihlarge prop erty incom e suppor ts taxes on labor incom e to f inanceredis t r ibu t ion but opposes taxes on income f rom proper tyIn> ouranalysis , the re is neith er capital nor taxes on prop erty, so the increasein social security recipients has an e ffec t s imilar to an exte nsion of the^ Ou rTs sum ptio n that vo ters are fu lly infor me d about the s ize ofgovernm ent d i f fers f ro m much recent l i te ra ture . Th ere , taxpayersare por t rayed as the prey sought by many predators who conspire tor a i s e taxes relative to income by diffu sin g costs and conc entrat ingbenefits or in other ways (Buchanan and Tullock 1962; Olson 1965;Niskanen 1971; Hayek 1979). We acknowledge that voters are . linformed about the costs of particular projects when, as is often thecase, i t is rational to avoid learni ng details . Kno wledg e of detail is norequired to learn that the s ize of government has increased and thattaxes have increased relative to output or income. Long ago it becamerational for voters to anticipate this outcome of the polit ical process .


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S I Z E O F G O V E R N M E N T9 2 5Wagner's law, relat ing taxation to income, has generated a lame

^ g n e r 1

s k i L " i n d i S 5 / b r r v e d e C O n m i C g r O W t h r a i s e s t h e k e r n e s ofskilled individuals relative to the incom es of the un skilled. In this waveconomic growth can lead to rising inequality and , if our h y p o t h e l kcorrect to votes for redistribution. Th e rising r e l i v e s L e o i g o v e r nment slows when the relat ive changes come to an end and reveries i ithe relat ive changes reverse in a mature stat ionary economyThe distinctive feature of our analysis is not the voting rule but therelation between individual and collective choice, l a c h person

Anvon6: w h o S U m P i , 0 n ^ ^ b y ^ ^ the usual wayAnyone who works receives a wage equal to his marginal productTaxe s on labor income provide revenues for redistribudon however

f r m d e d S i 0 n S t 0 ^ - - a cosM vhenThe analysis explains why the size of government and the tax rate

c T t i z e T i h ^ * o ve rw he lm in g m ^ i t y ofp r e f " ' a d ! f i e a T " ^ 3 1 ^ u r n neariy everyoneprefers a different outcome. If unconstrained by the voting rule

To pursue these questions more fully and to analyze an y effect of

- - VReferences^ I S ^ S T S ^ P Ub HC E X p e n d l t U r e " MulfHthed. St. Louis:A G r w " h oPf G ^ e ^ e ^ t d T t i / r ' V ^ Theories of theSpending ^'m ' t s - " ^ u k i t k h e d P k t s b u r ^


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1 6 J O U R N A L O F P O L I T I C A L E C O N O M YB r o w n i n g , E d g a r K a n d J o h n s o n , W i l l i a m R ^ ^ - of the Tax

Bur J . G o v e r n m e n t : T h eSchweizerische Zeitschrift Volkunrtschaft

und Statis 1 1 4 (Septernbe^ m S ) : 6 4 9 - 8 0 ^ ^ C o n j w , . L o g l c a lB u c h a n a n , J a m e s M . , a n d IUUOCK, 1 J n i v M i c h i g a n P r e s s ,Foundations of Constitutional Democracy. A n n A r b o r . U n i v. Mien g^ 1 9 6 2 ' n * v i d " T h e E x p a n s i o n o f t h e P u b l i c E c o n o m y : A C o m p a r a t i v e

K L n for

Downs,CAnSiony^n Theory of Democracy. New Y ork: Ha rper 8: Row,H a v ' c k , F r i e d r i c h A . t a . L e g i s l a t i o n V o l . 3 , ^ O r ^ / H ^ a S ! " ' *King~Mervyn A -How ^ ^ ^ J ^ V S t ^Distr ibut ion of Income and Weal tn ."K u z S , Simon. I * G row * and I n e ^ y . "

( M a r c h 1 9 5 5 ) : 1 - 2 8 . T W n r i y i n f f a b o u t t h e G r o w t h a n d

M e W ^ S a l S , SCO F . " W h y G o v e r n m e n t G r o w s ( a n dS s ) in a P ^ ^ p 3 ^ j " A ^ S u r w y J ^ Litlraturl 14 ( J u n eM u e l l e r , D e n n i s C . " P u b li c C h o i c e . A s u r v e y , j

M u s g r a v e ! ^ R i c h a r d A . The Theory of Public Fir^ce: Study in Public Economy.^ ^ W m T Z ' ^ ^ y a n * R e p r e s e n t Government. C h ic a g o :N u t t e d G ^ W a r re n '. GroL of Government in the West. W a s h i n g t o n : A m e r i c a n

lT L0g ic of Collective Action: Public Goods and the Theory of

P^^^^^^^^^^ 111 ^ Experuiiture in the

S Z L ^ g Z r a n d ^ n i ; 5 3 S ^ * ^ "M U l t a i t h e d " C h i C a g : U n i V '

a n d O r d e s h o o k , P e t e r C. An Induction to Positive PoliticalThe'Z E n g l e w o o d C l i f f s , N . J , P r e n U c e - H a U , ^ Publk Econ. 8R o b e r t s , K e v i n W . S . " V o t i n g o v e r I n c o m e T a x S c h e d u l e s , j( D e c e m b e r 1 9 7 7 ) : 3 2 9 - 4 0 . M a i n r i t v V o t i n g , a n d t h e P r o p e r t i e s o f


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S I Z E O F G O V E R N M E N T 9 2 7Rmer, Thomas, and Rosenthal, Howard. "The Elusive Median Voter " /Public Econ. 12 (October 1979): 143-70.Sahota, Gian Singh. "Theories of Personal Income Distribution: A Survey " JEcon. Literature 16 (March 1978): 1-55.Sheshinski, Eytan. "The Optimal Linear Income Tax." Rev. Econ. Studies 39(July 1972): 297-302.de Tocqueville, Alexis. Democracy in America. 1835. Reprint ed. O xford* Ox-ford Univ. Press, 1965.Wickseil, Knut. "A New Principle of Jus t T axation." R eprinted in Classics inthe Theory of Public Finance, edited by Richard A. Musgrave and Alan TPeacock. New York: St. Martin's, 1958.


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885. Optimal Incentive Contracts with Imperfect Information. Milton Harris and Artur Raviv.886. On the Use of Facet Analysis in Organizational Behavior Research: Some ConceptualConsiderations and an Exam ple. Zur Shapira and Eli Zevulun.887. Writer-Based Prose: A Cognitive Basis for Problems in Writing. Linda Flower.888. Issues and Models in Empirical Research on Aggregate Consumer Expenditure. WalterDolde.889. Rational Decision Making in Business Organizations. Herbert A. Simon.890. Optimal Contracts and Competitive Markets with Costly State Verification. Robert M.Townsend.891. Towards a Better Microeconomic Theo ry. Richard M. Cyert and Qarrel Pottinger.892. The Effects of Rate-of-Return Regulation on the Intensity of Use and Durability of C apital.Dennis Epple and Allan Zelenitz.893. Comparison of Experiments and Information Measures. Prem K. Goel and Morris H.DeGroot.894. Capital Allocation Within a Firm. R. M. Cyert, M. H. DeGroot, and C. A. Holt.895. T he Information Content of Discounts and Premiums on Closed-End Fund Shares. RexThompson.896. Developing a Financial Planning Model for an Analytical Review: A Feasibility Study.Robert S. Kaplan.897. Evaluating the Quality of Information Systems. Charles H. Kriebel.898. Strengthening Cuts for Mixed Integer Programs. Egon Balas and Robert G. Jeroslow.899. Dynamic Optimal Taxation, Rational Expectations and Optimal Control. Finn E. Kydlandand Edward C. Prescott.900. The Effects of Uncertainty on Investment Under Risk Neutrality with Endogenous Infor-mation. Alex Cukierman.901. Cutting Planes from Conditional Bounds: A New Approach to Set Covering. Egon Balas.902. Set Covering Algorithms Using Cutting Planes, Heuristics, and Subgradient O ptimization:

A Computational Study. Egon Balas and Andrew Ho.903. Stein's Paradox and Audit Sampling. Yuji Ijiri and Robert A. Leitch.904. Political Resource Allocation, Controlled Agendas, and the Status Quo. Thomas Romerand Howard Rosenthal.905. A New and Efficient Algorithm for a Class of Portfolio Selection Problems. Jong-Shi Pang.907. Recursive Competitive Equilibrium: The Case of Homogeneous Households. Edward C.Prescott and Rajnish Me hra.909 . D iscussion. Sc ott F. Richard .910. Comments on Externalities and Financial Reporting. Stanley Baiman.911. The Cognition of Discovery: Defining a Rhetorical Problem. Linda Flower and John R.Hayes.912. Four Essays on Procedural Rationality in Economics. Herbert A. Simon.913. Pivot and Complement A Heuristic for 0-1 Programming. Egon Balas and Clarence H.Martin.914. Organization Capital. Edward C. Prescott and Michael Visscher.915. Recovery Rate and Cash Flow Accounting. Yuji Ijiri.916. Turnpike Horizons for Production Planning. Gerald L. Thompson and Suresh P. Sethi.917. An Economics Approach to Modeling the Productivity of Computer Systems. Charles H.Kriebel and Artur Raviv.918. Adjacent Vertices of the All 0-1 Programming Polytope. Egon Balas and Manfred W.Padberg.920. Estimation of the Correlation Coefficient from a Broken Random Sam ple. Morris H.DeGroot and Prem K. Goel.922. A Parametric Linear Complementarity Technique for Optimal Portfolio Selection with aRisk-free Asset. Jong-Shi Pang.923. An Algorithm for Large Zero-One Knapsack Problems. Egon Balas and Eitan Zemel.924. A Parametric Linear Complementarity Technique for the Computation of EquilibriumPrices in a Single Commodity Spatial Model. Jong-Shi Pang and Patrick S. C. Lee.925. Should Accounting Standards be Set in the Public or Private Sector? Robert S. Kaplan.926. A Competitive Theory of Fluctuations and the Feasibility and Desirability of StabilizationPolicy. Finn Kydland and Edward C. Prescott.

(continued on back cover)


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mmm

The present series contains articles written by the faculty of the Graduate Schoolof Industrial Administration. Publications began In the 1962-03 academic yearand continue through to date. You may request copies and receive them from:Reprint Secretary, GSIA, Carnegie-Mellon University, Pittsburgh, Penna. 15213.

927. Models of Money with Spatially Separated Agents. Robert M. Townsend.928. The Limitations of Log-Linear Analysis. Howard Rosenthal.929. Dynamic Effects of Government Policies in an Open Economy. Robert J. Hodrick.930. A Cost Operator Approach to Multistage Location-Allocation. Robert V. Nagelhout andGerald L. Thompson.931. An Activity Analysis Approach to Unit Costing with Multiple Interactive Products. Hiro-yuki Itami and Robert S. Kaplan.932. A Dimension of the Myths and Science of Accounting. Robert S. Kaplan.933. Discrete Programming. Set Covering with Cutting Planes from Conditional Bounds. Egon 'Bales.934. An Equivalence Between Two Algorithms for Quadratic Programming. Jong-Shi Pang.935. Multiple-Object, Discriminatory Auctions with Bidding Constraints: A Game-TheoreticAnalysis. Thomas R. Palfrey.936. A Latent Time Series Model of the Cyclical Behavior of Interest Rates. Kenneth J.Singleton.937. Maturity-Specific Disturbances and the Term Structure of Interest Rates. Kenneth J.Singleton.938. On Parsimonious Explanations of Production Relations. Herbert A. Simon.939. Stagflation, Persistent Unemployment and the Permanence of Economic Shocks. KarlBrunner, Alex Cukierman, an d Allan H. Meltzer.940. An Aversion to Positive Risks and Preference for Negative Risks. Benjamin Eden.941. Property Tax Consciousness. Peter C. Ordeshook.942. Vote Trading: An Experimental Study. Richard D. McKelvey and Peter C. Ordeshook.943. Political Disequilibrium and Scientific Inquiry: A Comment on William Riker's "Implica-tions from the Disequilibrium of Majority Rule for the Study of Institutions." Peter C.Ordeshook.944. Differential Inflationary Expectations and the Variability of the Rate of Inflation: Theoryand Evidence. Alex Cukierman and Paul Wach tel.945. Expectations Models of the Term Structure and Implied Variance Bounds. Kenneth J.Singleton.946. Realities of Improving the Quality of Work Life. Quality of Work Life Projects in the1980s. Paul S. Goodman.947. Optimal Challenges for Selection. Morris H. DeGroot and Joseph B. Kadane.948. An Introduction to Corporate Accounting Standards: A Review. Yuji Ijiri.952. Some n by dn Linear Complementarity Problems. Ikuyo Kaneko and Jong-Shi Pang.957. Database Location in Computer Networks. Marshall L. Fisher and Dorit S. Hochbaum.960. Rate of Return Indexes for GNMA Securities. Kenneth B. Dunn and John J. McConnell.961. Only Normal Distributions Have Linear Posterior Expectations in Linear Regression.Prem K. Goel and Morris H. DeGroot.963. The Strategic Petroleum Reserve: How Large Should It Be? Egon Bales.964. Rates of Return on GNMA Securities: The Cost of Mortgage Funds. Kenneth B. Dunn 'and John J. McConnell.966. Forward Algorithms for Forward-Thinking Managers. Thomas E. Morton.969. information About Hyperparameters in Hierarchical Models. Prem K. Goel and Morris H.DeGroot.970. Helium: Investments in the Future. Dennis Epple and Lester Lave.

Management information Systems: Progress and Perspectives (Carnegie Press, 1971).Editors: C. H. Kriebel, R. L. Van Horn, and J. T. Heames. Price: $11.50.The Employment Game . . . Where Do You Fit? C. Douglas Mlntmier, GSIA. Price: $5.95

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