THE JOURNAL OF POLITICAL ECONOMY Volume LXX JUNE 1962 Number 3 THE INCIDENCE OF THE CORPORATION INCOME TAX I.INTRODUCTION and the other each em- s paper aims to provide a theo- retical framework for the analysis of the effects of the corporation in- is vic ome tax the strikesthe a come tax and,also,to draw some infer- ings of capital in but not in the no corporate Both industries are assumed to be c ramifica- homogeneous of the first degre (em in genera bodying constant returns to scale).We qu nan partial- do not inquire into the short-run effects of tham of the imposition of the corporation tax, retical e main aracter ramework ti on the supposition that it is the long-run effects which are of greatest theoretical was inspir ng traditi and practical interest.In the very short Ohlin, the earnings of fixed capital equipment son,Metzl r,and in the affected industry,so long as our are among the most prominent. competitio applies Bu writers inquired into the effects of inter. in the capita marke national trade,or of particular trade poli- ne cies,on relative factor prices and the dis- the net tribution of income.Here we shall ex- amine the effects of the corporation in- the A redis come tax on these same variables. the resour of the Our model divides the economy into my two industries or sectors,one corporate in which the net rates of return to capital 215
216 ARNOLD C HARBERGER are equal in both sectors.In this long-run sources.that variations in the rate of in- equilibrium the wages of labor will also terest within the ranges observed in the be equal in the two sectors,and the avail- United States exert a substantial influ able quantities of labor and capital will be fully employed ence the level of out of any given level of income. We shall therefore I also assume that the available quan proceed on the assumption that the level tities of labor and capital in the economy of the capital stock at any time is the are not affected by the existence of the same in the presence of the tax as it 4tax.This assumption is rather innocuous in the would be in its absence;but in the con of labor,but in the ca uso of this paper we shall briey con sider how the results based on this as. highly likely that as a result of the im- sumption might be altered if in fact the position of the corporation tax.the net corporation income tax has influenced rate of return received by owners of capi-l the total stock of capital. tal will be lower than it would be in the The relevance of this approach for r the abser ce of this tax This eduction in th analysis of real- world night also return to capital can influence savings in be questioned on the ground that the two ways:first,because now the owners economy cannot reasonably be divided of capital have less total income and into a set of industries which are over. second.because the rate of return facing whelmingly “corporate,.” and another them is lower.On the first must bear set which is ove on mind that any alterna e wa o Thi objection has lidity,at raising the same revenue would entail the least in the case of the United States. In same reduction in income in the private the period 1953-55,for example,the sector;the impact on saving of the corpo- total return to capital in the private sec- ration tax would thus differ from that. tor of the United States economy aver e tax yieldin ag me $60 billion pe yea $34 bil same revenue,only as a result of suc being corporate profits an differences as may exist among economic lion being other return to capital.Of the groups in their savings propensities.On $26 billion which was not corporate the second,we must inquire into the profits,more than 80 per cent accrued to elasticity of the supply of savings with two industries- agriculture and real es- rate of inter If this in which the In all porate pre were neg zero in ligibl but seven industries in a net rate of interest facing savers will not forty-eight-industry classification,cor infuence the size of the capital stock at poration taxes averaged more than 25 any given time or the path along which ber cent of the total return to capital the capital stock grows through time.In and one can,for all practical purp the United states the fraction o of nation- tha dustrie except agriculture alincome saved ha rea sonably real estate and miscellaneous stant,in periods of full employment,for services paid less than 20 per cent of their nearly a century.Over this time span.in- total return to capital in corporation come levels have increased greatly and taxes,while the three named industries interest rates have fluctuated over rather wide ran all paid less than 4 per cent of their in- nge.We have clea from capital corporation taxe dence,from these data or from other Within the “corporate'”sector,different
THE INCIDENCE OF THE CORPORATION INCOME TAX 217 industries paid different fractions of their mand for different kinds of in stments At this pointwe must make clear that the "equalization"which our theory pos. tive use of debt and equity capital,partly tulates is equalization net of such-risk to the presence in some of these indus- premiums.So long as the pattern of risk tries of a fringe of unincorporated enter- differentials is not itself significantly al- tered by the prese nce of the corporati uch as loss. rryovers Irom prior yea ncome failure of full use of crent ossestoob theoretical results will be applicable without modification.And tain tax offsets,and so on.But these dif- even if the pattern of risk premiums ap ferences.in my view. are not large plying to different types of activities and enough to affect seriously the validity of obligations has chand the main distinction made here betweer re ult of the tax,it is highly likely tha the orporate no t uent modincation of our re. sector and sults would be of the second order of The relevance of the approach taken importance. in this paper might also be questioned on the ground that the capital market does II.OUTLINES OF THE INCIDENCE PROB. not in fact work the net rates LEM:THE COBB-DOUGLAS CASE pital different inc So long as the capital market works to this objection is based on the equilibrate rates of return net of taxes idea that the capital market might be and risk premiums,and so long as the poorly organized,or that participants in it might not be very adept at seeking the imposition of a c orporatio in does not itself ave a significant effect on best available net rett on their i the(pattern of)risk premiums associated he United States case.for in the United rejected fo with different types of activities,it is inevitable that in the long run the cor- States the capital market is obviously highly organized,and the bulk of the poratiotax in the pric of the product.That is,of two industries funds involved are commanded by able one people. corporate and one non-corporate and knowledgeable The e using the same combination of may,h wever, be the idea that labor and capital to produce a unit of rates of return in different indu tres,and product,the equilibrium price of the cor perhaps on different types of obligations porate product will be higher than the will differ even in equilibrium because of m price of the the risk premiums which investors de- produ -corporate by prec ely the amount of cor poration tax paid per unit of product Tax:An United Stat This result is taken by some people as evidence that the burden of the corpora- / eans Com tion tax is bo rne by consumers,that is. Office,November,1959) that the tax is shifted forward.Such an rief statement of the problem ofthe nce is far wide of the mark. a(pp 241-43 whic Perhaps the easier way of demonstrat- concerned with the res ing the error of the above inference is to all ather thants the corporation income tax present a simple counterexample.Con- sider an economy producing only two
218 ARNOLD C.HARBERGER products-product X,produced by firms in the corporate form,and product Y, nroduced by unincorporated enterprises. entrepreneurs for labor is also the price Let the demand characteristics of the received by the workers.and since econ equilibrium in the labor market is as sposable income ed the equilibrium ction the labor orce will be the sam tions in both industries be of the Cobb case as in the previous one,that is,300 Douglas type,with coefficients of for workers in each industry. both labo and capital:that is, The situation is different,however where L.and L when we come to capital.The price paid represent ar of labo used in by entrepren eu rs fo capital ultiplie the X and y industries,and K=and K by the amount capital 入 ll again the corresponding amounts of capital be $300 in each industry.But the price The total amounts of labor and capital Daid by entrepreneurs in industry x wil available to the economy are assumed to include the tax,while that paid in indus- respectively Under cor mpe itive con ons,pr t the total am tion in each industry will be carried to dustry will yount in in rece of tax the point where the value of the marginal product of each factor is just equal to the will be getting s300.For eauilibrium in the capital market to obtain,there must s of the in the ab ce of be twice as much capital in industry V axes, we have as in indu as a ult of the tax,the distributior of capital changes the total income the economy 1 instead of having 300 units of capital in S1.200,equally divided between X and each industry,we now have 200 units in Y,then labor in industry X will be earn industry X and 400 units in industry Y. $300,labor in indus try Y $300. Out of the total of s600 which entre in industry $30 an rs are pay r capital in both industry Y $300.It is clear that both the industries,one- will go to pital labor force and the capital stock will industry y.on which no tax will be paid have to be equally divided between in- one-quarter will go to capital in industry dustries X and Y.Choosing our units of x.net of tax.and one-quarter will go to labor a nd c capital so that in this the vernment as a tax payment.The um position P5 =S1.00, we have pric of capital will fall $1.00to the result that without any taxes there 50.75. will be 300 units of labor in industry X A crude calculation suffices to suggest and 300 in industry Y,and that the capi- the resulting tax incidence.out of a na tal stock will be similarly distributed tional income of $1,200,labor obtained Suppose nov w that a tax of 50 nt $600 before the imposition of the tax and is levied on the earnings of capital inin- but capita btained (net of tax) dustry X,and that the government,in only $450 after the tax was impose spending the proceeds of the tax,also against $600 before the tax,the differ divides its expenditures equally between ence of S150 going to the government the two ind ries Labor in industry X Capital is clearly bearing the brunt of
THE INCIDENCE OF THE CORPORATION INCOME TAX 219 the tax,in spite of the fact that in the group lose in income earned an aggregate tax situation.the tax is included in what amount equal to the amount received by consumers are paving for commodity x. the government.This reduction in the Of course,this does not tell the whole inco e from capital is spread over all of the incidence of the tax.Since apital,w employed in industryX of com X rises,and the or in industry Y,as s oon a the capita market is once again brought into equi with particularly strong preferences for librium after imposition of the tax.Inso- one or the other of the two goods will be far as individual consumers have the hurt or benefited in their role as consum- same expenditure pattern as the average ers,in addition to whatever be nefit they of all um ey neither gain no obtain or burden they bear in their role he e as con Insofar as owners of productive factors.It is im- individual consumers diffe Irom portant to realize,however,that the average,they gain if they spend a larger price of y does fall,and that this brings fraction of their budget on y than the to consumers as a group a benefit which ver and lose if they spend a larger counterbalances the burden they bear as fracti of their budge on X than t a result of the rise in the price of y average gains oft cons I would sum up the analysis of the in- who prefer Y,however,are counterbal anced by the losses of those who prefer cidence of the assumed tax on capital in industry X as follows:capitalists as X.If we are prepared to accept this can celing of gains and losses as the basis for The ounterbalancing is not r e owing to sta atement that consumers the fact that the group do not suffer as a consequence of the tax value of the duct of capital in industr then we can conclude that capital bears stry y by the am the tax.Otherwise.we must be content values to be to note that the gross transfers from in dividuals as capitalistsand consumers of exc ed the yield of the tax by an rate of sub mp amount equa to the gross transter to rent fr consumers of y. stitution of The above example is representative e re of the entire class of cases in which ex- penditures are divided among 0 given propo ts a tomary in discu and each good is determined by a C efrects of changes in the ices of x and Yas Douglas function.The exponents of the a ing exac of sum Cobb-Douglas functions can differ from g what happens to the prices industry to industry,and even the tax of the th s of capital can be or in cas taxe which the Pb ices (net of tax)of la. ent in yet the conclusion that capital bears th esult of the tax.it is just as correct to say tax,in the sense indicated above, re. the ta bore by the mains It is easy to demonstrate the tion to their initial contributions to the national truth of the above assertion.Let A:be of such cases are given belo the fra ction of the national income spent
220 arnold c.HarBerger on the product of industry i,B:be the relative prices will,to a first approxima- coeffcient of the labor input in the ith tion.be offset by the losses of those con industry (equal to the fraction of the re- sumers who lose:thus.if we accept this ceipts of the ith industry which is paid of effects as far ages to labor),and C:(=1-B:)be ar the capital input inth as peopl s consum concern ed,we can say that capital bears ith industry (equal to the fraction of the the full burden of the tax. receipts of the ith industry which is paid [gross of tax]to capital).Then 2A B:will THE CASE OF FIXED PROPORTIONS be the fraction of national income IN THE TAXED INDUSTRY to labor both in the the cas in which taxes tax situation andn Returning now to an example in which are absent.Im there are only two industries,let us as- mediately one can conclude that labor's sume that the taxed industry is not char. share in the national income will remain acterized by a Cobb-Douglas production the same in the two cases.Moreover,the function,but instead by a productio distribution of labor among industr functio in which the factors will also uncha strictly nxe indu proportions.Let us retain try employ fraction all of the other assumptions of the pre- A:B:/(ZA B,)of the labor force in both ceding example-that expenditure cases .Likewise,capital will receive a divided equally between the two prod- fixed fraction of the national income ucts,that production in industry v is (gross of tax)equal to A.C When er ned by the tion tax is levied that there are 600 units of each factor, ceive 24.C(1 apital,capital net of tax,and the and that the prices of the two factors are government will receive 2A,Ci,where initially each $1.00.These assumptions determine that the initial.pre-tax eaui. try.Thus capital as a whole librium will be the same as before with will los 300u factor occ apied in each fraction of the national inc industry.The fixed-proportions produc to that garnered by the govern- tion function for industry x which is ment in tax receipts.As in the case pre consistent with these assumptions is sented in the above example,the dis- X=Min (L K) tribution of capital among industries will What happen when a tax of 50 pe change as a result of the im of the tax,the fra 1P03e the i om capl tion of the e tota apita tal in industry X?It is clear that what- ith industry being AC:/(AC ever reduction in output may occur in in the absence the tax and industry X,the two factors of production A C:(1-)/[ZA C:(1-)]in its pres- will be released to industry r in equal ence.Except when the tax rate on income ch industry amounts. indu stry y is alr a0】 from capital is e will be on relative prices, it can absorb increments in these two fac and transfers of income among consum- tors in the same ratio without altering ers,of the same general nature as those the marginal productivity of either factor outlined above for the simpler case.But in physical terms.The price of Y will as before.the gains of those e consumers ha e to fall,h wever in der to who do gain as a result of the changes in create an increased demand for it.Whatever
THE INCIDENCE OF THE CORPORATION INCOME TAX 221 may be this fall in the price of Y,it will to the production of X,with the produc- induce a proportionate fall in the price of tion function for X requiring that labor each of the factors(since their marginal and capital be used in these fixed propor- physical productivities are unchanged). tions,that is,X=Min [(L/2). As. We thus have the result that the e final sume as before that the in itial price equilibrium after the tax,$600 will be labor and capital were $1.00,and that spent on the product of industry Y,with national income remains unchanged at half going to capital and half to labor, $1,200 after the imposition of the tax. and $600 will be spent on the product of Likewise retain the assumption that ex- industry x with s200 going to lab is divided equally betweer $200 to capital (net of tax),ar d$200 pendi goods X and Y. the government.The price of labor will The post-tax equilibrium in this case have fallen from S1.00 to S(5/6).and the will be one in which the price of labor is price of capital will also have fallen from S0.83916,the price of capital $0.91255. $1.00 to $(5/6).The tax will have fallen Industry X will use 171.25 units of capi- pr portion to al and 342.5 units of labor: capital in h onal dustrywill receive a net me c income $156.274,and the government,with a 50 It should be evident that the result per cent tax on the gross earnings of capi just obtained,of labor and capital suffer- tal in industry X,will get an equal ing the same percentage burden,depends nt:labor in industryX will receive critically on the fact that in the example industry $287.412.These three shares in the prod 0 uct of industry x add up (but for a small absorb capital and labor in precisely the rounding error)to $600,the amount as- proportions in which they were ejected sumed to be from industry x without a change in the t on.Industry will relative prices of the two factors.If in- employ328.75(=500 171.25)unit of capital and 357.5 (=700-342.5) X had ejected two units of labor for each unit of capital,while e industry units of labor,and the total receipts of had initially been usingqu quantities each factor in industry will be,as before.S300. of the two factors.the price of labor would have had to fall relative to the Let W be the net earnings of capital in ind price of capital in order to induce the ecessary re.in the crease in the labor to W/(S3 capital in indu Dost-tax case,labor would bear more tax,relative $600is the total amount spent to its share in the national income,than cived by capital inindustr X.labor in x mu capital.The following example will dem- nd an amo onstrate that this is s $300.total labo Supp e that in the initial equilibriu will be 300 units of labor and 300 units of capita W (600 3000 are engaged in the production of Y,and W().(Recall thatm this e that the production function here is,as are my.The production function for before,Y =.Suppose also,how ever,that 400 units of labor and 200 that 2W) /(S900 units of capital were initially dedicated 2W) (700)in the post-tax equilibrium. Solution of thi
222 ARNOLD C.HARBERGER Since the price of capital has gone whole tax regardless of the proportions down from $1.00 to $0.91255,and the in which capital and labor ombined in price of labor has gone down from 100 the two ind we find in the presen to S0.83916,it is clear that is at the relative proportions are of roughly twice as heavily burdened by critical importance.The fact is that once this tax (a tax on the earnings of capital nxed proportions are assumed to prevail in industry x)than is capital each fac- in the taxed industry,it matters little tor's burden being taken relative to its whether the tax is nominally placed on initial share in the natio The the ea more labor-intensive isindu pital in on the e rela ings of labor in X,or on the sales of in- tive to the proportions in which the fac- dustry X.A tax on any of these three tors are initially used in industry y the bases will lead to the ejection of labor and heavier will be the relative burden of the capital from industry X precisely in the tax upon labor For example,if initially industry X had used 500 units of labor If indus in just thes ng the e use and 100 units of capital,while industry proportions,there will be no Y again used 300 of each with the sam change in their relative prices.and thev production function as before, will bear the tax in proportion to their the end result of a tax of 50 per cent of the earn- initial contributions to the national in- ings of capital in industry X would have come.If industry Y is initially more re capi a fall in the price of capital from tal-inten ve than X the pric S1.00 to S0.9775.and in the price of labor must fall relative to that of capital in from S1 to $0.8974.The burden on labor, order to induce the absorption in y of the tactors released by and labor will relative to its initial share in the national income,would be more than five times ational in that on capital.4 com If,on the oth. r hand,in Whereas,in the Cobb-Douglas case ry yi dis -intensive than X,the cussed in Section II,capital bore the tially more labo opposite result will occur,and capital will bear a larger fraction of the tax burden than its initial share in national income. to the tota IV.THE CASE OF FIXED PROPORTIONS units of c In THE UNTAXED INDUSTRY nd2D/900 W)of the labor When production in the taxed indus- employed in e have the we calo ulate the try is governed by a Cobb-Douglas func- th。 yed tion,and fixed proportions prevail in the -00 a total untaxed indu of the ta f th c in I that must be solved has very different n those the case just discussed.Now the normal result is on of these inad- for capital to bear more than the full bur- den of the tax,while labor enjoys an ab- solute increase in its real income.The 2W)1(800).The solution is W=91,K =93.1, Capital in degre e of in in labor' s real incom industr et of ta th depends on the relative factor propor- gets $91,and labor in industry earns $18. tions in the two industries,but the fact
THE INCIDENCE OF THE CORPORATION INCOME TAX 223 that labor will get such an increase is not income of $1,200,the government will dependent on these proportions. get $150,capital will get $350,and labor The reason for this apparently anoma- will get s700.The price of capital will lous result is that,in order for the untaxed fallen from s1.00tos0.5833,ar industry y toabsorbany capital at all from that of labor will have risen from $1.00 the ta ind try,it must als )absorb to $1.1667.Capital will have lost a total some labor,for it uses the two factors in of $250 in income,of which $150 will fixed proportions.However,since in our have gone to the government in taxes example the fraction of national income and $100 will have been gained by labor nsider a cas in which the nce the Cobb-Douglas taxed industry i nore labor-intensive mine that e share of this fraction go than the untaxed industry.Let industry ing to labor is fixed,it follows that any r use twice as manv units of canital as reduction in the amount of labor used in of labor,and let Y's initial levels of factor the taxed industry will carry with it a use be 400 capital and 200 labor, other rise in the wage of labor. 1. the same assump A few e in the amples s of th type pre nted before.In this ase,as a result of a 50 per e preceding sector will serve both to cent tax on the earnings of capital in clarify this general result and to show industry X,the price of capital will fall how the degree of labor's gain depends from $1.00 to $0.677855,and that of on the relative factor proportions in the labor will rise from $1.00 to $1.15100 two industries first that the initial Capital will have lost a total of $225.5 in the fac income,of which $75.5 will have been are the e same in the two in gained by labor 5 dustries.Let the production function for In a more extreme case,let industry Y Xbe=and that for y be use five times as many units of capital as Y=Min (K L),and let there be initially 300 units of each factor in each of labor.and let r'sinitial levels of factor industry earning a pric of$1.00. e be 500 capital and 100 labor,again again let total expenditures be dividec retaining our other umptions.Now equally between the two products.It fol- the price of capital falls from $1.00 to lows that,after a tax of 50 per cent is Let Zstand for the (as yet unknown)total earn imposed on the earnings of capital in in- capital in will be our other a n in the hat earn $150 net of tax labor in X will be 训be ning $150 net of tax. getting $300 Since there are just as many units of labor as of capital in the moun economy,and since industry Y uses one ing ($600 nd labo unit of labor per unit of capital,industry unied in X must,in the final e uilibriur the will be this 4 of lak tsof labor in the total earnings of labor in X inmust be twice the number of must be twice the total after-tax earnings [Z/$150+z17002 of capital in that industry,it follows that turns out to be $324.5 =478.714 ust be twice the this number.Likewis ix $300 divided unit price by 260.643,the number of units of labor in
224 ARNOLD C.HARBERGER $0.774393,and that of labor rises from tity so chosen that their prices are initial- $1.00 to $1.076272.Capital loses a total ly equal to unity.Demand for each prod- of $180.5 in income from the pre-tax to uct will depend on its relative price and the post-tax situation,of which S30.5 is gained by labor.s on the level of income of demanders.The It is clear that the more capital-inten umers will naturally fall sive is the untaxed industry,the less is as a result of the imposition of the tax, and through the consequent restriction the percentage reduction in income that of their demand for goods,command capital must sustain as a result of the over resources will be released to the tax.If the untaxed industry is more nent The ult mate demand posi- w consumers reac capital is made ever off by th to the change in their income and to than in the case of initially equal factor whatever price change takes place,and proportions.Where the untaxed industry on how the government chooses to spend is twice as labor-intensive as the taxed the proceeds of the tax.Assume for the industry.for example.the sake of simplicity that the wa y in which of the tax capital 1 the government would spend the tax pro- ng some $230 ceeds,if the initial prices continued to total income,of which $86 is gained by prevail,would just counterbalance the labor. reductions in private expenditures on the V.A GENERAL MODEL THE INCIDENCE two goods.This ssumption,plus the OF THE CORPORATION TAX additional assumption that redistribu- tions of income among consumers do not Although the examples presented in the three preceding sections give some change the pattern of demand,enable us insight into the nature of the incidence to treat changes in demand as a function problem and into the factors which are of changes in relative prices alone.Since likely to govern the incidence of the cor- full employment is also assumed,the de- poration income tax,they suffe m the mand functions for and yare not in- defect of being b sed on particular re- dependent;once the level of demand for strictive assumptions about the nature X is known,for given prices and full em- of demand and production functions.In ployment income,the level of demand this section I shall present a model of or y can be derived from the available substantially greater generality nformation.We may therefore sum Let there be two cts in the econ marize conditions of demand in our omy,X and y. with their units of quan- model by an equation in which the quar tity of X demanded depends on () Differentiating this function we obtain This assumes that dx =Ed(力/) =E(dpa-dpy) (The ke nis(27/g150 (1) Z)/s900 2)700. (Demand for X), the of the in in the where E is the price elasticity of demand the for X,and where the assumption that which in this case is $500 as against initial prices were unity is used to obtain e equal-proportions case treated earlie the final expression