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