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Can Tax Cuts Increase Investment in A Unionised Economy?*
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CAN TAX CUTS INCREASE INVESTMENT IN A UNIONISED ECONOMY?'
John Creedy and Ian McDonald University of Melbourne Parkville Victoria 3052
This paper derives conditions for lax cuts to stimulate output without crowding out invesuucnt. In the model the level of output is constrained by an aggregate supply constraint. This constraint is based on the real wage demands of an insider-dominated trade union seeking to maximize its objective function. It is found that, in the model, tax cuts have a powerful supply-side effect and, for reasonable values of the parameters, will not force a crowding-oul of invcsunent. Of the tax cuts considered, raising the income tax threshold has a larger supply side effect than reducing the marginal tax ratc.
I.
INTRODUCTION
The idea of using tax cuts to moderate the wage demands of trade unions was put forward several times in the 1970s and 1980s. Faxtn (1982) has called such a policy 'tax bribery'. However, a policy of tax cuts runs the risk of forcing a reduction in investment spending and thereby reducing future levels of consumption. For example, Weale et al. (1989, pp.14-5) have argued that "[I]t becomes all too easy, even with the most innationary cost-push wage-selting institutions, to combine full employment with uninflated prices by means of lax fiscal policy ... Full employment is achieved by living on capital (eating up the seed com or "selling the family silver") with adverse longer-teon results". This risk is the motivation for this paper. If tax cuts can expand output without forcing a reduction in investment then they can be recommended. If, instead, Lhey force a reduction in investment, then the economy is "living on capital" and the case for tax cuts is weakened. The complexity arises because a tax cut has both a demand and a supply effect. In the early 1980s several papers showed how employment subsidies have hoth a demand and a supply effect; see Layard and Nickell (1980), Oswald (1979) and Sampson (1983). Those papers did not consider. however, Lhe implications of their analysis for aggregate investment. Another literature Concentrates on the effects on investment of trade union responses {Q a
•
This paper was presented in seminars at the AUSlralian National University and the Universities of Melbourne, Monash, Tasmania and Western Australia. We are grateful to participants at these seminars for thcir comments.
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reduction in personal income tax; see Corden and Dixon (1980), Corden (1981), Pitchford (1981), McDonald (1984) and, for a more elemcn'ary exposition, McDonald (1992, Chapter 14). However, these analyses did nol use a mooel of trade union behaviour and assumed instead that real posHax wages are held constant. The present paper has the advantage of examining investment while using a maximising model of the union. The analysis is set up in a way which allows investment to be treated as a residual. The model assumes monelary policy is set at whatever level is necessary to ensure that the actual level of investment is equal to the residually-detennined level. The precise setting of monetary policy would depend on the nature of the mechanism that determines investment, but the paper does not analyse this precise setting of monetary policy. It is simply assumed that the monetary authority can adjust the monetary base to induce a level of investment equal to the residually-determined level. The important point is that it is impossible for monelMy policy 10 induce a level of investment in excess of the residually-determined level; the resources would not be available. The anaJysis concentrates on the largest of Lhe possible outcomes for investment. Tbe effect of a tax change on investment cannot be predicted from qualitative analysis alone. The supply-side effect of the reduction in wage demands, resulting from the tax cut, will lead to an increase in employment and hence aggregate output. The demand-side effect is that aggregate demand will increase as a result of the increase in disposable incomes. If the increase in aggregate supply is large relative to the increase in aggregate demand, then investment will not be crowded out. The size of the supply-side effect depends on the product of three elasticities: the elasticity of output with respect (Q employment, the elasticity of employment with respect to wages, and the elasticity of wages with respect to taxation. The larger any of these elasticities the greater is the supply-side effect. The demand-side effect is influenced by the distribution of income between wages and profits and the pattern of consumer demand. A complete analysis therefore involves many elements. The present treatment is highly aggregative and abstracts from a number of complicating factors in order to clarify the essential features of the process. The nature of the tax system and the way in which unions may respond to tax changes are examined in Section II. The model includes taxes on incomes and profits in addition (0 a consumption tax. The debate has been largely restricted to the case of a reduction in the marginal rate of income tax, but the present paper shows tllat a richer variety of policies can usefully be considered. In particular, it will be seen that raising the income tax threshold bas a stronger supply-side effect than cutting the marginal rate of tax. Aggregate supply and demand are considered in Section III. Section IV solves the model and provides the substalltive results of the paper. The effect on tolal tax revenue is tben examined in Section V. Firsl, however, it is useful to consider the basic analytics of tax cuts in tcnns of the simple IS-LM model.
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1.1 The simple macroeconomics of tax cuts
FIGURE I
Nominal
Interest
Rate (i)
ASCI
i,
Y,
Y,
Real Outpul (Y)
In Figure 1 two IS curves and two aggregate supply constraints are shown. The aggrcgatc supply constraints show the maximum level of output finns are prepared to supply given the wagc demands of trade unions. Suppose that initially the aggregate supply constraint is ASCI and the IS curve is lSI, with the intersection al the point (ii, YI). Assuming the LM curve passes Ihrough this point, the economy achieves OUlput YI; to avoid cluttering the figure, the LM curve is not shown. Suppose that taxation is cut in some way, leading (Q an increase in aggregate demand and a rightward shift in the IS curve to IS2. If the tax cui also reduces the wage rale, then the aggregate supply constraint will also shift to the right as a result of the increased demand for labour; suppose that it shins to ASC2. With an appropriate monetary policy, the equilibrium point (i2, Y2) could be attained without causing excess demand and an upward pressure on the rate of inflation. The figure illustrates a situation in which thc equilibrium level of output has increased and the equilibrium ratc of interest has decreased, implying a highcr level of investment. Thus Figure I shows a case where the
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cut in laxation does nol crowd out investmenl, but instead allows investmerll 10 be increased. The condilion required for the lax cut to increase investmenl is Ihat the rightward shift in the aggregate supply conslraint musl exceed the rightward shift in the IS curve. The shift in the IS curve is lower, the lower is the marginal propensity 10 consume, while the shift in the supply conSLTainl is larger, the larger are the lhree elaSlicities mentioned earlier. The remainder of the paper derives lhe precise conditions for such a favourable result to occur, 2.
TIlE TAX STRUCTURE AND WAGE DEMANDS
2.1 The tax structure The model conlains three lypes of tax; income tax, sales lax'"Md profits tax. Let wand a respeclively denote the pre-tax real wage and the tax threshold, The wage or income tax. is imposed at a single marginal rate, I, on wages measured above the threshold; hence the lax paid per person is equal 10 t(w - a). The analysis absLTacts from the problems raised by the laxalion of inleresl income arising from pasl savings. Any other approach would involve allowance for the workers' saving behaviour and for the possibility of owning shares in finns. This would significalllly complicate the union's decision-making problem. It is assumed Ihal profils are taxed at a constant proportional rale, 'to The specification avoids the difficulty arising from a situation in which profits are taxed once al source and then again when, after being disLTibuled, they are counted as the taxable income of individuals. The dichotomy between wage income and profils will be continued in Section 1lI when consumption behaviour is examined, and in the following subsection. A consumption lax is applied at the proportional rate, v, to the taxexclusive price of goods, The lax-exclusive rate of v translates to a taxinclusive rate of v/(1 + v). The tax-exclusive price is normalised to unity, so that if the consumplion lax is fully shifted to consumers, the price of OUlput becomes I + v. The union's wage d.emand depends on the relation between the post-lax real wage, y, and the pre-tax real wage, w, A pre-tax real wage of w is judged by the union 10 yield an after-tax income for its members of y, where:'.
y=
at + w(l - l) 1+v
(I)
2.2 The insider-dominated union The economy is assumed 10 consist of many idenlical finns, al each of which wages are detennined by bargaining between a union and the finn. The union is dominated by a group of insiders, each member of which is ri~"-neulral, enjoys secure employmenl and seeks to maximize the post-tax real wage, y; see McDonald (1991). The assumption of risk-neutrality is not important for comparative statics, as shown in Creedy and McDonald (1991), If negoliations
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break-dowll and the union strikes, each member enjoys an altemative income of
x. The union is assumed not to include the finn's invesunem programme in its bargaining. Some papers, see Grout (1984) and Ulph and Ulph (1990), have shown, using partial equilibrium analysis of a single finn, Ihat if the union cannol commit ilself to a bargain made before the capital slock is inslalled then Ihe finn will, given the market rate of interesl, choose a capital stock thaI is less 111an the 0plimal level. By contrast Ihe analysis of investment in this paper is at the macroeconomic level; thc markct rale of inlerest is endogenous and will be assumed to adjusI, by the appropriate monetary policy, to induce the level of investment detennined by the analysis. If the union were assumed to be able to commit itself 10 a bargain then the effect on the analysis would be 10 change the equilibrium rate of inlcresl rather than 111e conditions derived for a tax cuI not to crowd out investment. The firm wishes to maximize profits, R(n) - wn, where R(n) is I1le concave revenue function and n is employment at the firm. The outcome of bargaining is the wage and employmenl combination which maximizes: [y-xj$/(I+$) [R(n) - wnjl/(l+$)
(2)
where ¢l measures the power of the union, and may take values between zcro and infinity. Choosing wand n 10 maximize (2) and using (1) 10 define y, gives a bargained wage: w=
x(l + v)
at
h(l - t)
(3 )
where h depends on the union's power parameter ¢l and the elasticity of OUlput with respect ~o employment, {x, and is given by: h= 1 +$ (I-l/a).
(4)
Given that a < I, it follows mat h < 1. As can be seen from (3), as h approaches zero the wage becomes infinilely large, so that for sensible results h must be greater than zero. This constraint jointly places an upper limil on ¢l and a lower lLmit on (X, 2,3 Tax changes and wage demands
Suppose the government decides 10 'give' a particular absolUle amount to each employed person in the form of a cut in personal income tax, based on the wage ruling before the policy change. This reduction may be achieved by reducing the marginal ralc of income lax, t, or by raising tile tax-free threshold,
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a. For example, a cut in tax of $1 per person can be achieved by reducing the marginal rate by an absolute amount l/(w-a) or by increasing the threshold by III. Differentiating (3) with respect 10 t and a respectively gives: aw = hw-a and aw = _"_'_ at h(I -I) aa h(I -t)
(5)
Thus, an increase in the threshold that cuts lax per person by lhe same amount as a one percentage poinl reduclion in t will reduce the wage demand by (wa)/(h(l-t)}. This exceeds lhe reduction in the wage demand that would occur as a result of a one percentage point reduction in I, so it is necessary to consider separately the effects of reducing t and raising a. Convert (5) into an elaslicity, so that:
c=.!.aw=_'_(l_J!...) w a, 1- t hw
(6)
As mentioned in the introduction, this elasticity is one component of the change in aggregate supply resulting from the change in t. If instead of maximising the objective function (2) the union aims simply to keep y constant as t changes, then the elasticity of wages with respect to the marginal rale of income tax is given by:
c=-' 1 - t (l-~) w
(7)
The only difference between (6) and (7) is the term h, which from (4) depends on 0. and 4>. As 0. approaches 1 or 4> approaches zero, h approaches unity and there is no difference between (6) and (7). Thus the previous literature is equivalent to the union model if either a = 0 (income tax is directly proportional) or if the demand for labour is perfectly elastic or if the union has no power. . A crucial assumption in considering the effect of tax changes is that the alternative income, x, is not affected by the tax change and is independent of the wage rate. For the insider-dominated unions examined here, McDonald (forthcoming) has argued that Ihis assumption is reasonable. However, it is harder to justify for the other union models in which the unemployed (that is outsiders) receive an equal weighting with the employed insiders in the union's objective function.
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AGGREGATE SUPPLY AND DEMAND
3.1 Aggregate supply Assume that the value of ex is COOSlanl, so that the good is produced under
conditions described by the following aggregate Cobb-Douglas production funclion, for a given input of capital: Y=AN
a
(8)
where Y is the real (tax-exclusive) value of aUlpUl and N is the aggregate level of employment. In insider-dominated bargains, each of the identical finns sets employment such that the wage equals Ule marginal revenue product of labour and so !.he aggregate level of employment is determined by: N = (w/aA)I/(a·1)
(9)
Substituting for N, from (9), into the production function (8) gives the
aggregate supply in tenns of the real wage as: Y = A(w/aA)a/(a-l)
(10)
Furthennore, substituting the value of w determined by the insider-dominated bargains, given by (3), gives the aggregate supply constraint, as:
al] a/(a-I)
'(1+V) Y=A [ aAh(1-I)
(II)
3.2 Aggregate demand Consumption, like output, is measured in tenns of its real tax-exclusive value. The approach allows for the possibility that the propensity to save from wage income differs from that of profits, but in each case consumption is proportional to real disposable income. If the marginal propensity to consume is y, aggregatc consumption from wage incomc is yNy. Although unions are not directly concerned with unemployment, it is necessary to allow for unemployment in detennining aggregate demand and tax revenue. If M is the total labour supply, and b the tax-exclusive level of unemployment benefits, then the aggregate value of benefits is b(M-N). It is reasonable to assume that all this income is spent on consumption goods. In the insider-dominated union model, wage and employment outcomes are on the labour demand curve. Given these outcomes, price-taking firms and the Cobb·Douglas production function, the share of wages in aggregate output is
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equal to the elasticity of output with respect to labour input, 0.. Then real after. tax profits, 1t, are given by 1t =
Y(l - T)(I - 0:)/(1 + v)
If the marginal and average propensity to consume out of profits is consumption demand, C, is
C
= yNy + ~1t
+ b(M-N)
( 12)
p,
total
(13)
Using 0: = wN/Y and equations (3), (4) and (12), (13) can be written as: C
= eY + bM
!ill.:!.) { Y+ h(yat-b(l+V»} + ~(I-o:)(I-T) h werec= I+v x(l+v)-at (1 +v)
(14) (15)
If the consumption functions contained constant terms, they would simply be added to (14) and would drop out when differentiating with respect to the tax parameters. Thus the assumption of proportionality does not affect Ule results of the paper.
4.
TAX CHANGES AND INVESTMENT
4.1 The determination of investment
In equilibrium aggregate demand is equal to aggregate supply given by (11), Aggregate demand is C+1+0, with consumption determined by (14). If government spending is exogenous, this leaves the level of investment as a residual as discussed in the introduction; it is equal to the output remaining after consumption and govemmem demand have been met. By combining (11) and (14) with the condition that aggregate demand is equal to aggregate supply, invcsunent is given by 1= (l-e)Y - bM - G
(16)
As already suggested. this really determines the maximum level of invesunent. A contractionary monetary policy could reduce investment below the level given by (16), in which case output would be demand-determined because the aggregate supply constraint would not be binding. An expansionary monetary policy cannot increase investment above the level giyen by (16); any attempt to increase investment above this level will lead to inflation, The effect on the maximum level of invesunent of a change in any of the tax paramclCrs can be determined by the appropriate differentiation of (16).
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This is the focus of the analysis in the remainder of the paper. 'The simplest tax parameter to deal with is the rate of profits tax, t. Since aggregate supply is not affected by t, but a reduction in the tax rate will stimulate demand, a cut in t will necessarily lead to a reduction in investment. The eXLra demand for consumption can only be met by reducing the amount of the good that is devoted to invesunent. This result is confmned from (16), since (17)
Differentiation of (16) with respect to the other tax parameters is rather awkward so, as a preliminary exercise, the following subsection focusses on a special case. 4.2 A special case
Consider a special case in which income tax is proportional to income, so that a == 0; the income tax and profits tax rates are equal, so that t == t; and LIle average propensily to consume out of wages is equal to the average propensity to consume out of profits, so that 'Y = ~. This is a useful reference point as these assumptions have usually been made in the earlier literature. Then (16) becomes:
t = (l-e)Y - bM-G
- = J!.:!2.. (I+v) {y-nhb/x}
with c
(18)
( 19)
Differentiation of (18) with respect to t yields, after some manipulation:
at = c-n Y at (I-I)(I-n)
(20)
A cut in the ratc of income tax increases invesunent if the numerator on the right hand side of (20) is negative. This reduces LO the following:
at at
-< 0 I'f ex >
h$+yx b(I+$)+(I+v)x/(I-I)
(21 )
This condition may be interpreted in terms of a m,inimum value of a. and a maximum value of the response of consumption to a rise in pre-tax income. A high ex implies a large response of aggregate supply to a tax cut, which reduces the pressure on resources available for invesunent following a tax cut. A small propensity to consume and large values of the income Lax raLe and the
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consumption lax rale imply a small increase in aggregate demand following a tax cut which, again, reduces the pressure on resources. If (18) is differentiated with respect to the consumption tax rate, v, it can be found Lhat precisely Ole same condWon as Lhat given in (21) also holds. This arises because when the threshold, a, is zero, both the income tax and the consumption tax are directly proportional. Furthennore, the simple assumption that the union seeks only to maintain the real value of the after-tax wage, makes no difference in this special case. The basic reason for this is given in Section 11, where the elasticity, C, in formulae (6) and (7) was seen to be identical when a = O. Suppose now that the threshold is still zero, but that t :#. t and 'Y '# p. Substitution into (15) and (16) and differentiation with respect to t yields the result timt a cut in the marginal rate of income tax increases investment if: (I) 'Y + (1)0 a...0(1 -t ) - $b(l-l) >·t -t P xa
-
b(l+$l(I-t) x
-
(1 +v)
(22)
Changing t now only influences demand through its effecl on disposable wage income. In the previous case where t=t, changing t changed the rate of tax from both profits and wages. Because of this difference (22) does not reduce to (21) simply by substitution of t=t and r=~. 4.3 The general case
Returning to the general case, differentiation of (16) with respect to t yields, after some manipulation: al_ y [ ah{yat-b(l+v)} ~ a(l-l)ba(xy-b) a(I-C)(X(I+V)-a}] at (l+v){x(l+v)-at) + I+v - {x(l+v)-at}2 - (l-a)(I-t){x(l+v)-at)
(23) For the tax cut to increase investment, the term in square brackets in (23) must be negative. In view of the awkwardness of this expression it is useful to examine some orders of magnitude involved. A realistic value for the propensity to consume out of disposable labour income, 'Y, is 0.8. Because of the retention of profits by corporations, the propensity to consume out of POSI-tax profits, ~, is much less; a value of 0.4 seems reasonable. A realistic value of bla, is 1, so that a suitable value of x/a is 2. For $, the union power parameter, the value of 0.5 was chosen. With , equal to 0.5, the insider-dominated union model gives a reasonable value for the bargained wage, given reasonable values of the other parameters (using equation (3». The critical value that (X has to cxceed for a cut in t to stimulate investment is inversely related to the threc lax rates, t, t and v. For example if v is 0.05 and t and t arc 0.125 men a has to exceed 0.4017 for allat < O.
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Raising both t and '[ to 0.2 reduces the critical minimum value of n 10 0.3655. If the consumption tax rate v is raised 100.1, then with t = '[ = 0.2, the critical minimum value of n is 0.3438. The higher are the rates of lax, the smaller the demand effect of a lax cut and so the smaller the supply effect needs to be to allow an increase in investment. The condilion on n is sensitive 10 x/a. Reducing unemployment benefils or raising the incomc tax threshold tcnds to raise the critical minimum value of n. For example, with t = t = 0.2 and v = 0.05, setting b/a = 0.5 and x/a = 1 yields a critical minimum value of n of 0.7128. The impact on the aggregate level of investment of a cut in the consumption lax rale can be determined by differentiating (16) with respect to v. This operation yields: ~ = V[Il
dv
(1+>)2
(1+V)2{x(l+V)-atJ
(I+V)2
(I+>j{x(I+,)-atJ2
a(l-c)x ] (I-aj{ x( 1+,)-at I
(24)
Numerical analysis of (24) reveals that the critical minimum value that a must exceed for a cut in the consumption tax rate to allow invesunent to increase is fairly insensitive to the parameters of the tax system. With y = 0.8, P = 0.4, b/a = 1, x/a = 2, 1= t = 0.125, v =0.05 and $ = 0.5 the crilical minimum value of cr. is 0.410 1. Raising t and t 10 0.2 reduces cr., as expected, but only to 0.3742. Wilh t ='[ = 0.2, a value of 0.1 for v reduces a to 0.3603. And reducing b/a to 0.5 and xla to 1 yields a critical minimum value of a of 0.3541 (with t =t = 0.2 and v = 0.05). In considering these values it should be borne in mind that the elasticity, a, also directly affects the distributive shares. Hence in practice the share of wages is higher than the critical minimum values obtained. Finally for increases in the income tax threshold differentiate (16) with respect to a. This yields:
ill. _ IV[ aa -
ap-c) ah(J-l)(XX-b)] (J-a){x(l+v)-al) - {x(l+v)-atj2
(25)
For each set of values used in the previous two cases, the expression in square brackets in (25) is positive for ail values of n between zero and one. So for the reasonable values of the parameters assumed here, an increase in the income tax threshold always allows an increase in the aggregate level of invesunent. An increase in the income tax threshold is more likely to allow an increase in the aggregate level of investment than would a reduction in the marginal rate of income tax or the rate of consumption tax because it has a greater effeci on the bargained wage. The greater wage effect is a result of the differential impact on the bargained wage of changes in the average ratc of tax compared with changes in the marginal rate of tax. As explained in Crcedy and McDonald (1992, p.49), a reduction in the average rate of tax holding the marginal rate of
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tax constant, will, by making employment more altractive, reduce the bargained wage whilst a reduction in the marginal rate of tax holding the average rale of tax constant will, by making wage increases more attractive, increase the bargained wage. An increase in the income lax threshold reduces the average rale of tax but not the marginal rale whilsl a decrease in t or v is a decrease in bOUI the average rate of tax and the marginal rate of tax. Thus a decrease in t or v leads 10 two offsening influences 011 the wage. The net downward effecl on the bargained wage is small, and may even increase the bargained wage. A smaller reduction in Ule bargained wage implies a smaller increase in Ihe level of aggregate supply and so less likelihood that investment may be allowed to increase. 5.
5.1
TOTAL TAX REVENUE
Total net revenue
The total revenue raised from wages is the sum of income tax and the consumplion tax, and is: N{'(w-a)+vyy}.
(26)
Revenue from profits is the sum of the profits tax and the tax on consumption out of profits and is: t(Y - wN) + vp"
(27)
Appropriate substitution into (26) and (27), with much manipulation, gives total revenue from wages and profits, R, as: R = {ex'(I+V) + exvy(I-t) + vlJ(l-ex)(l-t) + a,exh(l-t) (vr-(I+V)) + t(l-ex)] (l+v) x(l+v)-a, I+v
(28) The term in square brackets may thus be regarded as the overall proportional tax rate. To calculate the net revenue, unemployment benefits should be deducted from (28), remembering that benefits have been defined exclusive of laxation. Hence it is nol necessary to allow for the consumption lax revenue arising from the expenditure of benefits. As (M·N) people receive unemployment benefits of b then nCI revenue, Rn• is
,
R =R-b(M-N) n
(29)
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5.2 The special case Consider again the special case obtained by assuming a = 0, y = ~ and I = t. Then net revenue is R = Y{t + vy(1-t)/(1 + v») - b(M - N) n
(30)
The tenn in curly brackets has a slraightforward interpretation. It is the sum of the income lax rale and the effective consumption tax rate. The effective consumption tax rate is quite different from v because, for each dollar earned, only y(l - l) is spent and the consumption tax rate applied to the tax inclusive price of goods is v/(l + v). Assuming thai Y is determined by the aggregate supply conSlraint, the impact on nel revenue of a cut in the marginal rale of income tax is given by the derivative of (30). It is:
(31 ) A sufficient condition for net revenue to increase with a cut in the tax rate is that the tenn in the square brackets must be negative. A sufricient condition for this to hold is t > (l - ex). So if I is greater than (l . a.) there is a 'Laffer' effect, whereby decreases in tax rates increase net tax revenue and vice versa. The necessary condition for tax cuts to increase revenue can be derived from (31) by using (3) and (9) to detennine aN/at. Some manipulation yields:
aR n _ Y[I _1_ (--'!.:L + -.!!L + ah(b/X»)] a, - (I-a) (I+v) (l-,) (I+v)
(32)
If the term in square brackets is negative then tax cuts raise revenue. A policy of cuts in rates of tax that simultaneously raises investment and net revenue, while also reducing inOation, is of course unequivocably favourable. However, suppose there is a conflict such that tax cuts will raise investment but reduce net revenue? It is certainly possible for such a contlict to arise. For example, for the set of values y = 0.8, ~ = 0.4, ,= 0.125, v = 0.05, a ::: 0.6, 41 ::: 0.5 and xlb = 2, a cui in t will increase investment, from condition (23), and will reduce net revenue, by equation (32). In the event of a conflict between investment and net revenue it is necessary to consider expliCitly the costs of increasing the debt in relation to the benefits of higher investment. This is outside the scope of the present paper.
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I 6.
CONCLUSIONS
This paper has examined a model in which lax cuts may have a powerful supply side effect. Indeed for reasonable values of the parameters the supply side effect is larger than the stimulus, given by the lax CUIS, to aggregate demand, so thai tax cuts would not force a crowding-oul of invcsunenl. II was found that a policy of tax cuts is more likely to be effective in reducing wage demands and increasing investment if the tax cuts arc achieved by raising the lhreshold, rather than by reducing the marginal rate of income tax or the ratc of consumption tax. Thus, of the two ways of reducing taxes, the policy that increases the progressivily of the lax system has a greater supply side effect Ihan a policy Ihal reduces progressivity. This contrasts with the emphasis placed on the marginal rate of income tax in policy debates. The analysis has used a highly aggregative approach, and it would be useful to extend the model in several ways. In panicular, it would be of interest to extend the treatment to that of an open economy, rather than the closed economy considered here. In an open economy, to protect the future level of consumption the sum of the level of invcsunent and the current account surplus (that is, national saving) has to be protected, One would expect that an extension of the analysis to an open economy, in which national saving is treated as a residual in the way developed here for the treaunelU of invcsllncm, would yield similar results. It would be useful to consider alternative fonns of the production function, although this would considerably complicate the analysis. Finally, it should be noted that the supply·side effects examined here differ significantly from those relating to the labour supply incentive effects of taxation which have received considerably more emphasis in the literature.
REFERENCES
Carden. W.M. (1981). 'Taxation. Real Wage Rigidity and Employment". Economic JOl/rna/. 91(2), pp.309-330. Corden, W.M. and P.B. Dixon (1980), "A Tax-Wage Bargain in Australia: Is a Free Lunch Possible?", Economic Record, 56(154), pp.209-21. Creedy, 1. and I.M. McDonald (1991), "Models of Trade Union Behaviour: A Synthesis", Economic Record. 67, pp.346·359. Creedy, J. and I.M. McDonald (1992), "Income Tax Changes and Trade Union Wage Demands", Australian Economic Papers, June, pp.47·57. Faxen, K.-Q. (1982), Incomes Policy and Centralized Wage Formation, Swedish Employers' Confederation (SAAF), Stockholm. Grout, P.A. (1984), "Invesunent and Wages in the Absence of. Legally Binding Labour Contracts: A Nash Bargaining Approach", Econometrica, 52,
pp.449·60.
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Layard, P.R.G. and S. Nickell (1980), "The Case for Subsidizing Extra Jobs", Economic Journal, 90, pp.51-73. McDonald, I.M. (1984), "Anti-Stagnationary Tax CulS and Ihe Problem of Invesunent", Economic Record, 60(170), pp.284-93. McDonald, I.M. (1991), "Insiders and Trade Union Wage Bargaining", Manchester School of Economic and Social Studies, LlX, pp. 395-407.
McDonald, I.M. (1992), Macroeconomics, Jacaranda-Wiley, Brisbane. McDonald, I.M. (forthcoming), "Models of the Range of Equilibria" in R. Cross (ed.), The Natural Rate Hypothesis Twenty-Five Years On, Cambridge University Press, Cambridge.
Oswald, AJ. (1979), "Wages, Employment and Innatioo in a Unionised Economy", mimeo.
Pitchford, J.D. (1981), "Taxalion, Real Wage Rigidity and Employment: The Flexible Price Case", Economic Journal, 91, pp.716-20. Sampson, A.A. (1983), "Employment Policy in a Model with a Rational Trade Union", Economic Journal, 93, pp.297-311. Ulph, A. and D. Ulph (1990) "Union Bargaining: A Survey of Recent Work", in D. Sapsford and Z. Tzannatos (eds.), Current Issues in Labour Economics. Macmillan, BasingSloke, pp.86-125. Weale, M., A. Blake, N. Chrislodoulakis, 1. Meade and D. Vines (1989), Macroeconomic Policy: Inflation, WealIh and the Exchange Rate, Unwin Hyman, London. .
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CAN TAX CUTS INCREASE INVESTMENT IN A UNIONISED ECONOMY?'
John Creedy and Ian McDonald University of Melbourne Parkville Victoria 3052
This paper derives conditions for lax cuts to stimulate output without crowding out invesuucnt. In the model the level of output is constrained by an aggregate supply constraint. This constraint is based on the real wage demands of an insider-dominated trade union seeking to maximize its objective function. It is found that, in the model, tax cuts have a powerful supply-side effect and, for reasonable values of the parameters, will not force a crowding-oul of invcsunent. Of the tax cuts considered, raising the income tax threshold has a larger supply side effect than reducing the marginal tax ratc.
I.
INTRODUCTION
The idea of using tax cuts to moderate the wage demands of trade unions was put forward several times in the 1970s and 1980s. Faxtn (1982) has called such a policy 'tax bribery'. However, a policy of tax cuts runs the risk of forcing a reduction in investment spending and thereby reducing future levels of consumption. For example, Weale et al. (1989, pp.14-5) have argued that "[I]t becomes all too easy, even with the most innationary cost-push wage-selting institutions, to combine full employment with uninflated prices by means of lax fiscal policy ... Full employment is achieved by living on capital (eating up the seed com or "selling the family silver") with adverse longer-teon results". This risk is the motivation for this paper. If tax cuts can expand output without forcing a reduction in investment then they can be recommended. If, instead, Lhey force a reduction in investment, then the economy is "living on capital" and the case for tax cuts is weakened. The complexity arises because a tax cut has both a demand and a supply effect. In the early 1980s several papers showed how employment subsidies have hoth a demand and a supply effect; see Layard and Nickell (1980), Oswald (1979) and Sampson (1983). Those papers did not consider. however, Lhe implications of their analysis for aggregate investment. Another literature Concentrates on the effects on investment of trade union responses {Q a
•
This paper was presented in seminars at the AUSlralian National University and the Universities of Melbourne, Monash, Tasmania and Western Australia. We are grateful to participants at these seminars for thcir comments.
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reduction in personal income tax; see Corden and Dixon (1980), Corden (1981), Pitchford (1981), McDonald (1984) and, for a more elemcn'ary exposition, McDonald (1992, Chapter 14). However, these analyses did nol use a mooel of trade union behaviour and assumed instead that real posHax wages are held constant. The present paper has the advantage of examining investment while using a maximising model of the union. The analysis is set up in a way which allows investment to be treated as a residual. The model assumes monelary policy is set at whatever level is necessary to ensure that the actual level of investment is equal to the residually-detennined level. The precise setting of monetary policy would depend on the nature of the mechanism that determines investment, but the paper does not analyse this precise setting of monetary policy. It is simply assumed that the monetary authority can adjust the monetary base to induce a level of investment equal to the residually-determined level. The important point is that it is impossible for monelMy policy 10 induce a level of investment in excess of the residually-determined level; the resources would not be available. The anaJysis concentrates on the largest of Lhe possible outcomes for investment. Tbe effect of a tax change on investment cannot be predicted from qualitative analysis alone. The supply-side effect of the reduction in wage demands, resulting from the tax cut, will lead to an increase in employment and hence aggregate output. The demand-side effect is that aggregate demand will increase as a result of the increase in disposable incomes. If the increase in aggregate supply is large relative to the increase in aggregate demand, then investment will not be crowded out. The size of the supply-side effect depends on the product of three elasticities: the elasticity of output with respect (Q employment, the elasticity of employment with respect to wages, and the elasticity of wages with respect to taxation. The larger any of these elasticities the greater is the supply-side effect. The demand-side effect is influenced by the distribution of income between wages and profits and the pattern of consumer demand. A complete analysis therefore involves many elements. The present treatment is highly aggregative and abstracts from a number of complicating factors in order to clarify the essential features of the process. The nature of the tax system and the way in which unions may respond to tax changes are examined in Section II. The model includes taxes on incomes and profits in addition (0 a consumption tax. The debate has been largely restricted to the case of a reduction in the marginal rate of income tax, but the present paper shows tllat a richer variety of policies can usefully be considered. In particular, it will be seen that raising the income tax threshold bas a stronger supply-side effect than cutting the marginal rate of tax. Aggregate supply and demand are considered in Section III. Section IV solves the model and provides the substalltive results of the paper. The effect on tolal tax revenue is tben examined in Section V. Firsl, however, it is useful to consider the basic analytics of tax cuts in tcnns of the simple IS-LM model.
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1.1 The simple macroeconomics of tax cuts
FIGURE I
Nominal
Interest
Rate (i)
ASCI
i,
Y,
Y,
Real Outpul (Y)
In Figure 1 two IS curves and two aggregate supply constraints are shown. The aggrcgatc supply constraints show the maximum level of output finns are prepared to supply given the wagc demands of trade unions. Suppose that initially the aggregate supply constraint is ASCI and the IS curve is lSI, with the intersection al the point (ii, YI). Assuming the LM curve passes Ihrough this point, the economy achieves OUlput YI; to avoid cluttering the figure, the LM curve is not shown. Suppose that taxation is cut in some way, leading (Q an increase in aggregate demand and a rightward shift in the IS curve to IS2. If the tax cui also reduces the wage rale, then the aggregate supply constraint will also shift to the right as a result of the increased demand for labour; suppose that it shins to ASC2. With an appropriate monetary policy, the equilibrium point (i2, Y2) could be attained without causing excess demand and an upward pressure on the rate of inflation. The figure illustrates a situation in which thc equilibrium level of output has increased and the equilibrium ratc of interest has decreased, implying a highcr level of investment. Thus Figure I shows a case where the
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cut in laxation does nol crowd out investmenl, but instead allows investmerll 10 be increased. The condilion required for the lax cut to increase investmenl is Ihat the rightward shift in the aggregate supply conslraint musl exceed the rightward shift in the IS curve. The shift in the IS curve is lower, the lower is the marginal propensity 10 consume, while the shift in the supply conSLTainl is larger, the larger are the lhree elaSlicities mentioned earlier. The remainder of the paper derives lhe precise conditions for such a favourable result to occur, 2.
TIlE TAX STRUCTURE AND WAGE DEMANDS
2.1 The tax structure The model conlains three lypes of tax; income tax, sales lax'"Md profits tax. Let wand a respeclively denote the pre-tax real wage and the tax threshold, The wage or income tax. is imposed at a single marginal rate, I, on wages measured above the threshold; hence the lax paid per person is equal 10 t(w - a). The analysis absLTacts from the problems raised by the laxalion of inleresl income arising from pasl savings. Any other approach would involve allowance for the workers' saving behaviour and for the possibility of owning shares in finns. This would significalllly complicate the union's decision-making problem. It is assumed Ihal profils are taxed at a constant proportional rale, 'to The specification avoids the difficulty arising from a situation in which profits are taxed once al source and then again when, after being disLTibuled, they are counted as the taxable income of individuals. The dichotomy between wage income and profils will be continued in Section 1lI when consumption behaviour is examined, and in the following subsection. A consumption lax is applied at the proportional rate, v, to the taxexclusive price of goods, The lax-exclusive rate of v translates to a taxinclusive rate of v/(1 + v). The tax-exclusive price is normalised to unity, so that if the consumplion lax is fully shifted to consumers, the price of OUlput becomes I + v. The union's wage d.emand depends on the relation between the post-lax real wage, y, and the pre-tax real wage, w, A pre-tax real wage of w is judged by the union 10 yield an after-tax income for its members of y, where:'.
y=
at + w(l - l) 1+v
(I)
2.2 The insider-dominated union The economy is assumed 10 consist of many idenlical finns, al each of which wages are detennined by bargaining between a union and the finn. The union is dominated by a group of insiders, each member of which is ri~"-neulral, enjoys secure employmenl and seeks to maximize the post-tax real wage, y; see McDonald (1991). The assumption of risk-neutrality is not important for comparative statics, as shown in Creedy and McDonald (1991), If negoliations
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break-dowll and the union strikes, each member enjoys an altemative income of
x. The union is assumed not to include the finn's invesunem programme in its bargaining. Some papers, see Grout (1984) and Ulph and Ulph (1990), have shown, using partial equilibrium analysis of a single finn, Ihat if the union cannol commit ilself to a bargain made before the capital slock is inslalled then Ihe finn will, given the market rate of interesl, choose a capital stock thaI is less 111an the 0plimal level. By contrast Ihe analysis of investment in this paper is at the macroeconomic level; thc markct rale of inlerest is endogenous and will be assumed to adjusI, by the appropriate monetary policy, to induce the level of investment detennined by the analysis. If the union were assumed to be able to commit itself 10 a bargain then the effect on the analysis would be 10 change the equilibrium rate of inlcresl rather than 111e conditions derived for a tax cuI not to crowd out investment. The firm wishes to maximize profits, R(n) - wn, where R(n) is I1le concave revenue function and n is employment at the firm. The outcome of bargaining is the wage and employmenl combination which maximizes: [y-xj$/(I+$) [R(n) - wnjl/(l+$)
(2)
where ¢l measures the power of the union, and may take values between zcro and infinity. Choosing wand n 10 maximize (2) and using (1) 10 define y, gives a bargained wage: w=
x(l + v)
at
h(l - t)
(3 )
where h depends on the union's power parameter ¢l and the elasticity of OUlput with respect ~o employment, {x, and is given by: h= 1 +$ (I-l/a).
(4)
Given that a < I, it follows mat h < 1. As can be seen from (3), as h approaches zero the wage becomes infinilely large, so that for sensible results h must be greater than zero. This constraint jointly places an upper limil on ¢l and a lower lLmit on (X, 2,3 Tax changes and wage demands
Suppose the government decides 10 'give' a particular absolUle amount to each employed person in the form of a cut in personal income tax, based on the wage ruling before the policy change. This reduction may be achieved by reducing the marginal ralc of income lax, t, or by raising tile tax-free threshold,
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a. For example, a cut in tax of $1 per person can be achieved by reducing the marginal rate by an absolute amount l/(w-a) or by increasing the threshold by III. Differentiating (3) with respect 10 t and a respectively gives: aw = hw-a and aw = _"_'_ at h(I -I) aa h(I -t)
(5)
Thus, an increase in the threshold that cuts lax per person by lhe same amount as a one percentage poinl reduclion in t will reduce the wage demand by (wa)/(h(l-t)}. This exceeds lhe reduction in the wage demand that would occur as a result of a one percentage point reduction in I, so it is necessary to consider separately the effects of reducing t and raising a. Convert (5) into an elaslicity, so that:
c=.!.aw=_'_(l_J!...) w a, 1- t hw
(6)
As mentioned in the introduction, this elasticity is one component of the change in aggregate supply resulting from the change in t. If instead of maximising the objective function (2) the union aims simply to keep y constant as t changes, then the elasticity of wages with respect to the marginal rale of income tax is given by:
c=-' 1 - t (l-~) w
(7)
The only difference between (6) and (7) is the term h, which from (4) depends on 0. and 4>. As 0. approaches 1 or 4> approaches zero, h approaches unity and there is no difference between (6) and (7). Thus the previous literature is equivalent to the union model if either a = 0 (income tax is directly proportional) or if the demand for labour is perfectly elastic or if the union has no power. . A crucial assumption in considering the effect of tax changes is that the alternative income, x, is not affected by the tax change and is independent of the wage rate. For the insider-dominated unions examined here, McDonald (forthcoming) has argued that Ihis assumption is reasonable. However, it is harder to justify for the other union models in which the unemployed (that is outsiders) receive an equal weighting with the employed insiders in the union's objective function.
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AGGREGATE SUPPLY AND DEMAND
3.1 Aggregate supply Assume that the value of ex is COOSlanl, so that the good is produced under
conditions described by the following aggregate Cobb-Douglas production funclion, for a given input of capital: Y=AN
a
(8)
where Y is the real (tax-exclusive) value of aUlpUl and N is the aggregate level of employment. In insider-dominated bargains, each of the identical finns sets employment such that the wage equals Ule marginal revenue product of labour and so !.he aggregate level of employment is determined by: N = (w/aA)I/(a·1)
(9)
Substituting for N, from (9), into the production function (8) gives the
aggregate supply in tenns of the real wage as: Y = A(w/aA)a/(a-l)
(10)
Furthennore, substituting the value of w determined by the insider-dominated bargains, given by (3), gives the aggregate supply constraint, as:
al] a/(a-I)
'(1+V) Y=A [ aAh(1-I)
(II)
3.2 Aggregate demand Consumption, like output, is measured in tenns of its real tax-exclusive value. The approach allows for the possibility that the propensity to save from wage income differs from that of profits, but in each case consumption is proportional to real disposable income. If the marginal propensity to consume is y, aggregatc consumption from wage incomc is yNy. Although unions are not directly concerned with unemployment, it is necessary to allow for unemployment in detennining aggregate demand and tax revenue. If M is the total labour supply, and b the tax-exclusive level of unemployment benefits, then the aggregate value of benefits is b(M-N). It is reasonable to assume that all this income is spent on consumption goods. In the insider-dominated union model, wage and employment outcomes are on the labour demand curve. Given these outcomes, price-taking firms and the Cobb·Douglas production function, the share of wages in aggregate output is
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equal to the elasticity of output with respect to labour input, 0.. Then real after. tax profits, 1t, are given by 1t =
Y(l - T)(I - 0:)/(1 + v)
If the marginal and average propensity to consume out of profits is consumption demand, C, is
C
= yNy + ~1t
+ b(M-N)
( 12)
p,
total
(13)
Using 0: = wN/Y and equations (3), (4) and (12), (13) can be written as: C
= eY + bM
!ill.:!.) { Y+ h(yat-b(l+V»} + ~(I-o:)(I-T) h werec= I+v x(l+v)-at (1 +v)
(14) (15)
If the consumption functions contained constant terms, they would simply be added to (14) and would drop out when differentiating with respect to the tax parameters. Thus the assumption of proportionality does not affect Ule results of the paper.
4.
TAX CHANGES AND INVESTMENT
4.1 The determination of investment
In equilibrium aggregate demand is equal to aggregate supply given by (11), Aggregate demand is C+1+0, with consumption determined by (14). If government spending is exogenous, this leaves the level of investment as a residual as discussed in the introduction; it is equal to the output remaining after consumption and govemmem demand have been met. By combining (11) and (14) with the condition that aggregate demand is equal to aggregate supply, invcsunent is given by 1= (l-e)Y - bM - G
(16)
As already suggested. this really determines the maximum level of invesunent. A contractionary monetary policy could reduce investment below the level given by (16), in which case output would be demand-determined because the aggregate supply constraint would not be binding. An expansionary monetary policy cannot increase investment above the level giyen by (16); any attempt to increase investment above this level will lead to inflation, The effect on the maximum level of invesunent of a change in any of the tax paramclCrs can be determined by the appropriate differentiation of (16).
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This is the focus of the analysis in the remainder of the paper. 'The simplest tax parameter to deal with is the rate of profits tax, t. Since aggregate supply is not affected by t, but a reduction in the tax rate will stimulate demand, a cut in t will necessarily lead to a reduction in investment. The eXLra demand for consumption can only be met by reducing the amount of the good that is devoted to invesunent. This result is confmned from (16), since (17)
Differentiation of (16) with respect to the other tax parameters is rather awkward so, as a preliminary exercise, the following subsection focusses on a special case. 4.2 A special case
Consider a special case in which income tax is proportional to income, so that a == 0; the income tax and profits tax rates are equal, so that t == t; and LIle average propensily to consume out of wages is equal to the average propensity to consume out of profits, so that 'Y = ~. This is a useful reference point as these assumptions have usually been made in the earlier literature. Then (16) becomes:
t = (l-e)Y - bM-G
- = J!.:!2.. (I+v) {y-nhb/x}
with c
(18)
( 19)
Differentiation of (18) with respect to t yields, after some manipulation:
at = c-n Y at (I-I)(I-n)
(20)
A cut in the ratc of income tax increases invesunent if the numerator on the right hand side of (20) is negative. This reduces LO the following:
at at
-< 0 I'f ex >
h$+yx b(I+$)+(I+v)x/(I-I)
(21 )
This condition may be interpreted in terms of a m,inimum value of a. and a maximum value of the response of consumption to a rise in pre-tax income. A high ex implies a large response of aggregate supply to a tax cut, which reduces the pressure on resources available for invesunent following a tax cut. A small propensity to consume and large values of the income Lax raLe and the
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consumption lax rale imply a small increase in aggregate demand following a tax cut which, again, reduces the pressure on resources. If (18) is differentiated with respect to the consumption tax rate, v, it can be found Lhat precisely Ole same condWon as Lhat given in (21) also holds. This arises because when the threshold, a, is zero, both the income tax and the consumption tax are directly proportional. Furthennore, the simple assumption that the union seeks only to maintain the real value of the after-tax wage, makes no difference in this special case. The basic reason for this is given in Section 11, where the elasticity, C, in formulae (6) and (7) was seen to be identical when a = O. Suppose now that the threshold is still zero, but that t :#. t and 'Y '# p. Substitution into (15) and (16) and differentiation with respect to t yields the result timt a cut in the marginal rate of income tax increases investment if: (I) 'Y + (1)0 a...0(1 -t ) - $b(l-l) >·t -t P xa
-
b(l+$l(I-t) x
-
(1 +v)
(22)
Changing t now only influences demand through its effecl on disposable wage income. In the previous case where t=t, changing t changed the rate of tax from both profits and wages. Because of this difference (22) does not reduce to (21) simply by substitution of t=t and r=~. 4.3 The general case
Returning to the general case, differentiation of (16) with respect to t yields, after some manipulation: al_ y [ ah{yat-b(l+v)} ~ a(l-l)ba(xy-b) a(I-C)(X(I+V)-a}] at (l+v){x(l+v)-at) + I+v - {x(l+v)-at}2 - (l-a)(I-t){x(l+v)-at)
(23) For the tax cut to increase investment, the term in square brackets in (23) must be negative. In view of the awkwardness of this expression it is useful to examine some orders of magnitude involved. A realistic value for the propensity to consume out of disposable labour income, 'Y, is 0.8. Because of the retention of profits by corporations, the propensity to consume out of POSI-tax profits, ~, is much less; a value of 0.4 seems reasonable. A realistic value of bla, is 1, so that a suitable value of x/a is 2. For $, the union power parameter, the value of 0.5 was chosen. With , equal to 0.5, the insider-dominated union model gives a reasonable value for the bargained wage, given reasonable values of the other parameters (using equation (3». The critical value that (X has to cxceed for a cut in t to stimulate investment is inversely related to the threc lax rates, t, t and v. For example if v is 0.05 and t and t arc 0.125 men a has to exceed 0.4017 for allat < O.
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Raising both t and '[ to 0.2 reduces the critical minimum value of n 10 0.3655. If the consumption tax rate v is raised 100.1, then with t = '[ = 0.2, the critical minimum value of n is 0.3438. The higher are the rates of lax, the smaller the demand effect of a lax cut and so the smaller the supply effect needs to be to allow an increase in investment. The condilion on n is sensitive 10 x/a. Reducing unemployment benefils or raising the incomc tax threshold tcnds to raise the critical minimum value of n. For example, with t = t = 0.2 and v = 0.05, setting b/a = 0.5 and x/a = 1 yields a critical minimum value of n of 0.7128. The impact on the aggregate level of investment of a cut in the consumption lax rale can be determined by differentiating (16) with respect to v. This operation yields: ~ = V[Il
dv
(1+>)2
(1+V)2{x(l+V)-atJ
(I+V)2
(I+>j{x(I+,)-atJ2
a(l-c)x ] (I-aj{ x( 1+,)-at I
(24)
Numerical analysis of (24) reveals that the critical minimum value that a must exceed for a cut in the consumption tax rate to allow invesunent to increase is fairly insensitive to the parameters of the tax system. With y = 0.8, P = 0.4, b/a = 1, x/a = 2, 1= t = 0.125, v =0.05 and $ = 0.5 the crilical minimum value of cr. is 0.410 1. Raising t and t 10 0.2 reduces cr., as expected, but only to 0.3742. Wilh t ='[ = 0.2, a value of 0.1 for v reduces a to 0.3603. And reducing b/a to 0.5 and xla to 1 yields a critical minimum value of a of 0.3541 (with t =t = 0.2 and v = 0.05). In considering these values it should be borne in mind that the elasticity, a, also directly affects the distributive shares. Hence in practice the share of wages is higher than the critical minimum values obtained. Finally for increases in the income tax threshold differentiate (16) with respect to a. This yields:
ill. _ IV[ aa -
ap-c) ah(J-l)(XX-b)] (J-a){x(l+v)-al) - {x(l+v)-atj2
(25)
For each set of values used in the previous two cases, the expression in square brackets in (25) is positive for ail values of n between zero and one. So for the reasonable values of the parameters assumed here, an increase in the income tax threshold always allows an increase in the aggregate level of invesunent. An increase in the income tax threshold is more likely to allow an increase in the aggregate level of investment than would a reduction in the marginal rate of income tax or the rate of consumption tax because it has a greater effeci on the bargained wage. The greater wage effect is a result of the differential impact on the bargained wage of changes in the average ratc of tax compared with changes in the marginal rate of tax. As explained in Crcedy and McDonald (1992, p.49), a reduction in the average rate of tax holding the marginal rate of
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tax constant, will, by making employment more altractive, reduce the bargained wage whilst a reduction in the marginal rate of tax holding the average rale of tax constant will, by making wage increases more attractive, increase the bargained wage. An increase in the income lax threshold reduces the average rale of tax but not the marginal rale whilsl a decrease in t or v is a decrease in bOUI the average rate of tax and the marginal rate of tax. Thus a decrease in t or v leads 10 two offsening influences 011 the wage. The net downward effecl on the bargained wage is small, and may even increase the bargained wage. A smaller reduction in Ule bargained wage implies a smaller increase in Ihe level of aggregate supply and so less likelihood that investment may be allowed to increase. 5.
5.1
TOTAL TAX REVENUE
Total net revenue
The total revenue raised from wages is the sum of income tax and the consumplion tax, and is: N{'(w-a)+vyy}.
(26)
Revenue from profits is the sum of the profits tax and the tax on consumption out of profits and is: t(Y - wN) + vp"
(27)
Appropriate substitution into (26) and (27), with much manipulation, gives total revenue from wages and profits, R, as: R = {ex'(I+V) + exvy(I-t) + vlJ(l-ex)(l-t) + a,exh(l-t) (vr-(I+V)) + t(l-ex)] (l+v) x(l+v)-a, I+v
(28) The term in square brackets may thus be regarded as the overall proportional tax rate. To calculate the net revenue, unemployment benefits should be deducted from (28), remembering that benefits have been defined exclusive of laxation. Hence it is nol necessary to allow for the consumption lax revenue arising from the expenditure of benefits. As (M·N) people receive unemployment benefits of b then nCI revenue, Rn• is
,
R =R-b(M-N) n
(29)
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5.2 The special case Consider again the special case obtained by assuming a = 0, y = ~ and I = t. Then net revenue is R = Y{t + vy(1-t)/(1 + v») - b(M - N) n
(30)
The tenn in curly brackets has a slraightforward interpretation. It is the sum of the income lax rale and the effective consumption tax rate. The effective consumption tax rate is quite different from v because, for each dollar earned, only y(l - l) is spent and the consumption tax rate applied to the tax inclusive price of goods is v/(l + v). Assuming thai Y is determined by the aggregate supply conSlraint, the impact on nel revenue of a cut in the marginal rale of income tax is given by the derivative of (30). It is:
(31 ) A sufficient condition for net revenue to increase with a cut in the tax rate is that the tenn in the square brackets must be negative. A sufricient condition for this to hold is t > (l - ex). So if I is greater than (l . a.) there is a 'Laffer' effect, whereby decreases in tax rates increase net tax revenue and vice versa. The necessary condition for tax cuts to increase revenue can be derived from (31) by using (3) and (9) to detennine aN/at. Some manipulation yields:
aR n _ Y[I _1_ (--'!.:L + -.!!L + ah(b/X»)] a, - (I-a) (I+v) (l-,) (I+v)
(32)
If the term in square brackets is negative then tax cuts raise revenue. A policy of cuts in rates of tax that simultaneously raises investment and net revenue, while also reducing inOation, is of course unequivocably favourable. However, suppose there is a conflict such that tax cuts will raise investment but reduce net revenue? It is certainly possible for such a contlict to arise. For example, for the set of values y = 0.8, ~ = 0.4, ,= 0.125, v = 0.05, a ::: 0.6, 41 ::: 0.5 and xlb = 2, a cui in t will increase investment, from condition (23), and will reduce net revenue, by equation (32). In the event of a conflict between investment and net revenue it is necessary to consider expliCitly the costs of increasing the debt in relation to the benefits of higher investment. This is outside the scope of the present paper.
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I 6.
CONCLUSIONS
This paper has examined a model in which lax cuts may have a powerful supply side effect. Indeed for reasonable values of the parameters the supply side effect is larger than the stimulus, given by the lax CUIS, to aggregate demand, so thai tax cuts would not force a crowding-oul of invcsunenl. II was found that a policy of tax cuts is more likely to be effective in reducing wage demands and increasing investment if the tax cuts arc achieved by raising the lhreshold, rather than by reducing the marginal rate of income tax or the ratc of consumption tax. Thus, of the two ways of reducing taxes, the policy that increases the progressivily of the lax system has a greater supply side effect Ihan a policy Ihal reduces progressivity. This contrasts with the emphasis placed on the marginal rate of income tax in policy debates. The analysis has used a highly aggregative approach, and it would be useful to extend the model in several ways. In panicular, it would be of interest to extend the treatment to that of an open economy, rather than the closed economy considered here. In an open economy, to protect the future level of consumption the sum of the level of invcsunent and the current account surplus (that is, national saving) has to be protected, One would expect that an extension of the analysis to an open economy, in which national saving is treated as a residual in the way developed here for the treaunelU of invcsllncm, would yield similar results. It would be useful to consider alternative fonns of the production function, although this would considerably complicate the analysis. Finally, it should be noted that the supply·side effects examined here differ significantly from those relating to the labour supply incentive effects of taxation which have received considerably more emphasis in the literature.
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