- Email: [email protected]
Commodity tax harmonisation and public goods
JOURNALOF
PUBLIC ELSEVIER
Journal of Public Economics 63 (1997) 447-466
ECONOMICS
Commodity tax harmonisation and public goods Sophia Delipalla Department of Economics, Keynes College, University of Kent at Canterbury, Canterbury CT2 7NP, UK Received October 1994; final version received January 1996
Abstract This paper examines the welfare effects of commodity tax harmonisation incorporating in the analysis the important feature that tax revenue is not returned to the consumer as a lump sum but it is used to finance a local public good. Only under certain conditions, commodity tax harmonisation is potentially welfare improving. Introducing both transfers between consumers and transfers between governments, it is shown, inter alia, that the analysis is sensitive to the kind of transfers assumed, suggesting that arguments that rely on international transfers should be handled with care.
Keywords: Tax harmonisation; Public goods; International transfers JEL classification: H21; H41; H87
1. Introduction
The European Commission's proposals for tax harmonisation have been a subject of concern t o both policy makers and academics. In 1987, the European Commission proposed that excise duties should be uniform, with tax rates approximately equal to the average community level, to facilitate the abolition of fiscal frontiers. Certainly, it was not o b v i o u s - given that a number of distortions exist in each Member S t a t e - why a movement towards the average community distortion be an improvement. Interestingly enough, Keen (1987) shows that a move towards an appropriately weighted average of pre-existing destination-based commodity taxes, with the weights 0047-2727/97/$17.00 ~) 1997 Elsevier Science S.A. All rights reserved PII S0047-2727(96)01599-X
448
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
reflecting the different demand responses in each country, generates a potential Pareto improvement. The intuition is simple. This particular reform has no effect on global demand leaving production decisions unaffected. The only consequence of harmonisation is the more efficient allocation of commodities between (home and foreign) consumers: from consumers with low marginal valuation to consumers with high marginal valuation. Keen (1989) establishes conditions under which such a harmonising reform would lead to a strict Pareto improvement without any need for compensation, if the initial situation is one in which each country uses its domestic tax structure as a protective device taken the taxes of the other country as given) In fact, harmonisation never happened. In 1989, because of the strong opposition of Member States, the harmonisation proposals were replaced by proposals for the imposition of minimum rates. Nevertheless, there still exist pressures towards some degree of harmonisation. Even the minimum tax rates reforms have enforced a degree of harmonisation. A minimum rate, for example, on the VAT which was binding for some Member States implied a convergence of tax rates in the EU. Most of the Member States though were allowed to maintain their current tax rates and high tax countries are still exposed to the forces of tax competition. Tax competition might itself bring about tax harmonisation. There will be pressures for effective commodity tax harmonisation. There will be pressures for effective commodity tax harmonisation from cross-border shopping. Since 1st January 1993 the tax frontiers were abolished and, although the destination principle still applies for registered traders, final consumers are taxed in the country of purchase. Sinn (1990) argues that the only way to limit cross-border shopping seems to be a harmonisation of tax rates. For these reasons, the welfare effects of a commodity tax harmonisation as analysed by Keen (1987, 1989) are still of policy interest. In particular, Keen (1987, 1989) and later studies such as Turunen-Red and Woodland (1990) and Keen and Lahiri (1993) looked at the welfare effects of multilateral domestic tax reforms in a free trade area but they ignored the budgetary implications of such reforms. The aim of this paper is to contribute to the theoretical literature by incorporating into the analysis public goods and so the revenue effects, extending the analysis in Keen (1987). In two recent papers, Lahiri and Raimondos (1995) and Lockwood (1995) also investigate this issue but they treat the public good in a different set up (discussed below). Following the analysis in Keen (1987, 1989), we assume the destination
1 Lop6z-Garcia (1994) establishes a parallelism between Keen's analysis and its counterpart when taxes are origin-based.
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
449
principle applies.2 We assume that monitoring by governments of all individual purchases is possible so all goods are taxed under the destination principle) Section 2 sets up a competition model of a world comprising two countries which use their tax revenue to finance the provision of a local public good. The public good is modelled as a government purchase of a privately produced commodity. For ease of exposition, the public good is assumed to be traded between countries; 4 an example of such a good could be military equipment. Section 3 derives the comparative statics results. In section 4 we derive the expression that characterises the optimal public good provision in an open economy. Then, section 5 addresses the issue of commodity tax harmonisation when countries face binding revenue constraints. Section 6 concludes.
2. The model
We consider two countries referred to as "home" and "foreign". All variables and functions referring to the home country will be in lower case letters and those for the foreign country in the corresponding upper case ones. The framework is as in Keen (1987, 1989) only here destination-based taxes are levied to finance public expenditure (rather than returned to the consumer as a lump sum). In each country, there are N + 1 commodities, N private goods and one public good labelled O. Note that good O is a local public good so there are no spillover effects between the two countries. There is a single representative consumer and all goods are tradeable. We model the home consumer using the expenditure function e(q*,r,u); this gives the total income necessary to achieve utility level u when the level of public good provision is equal to a scalar r and consumer prices for private goods are given by the N-vector q*. Similarly E(Q*, R, U) is the expenditure function for the foreign consumer. We write q* as a partitioned vector, with the two partition 2 The ideal would be to model cross-border shopping explicitly. But Kanbur and Keen (1993) show that modelling cross-border shopping is hard even in a single good framework. Our framework may be a convenient way of looking at the effects of commodity tax harmonisation in a general equilibrium setting. 3 Haufler (1993) - who looks at the welfare effects of more general tax changes and not a harmonising reform towards a certain target - assumes that, in a framework with two private goods and one public good, one private good is taxed under the destination principle and the other under the origin principle. 4 Lahiri and Raimondos (1995) assume that the public good is produced by the government and it is non-tradeable. Lockwood (1995) also treats the public good in the same fashion but he considers a very specific model with only two goods and complete specialisation in production,
450
s. Delipalla / Journal of Public Economics 63 (1997) 447-466
blocks being ql, the price of good 1, and the ( N - 1 ) - v e c t o r q. In the absence of tariffs and transportation costs, and with the exchange rate normalised at unity, under the destination principle arbitrage equalises producer prices in both countries. The world prices p* are given by the partitioned (N + 1)-vector with the partition blocks being P0, the producer price of the public good, and p, the N-vector of producer prices of private goods. Vector p is further partitioned into p~, the world price of good 1, and /~, the world prices of the remaining N - 1 private goods. The N-vector of specific taxes on private goods 6 is denoted by t*, in home country, with t* = q * - p , or
where t~ denotes the tax on good 1 and t is an ( N - 1 ) - v e c t o r of taxes. Similarly, for the foreign country. The production sectors are characterised by the profit functions ~'(p*) and Fl(p*) for the home and foreign country respectively. We assume perfect competition with decreasing returns to scale. On efficiency grounds, income from immobile and inelastically supplied factors of production is taxed at a 100 per cent. We also assume that one good is internationally mobile with a variable supply res~aonse; for example, labour that the consumer may sell home or abroad. We indicate the derivatives with respect to P0 and p~ by the subscripts 0 and 1 respectively, and the vector of derivatives with respect to prices of the N-1 private goods by the subscript /~ and q or Q as appropriate. Then assuming an equilibrium exists, we can write the market-clearing conditions for both countries taken together as
eq.( q*, r, u) + E e . ( Q * , R, U) - z g ( p * ) - He(p*) = ON
(2.2)
r + R = 7ro(p* ) + / / o ( P * ) •
(2.3)
and
The N market-clearing equations (2.2) represent the world market clearing conditions for all private goods and equation (2.3) for the public good. The home demand function eq.(q*, r, u) is partitioned into e 1 and the ( N - 1)-vector eq. The home supply function ~rp.(p*) is partitioned into 7r0 5This is without loss of generality since specific and ad vaiorem taxes are equivalent under perfect competition. 6Note that public sector's purchases of public good are untaxed. 7Mintz and Tulkens (1986) make the same assumption in a similar context. One can interpret labour services performed abroad as importation of leisure by the foreign country.
s. Delipalla / Journal of Public Economics 63 (1997) 447-466
451
and ~rp, with rrp further partitioned into ,r~ and the ( N - 1)-vector ~r#. The budget constraints of the private sector, are e ( q * , r, u) = - p o b
(2.4)
E ( Q * , R, U ) = po b ,
(2.5)
and
where b is a scalar denoting transfers between consumers of good O from h o m e to foreign country. It proves useful for later purposes to point out that it is important whether the international transfers are transfers between individuals or transfers between governments. Therefore, to develop some intuition, we use here both kind of transfers. Denoting by /3 the government transfer from h o m e to foreign country, and with prime denoting transposition, the budget constraints of the public sector in each country are po r = t*' eq.( q*, r, u) + ~r(p* ) - Po/3
(2.6)
po R = T * ' E e . ( Q * , R, U ) + H ( p * ) + Po/3 ,
(2.7)
and
that is, the governments raise revenue through commodity and rent taxation to finance the public good provision. We assume that 100% rent taxation is not enough to finance the public good provision and that any lump sum transfer between the government and the consumers is ruled out. ~ The system of equations (2.2)-(2.7) is separately homogeneous in p* and q*. Since the supply function is homogeneous (of degree zero) in producer prices and the demand function is homogeneous (of degree zero) in consumer prices alone in absence of income, one can normalise by fixing one producer price and one consumer price. Note that transfers b and/3 are considered as exogenous. Then, the revenue constraint is h o m o g e n e o u s (of degree zero) in prices alone, as well. Thus, it will not be restrictive to impose that one of the prices is predetermined, so set P0 = PG, where P c is fixed, and one good is untaxed, say t~ = 0. G o o d 1 is the arbitrarily untaxed good in both countries. 9 8 In the model there are only two purchasers of the public good, the two governments. However, they cannot make any use of their duopsony power. The demand of public good is determined by the budget constraints of the governments and there are no lump sum transfers between government and consumers. If such transfers were allowed, each government would be able to use its duopsony power by optimally allocating resources between consumers and itself. This observation is due to a referee. 9 By assuming 100% profit taxation, we gain an additional normalisation. See Auerbach (1985) for a discussion on numeraires and untaxed commodities. Note that we do not set Pc = 1, because it proves helpful for some intuition to have Pc in formulae.
452
s. Delipalla / Journal of Public Economics 63 (1997) 447-466
By Walras law, we can drop one equation as being implied by the rest; we drop the market-clearing equation for commodity 1. The system then becomes e q( q*, r, u) + E Q ( Q * , R , U ) - rr¢(p*) - I I p ( p * ) = ON_ 1
(2.8)
r + R = 1to(p* ) + H o ( p * )
(2.9)
e ( q * , r, u) = - p ~ b
(2.10)
E(Q*, R, U) = pcb
(2.11)
pG r = t ' e q ( q * , r, u) + 7r(p*) --Pal3 = t'x + 7r --PG/3
(2.12)
pGR=T'Eo(Q*,R,U)+H(p*)+pG/3=T'X+H+pc;/3,
(2.13)
where x = eq(q*, r, u) and X = E o ( Q * , R , U ) . The above system has N + 4 equations to solve for N + 4 unknowns (N relative prices p and u, U, r, R) given the two (N - 1)-vectors of taxes (t, T) and lump sum transfers b and/3. We assume that a solution with qi > 0 for all private goods exists, and in the next section we examine how changes in the policy instruments affect the equilibrium conditions.
3. Comparative statics To derive the welfare consequences of tax changes, we consider now a commodity tax reform {dt, dT} combined with transfer reforms db and d/3. Taking total differentials in the consumer's budget constraint (2.10), and using (2.1) and dt I = 0, we have: e . du
=
-
e'q .
(3.1)
dp - x ' dt - e r dr - p a db ,
where e. is the inverse of marginal utility of income and e r < 0 is the marginal rate of substitution (MRS) between the public good and lump sum income. Without loss of generality, we normalize the marginal utility of income in the initial equilibrium at unity, that is e u = 1. Perturbing the revenue constraint (2.12), recalling dp0 = 0, PG dr = t' dx + x' dt + Irp dp - P c d/3.
(3.2)
Substituting for x' dt in (3.1) using (3.2), and denoting by m* the vector of imports of private goods for the home country, that is, m* eq. - 77"p, we have =
du = - m * ' dp + t' dx - (PG + er) dr - p G ( d b + d/3).
(3.3)
Equation (3.3) shows that the effect on home welfare of an arbitrary tax
S, Delipalla / Journal of Public Economics 63 (1997) 447-466
453
reform consists of three terms. The first is the effect on the terms of trade: home country's terms of trade improve if, in the face of a slight change in the tax vector, the initial import vector (m*) is cheaper at the new world prices than at the old, that is, if m*' dp < 0 . The second term is the change in the deadweight loss (first order effect) resulting from marginal commodity tax changes; this is beneficial if the tax reform reduces the distortionary effect on the demand of the initial tax structure. The third term relates to the deviation of the public good provision from that implied by the Samuelson rule. In the present context, the Samuelson rule simply requires that Pc = -e~. Note that here the Samuelson rule is not generally optimal. The public good provision is financed by distortionary taxation and, moreover, our economy is not a closed one (see section 4 for more detail on this point). To evaluate tax reforms, we now need to relate the change in welfare, du and dU, directly to changes in tax instruments. To simplify the analysis, which becomes notationally very complex and unpleasantly difficult to conclude otherwise, we assume first that there are no income effects for the N - 1 taxed commodities; that is, good 1 picks up all the income effects 1° a n d equ = EQU = ON_ 1. Second, we assume that the demand for the N - 1 private goods is independent of the public good provision, that is, eqr = EQR = ON_ 1. After this simplification, we perturb the equilibrium conditions to derive an expression for the change in world prices and tax revenues in terms of the policy instruments. First, we perturb the market-clearing condition for the private goods (equation (2.8)). Using q* = p + t*, dt 1 = 0 and dp0 = 0, and introducing the d e f i n i t i o n [eql ]eqq] = eqq. and [7r~1 ] ~-~] = 7r~p, we get eqq dt + EQQ d T = (Tr¢p + H~p - eqq. -- EQQ,) d p .
(3.4)
Note that eqq and E o o are ( N - 1 ) x ( N - 1 ) matrices and eqq., EOQ. , "lr~p and II~p are [ ( N - 1 ) x N] matrices. Now perturbing the market-clearing condition for the public good (equation (2.9)), and recalling dp0 = 0, we have dr + d R = (Trop + Hop ) d p .
(3.5)
From the revenue constraint for the home country, equation (2.12), using (2.1) and recalling that dti = 0 and dp0 = 0, Pa dr = (e'q + t' e qq) dt + (Trp + t' e qq. ) dp - Pa dfl .
(3.6)
Using (3.6) and the analogue for the foreign country in expression (3.5), we obtain ~°This is an assumption used by Keen (1989, p. 5).
454
S. Delipalla / Journal of Public Economics 63 (1997) 447-466 (e'q + t'eqq) dt + (E6 + T'EoQ ) d T = [pG(Trop + Hop )
- (Tr'p + t'eqq. + 1I~ + T'EQQ.)] d p .
(3.7)
Stacking (3.7) and (3.4) together one gets
Ie'q + t'eqq] [ g ' e + T'Eo.o.]. L " ' e q ; " ' j d, + I d r = a dp
(3.8)
where
[pG(Trop + H~p)-'rr'p-t'eqq.-_Fl'p- T'EQQ.] A = ~_. . . . . . . . ~r:'p""q-'Hl3;"--'eqq'."--'f_,Q;'." . . . . . . . . ?
(3.9)
is an (N x N) matrix. Before we proceed, we need to consider matrix A more closely. For analytical convenience, we rewrite it as
(3.10)
A= [Azl:A22 j where, making use of (2.2), A 11 = P o ( % l A12
+//Ol) -
t
t'eql -- T ' E o l - el - E1 ,
t
¢
= pa(Tr0p + Hop ) - t eqq
__
¢
t
T'Ef)Q - eq - E o ,
(3.11) (3.12)
m21 = ~pl +//pl
- eql -
Eol ,
(3.13)
A 2 2 = 7rpp + / / p p
- eqq -
EOO .
(3.14)
We assume A to be non-singular and obtain"
(3.15)
A - l = [ nil i B12] where Bll
~ (All
B12 = -A
-- A12A;21A21)
-1 ,
;11A12(A22 - A21A
B21 = -A2-21A21nll
?11A12) - I ,
,
B22 = (A22 - A21A~11A12) -l . With
A -1
given by (3.15)-(3.19), expression (3.8) implies
11See Dhrymes (1978) for basic operations with partitioned matrices.
(3.16) (3.17)
(3.18) (3.19)
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
e'q + t'eqq EQ + T'EQQ dp= a-'{['"'e'q'q"-] dt + [ .... E'o-Q.... ] d T } .
455 (3.20)
Finally, substituting for dr and dp in (3.1), using (3.6) and (3.20), we obtain the following expression for the effect of an arbitrary tax reform on home welfare: du=-
{
er [ G , ] e'q+~-~(e'q+t'eqq)+ eq,'+~-~(%+t'eqq.) A-'
×[eq+t'eqq]~dt
I_e~q-- j j e q.
xdr-pc
PG (Tr'p +
qq, j
L . . . . EQ-Q''''~
( db + Pae, dE 1 .
(3.21)
Equation (3.21) and the analogue for the foreign country relate the welfare effects directly to the policy instruments, taxes and international transfers, and serve as a basis for the succeeding analysis.
4. Optimal commodity taxation and public good provision
We assume in this section that each country chooses its commodity taxes-and hence, through its revenue constraint, the level of the public good provision - so as to maximise its own national welfare, taking the other country's taxes as given. Then, commodity taxes are optimal, from the point of view of the country though not necessarily of the world as a whole, if the coefficient of dt in expression (3.21) is equal to zero. Thus, the ( N - 1 ) conditions that characterise the optimal commodity taxes in home country are e ' e'q+~(e'q+teqq)
=-
[ ' er eq.+~(vr'p+
I eqq,) ] A 1 [ e'q + t'eqq ] ' L---~;q--- j
(4.1) Collecting terms in (4.1) and post-multiplying by t, gives er[
Pc
,
(e'qt+t'eqqt)+(Tr'p+teqq,)A
[fe'qt
1[
, -1 [e'qt + t'eqqt] ] +eq,A [''"edqt''"J~"
y~!+t'eqqt
G
]~
JJ (4.2)
456
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
The analogue of (4.2) holds for the foreign country. Then follows Proposition 1: When the home country sets its commodity taxes and thus the " public good provision optimally, the condition that characterizes the optimal public good provision in an open economy is ol M R T = -~ M R S
(4.3)
where a = e'qt+teqqt+(Tr;+ ' t 'eqq.)A -1[[ 'e'qt+t'eqqt] ' " d q q t " " J and
A =e'qt + e;,A ,[e'qt + t'eqqt] i---G-c-- ] • We must stress that condition (4.3) characterizes the optimal public good provision under certain assumptions: there are no income effects and demand for taxed goods is independent of public good provision. Under these conditions, a special case of a well known result in public finance literature is that MRS must exceed MRT at an optimum (see Atkinson and Stern (1976), Browning (1976), Wildasin (1979)). But does this result hold when we hove an open economy? Condition (4.3) shows that following the Samuelson rule, incorrectly, would not necessarily lead to oversupply of the public good; it could lead to undersupply. What might reverse the conclusion drawn in the case of a closed (or a small open) economy 12 is that, now, financing an extra unit of public good by commodity taxation has an additional effect: a change in the tax rates affects the terms of trade through the change in world prices. If the terms of trade improve "enough" to outweigh the (negative) deadweight loss effect, Samuelson rule may underestimate the benefits of an extra unit of public good provided. We must stress though that we find hard to believe that the Member countries in the EU follow the rule given by (4.3), that is, that they are at a nationalistic optimum. This section's purpose was to help us with our intuition for the results that follow by showing that the Samuelson rule is not generally optimal in an open economy with distortionary taxation. Having established this, we proceed, in the next section, to the analysis of tax harmonisation and its welfare effects focusing on the case considered by Keen (1987), that is, starting from an arbitrary tax equilibrium, 12See Delipalla (1994) for a discussion on optimal public good provision in a small open economy.
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
457
5. Commodity tax reform from an arbitrary tax distorted equilibrium In this section we examine the effects of commodity tax harmonisation on welfare. We consider the reform dT
H-
,]
T
(5.1)
'
where H = (eqq + E o o ) - l ( e q q t + E o o T ) ,
(5.2)
a reform familiar from Keen (1987, 1989). Reform (5.1) requires both countries to converge towards the common target H, which is a loose interpretation of a weighted average of initial tax structures of the kind proposed by the European Commission. If eqq = EQQ, that is, the home and the foreign country face the same demand responses, it is simply the arithmetic mean of the initial tax rates. Let us examine now the effect of a small move of both taxes, t and T, towards H. Using (5.2) in expression (5.1), one gets
dt = (eqq q- EQQ)-l(eqqt + EQQT ) - t = (eqq d- EOQ)-IEQQ(T -- t)
(5.3)
d Z = - (eqq + Eao)-leqq(T - t ) .
(5.4)
and
Define -1
1 -1
S = eqq(eqq + E Q Q ) - I E Q Q = [eqq (eqq + EQQ)EQQ] = EQQ(eqq + E Q Q ) - l e q q .
(5.5)
Note S is a negative definite matrix since both eqq and EQQ a r e negative definite matrices, a3 Then making use of (5.5), we can easily see from (5.3) and (5.4) that for this particular reform
eqq dt + EQO d T = 0.
(5.6)
In Keen (1987, 1989) the harmonisation reform (5.1)-(5.2) ensures that harmonisation has no effect on total demand so that world prices are unaffected. Here tax revenue is not returned to the consumer as a lump sum; instead, it finances the public good provision. Thus, when taxes change, it is not only the change in total demand that matters but also the 13 It is assumed that there is enough substitutability in demand between the taxed goods and the untaxed (private) good so that eqq and EeQ are negative definite: see Dixit and Norman (1980), p. 130.
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
458
change in tax revenue and the implied change in the level of public good provided. Hence, the question is, would the result of Keen (1987) still hold in a more realistic setting when countries face binding constraints on the tax revenue required? For further analysis, using the particular feature (5.6) of the harmonisation reform, it is helpful to rewrite (3.21) as
e r "x , l+-~-~G)(e q +t'eqq)dt+t'eqqdt
du=- -
[ 'eq. + - -er t )1 -1 P G ( TI'p"k-t qq, A '
×[(e;+t'eqq)dt+(EQ+T'gQQ)DT]
-
-
( db
PG
(5.7)
Let us now call a reform "conditionally revenue neutral" if it is revenue neutral at constant p. That is, for the world as a whole,
(e'q + t'eqq) dt + (E~ + T'EQQ) dT = 0.
(5.8)
When this holds, from (3.20) the reform (5.1)-(5.2) implies dp = 0. With world prices constant, profit tax revenue is also unaffected. Since a conditionally revenue neutral reform implies that dp = 0 , conditional revenue neutrality here is sufficient for unconditional revenue neutrality. Then,
Proposition 2. Commodity tax harmonisation in the sense o f (5.1)-(5.2) is potentially improving if (i) it is conditionally revenue neutral for the worm as a whole, and (ii) both transfers between governments and transfers between individuals can be deployed. Proof: Using (5.8) and (5.6), expression (3.21) becomes
du=-{e'q+
er-~c(eq'+teqq)}dt-pG(db'
er
+ ~--~d/3) .
(5.9)
Using the analogue for the foreign country and choosing d/3 to leave utility in foreign country unchanged,
E R dfl = E ~ d T -
ER Pc (e'q + t'eqq) dt - P c d b ,
(5.10)
where use has been made of (5.8). Multiplying (5.10) by e,/E R, and then using it to substitute for e, d/3 in (5.9), expression (5.9) becomes
S. Delipalla / Journal o f Public Economics 63 (1997) 447-466
d u = - e ' q d t - E o d'T +
(e-~n) -1
(padb-E~dT).
459
(5.11)
Finally, it is easy to see that if we set Pc db = E~ dT, and make use of assumption (5.8), expression (5.11) becomes
du = t'eqq dt + T'EQo d T .
(5.12)
Using (5.3) and (5.4) and definition (5.5),
du = - ( T - t ) S ( T - t),
(5.13)
which is positive. QED. It is interesting that, according to Proposition 2, we have to be able to use both types of transfers for harmonisation to be potentially Pareto improving. Transfers between governments are needed to ensure that tax revenue is constant in both countries and transfers between individuals are needed to ensure that gain from reduced consumption inefficiency goes to both individuals. But what can one say when harmonisation is conditionally revenue neutral for the world as a whole and we can only use one kind of transfers? We look first at the case where only transfers between individuals are available, that is, set d/3 = 0. Then
Proposition 3. Suppose that only transfers between individuals can be deployed. Then, commodity tax harmonisation in the sense of (5.1)-(5.2)/s strictly potentially improving if (i) it is conditionally revenue neutral for the worm as a whole, and (ii) it conditionally increases revenue in whichever country has higher Marginal Social Cost of Public Funds (MSCPF). Proof. Since (5.8) combined with (5.6) imply dp = 0 , expression (5.7) becomes du .
. 1. + . P6
eq +
t'eqq) dt + t'eqq dt - P c db.
(5.14)
Then using its foreign analogue and defining db to leave utility in foreign country unchanged, (5.14) becomes
du = +
(er) (p~) 1 +-~a (e'q+ t'eqq) d t - 1 +
(E~ + T'EQQ) dT
t'eqq dt + T'EQQ d T .
Making use of (5.8), expression (5.15) becomes
(5.15)
460
S. Delipalla / Journal o f Public Economics 63 (1997) 447-466
du = -
(er
P-~c
E_~)
(eq -~ t'eqq) dt + t'eqq dt + T'EQQ d T
= (MSCPF h - MSCPFf)(e'q + t'eqq) dt + t'eqq dt + T'EQo d T , (5.16) where with MSCPF h and MSCPF: we denote the Marginal Social Cost of Public Funds for home and foreign country respectively. Since t'eqq dt + T'EQQ dT > 0, the result follows from assumption (ii). QED. Since the only available transfers now are transfers between individuals, conditional revenue neutrality for the world as a whole cannot ensure revenue neutrality for each country. Then harmonisation is potentially improving if r e v e n u e - and hence the level of public good provisionincreases in the country of the individual with the higher marginal valuation of the public good. Then, the transfers between individuals are needed to ensure that both individuals gain. If we now assume that can only use transfers between governments, that is, set db = 0, then,
Proposition 4. Suppose that only transfers between governments can be deployed. Then, commodity tax harmonisation in the sense of (5.1)-(5.2) is potentially improving if (i) it is conditionally revenue neutral for the worm as a whole, and (ii) it increases revenue at unchanged behaviour in whichever country has higher Marginal Social Cost of Public Funds (MSCPF). Proof. Recall from Proposition 2 that, setting d/3 so that foreign utility is unchanged, the effect on home welfare is given by (5.11). Setting db = 0 in (5.11), and using (5.8) then gives er \
,
d u = t 'eqq dt + T'EQQdT + 1----E~n)EQdT.
(5.17)
Since the sum of the first two terms is positive, home welfare increases if E~ d T > 0 and E R > er, that is, revenue rises at unchanged behaviour in the country with the highest MSCPF. QED. Note that when only transfers between individuals can be used, for harmonisation to be potentially Pareto improving we need conditional revenue increase in the country with the highest MSCPF; Proposition 3. When only transfers between governments can be used, we need an increase in revenue at unchanged behaviour in whichever country has the highest MSCPF. The reason is simple. In the first case government transfers are not
S, Delipalla / Journal of Public Economics 63 (1997) 447-466
461
available and it is important that the revenue effect will not be detrimental in both countries. Note that here the revenue effect depends on both the tax rate change (x' dt) and the effect on the consumer demand for taxed goods (t' dx). In the second case, government transfers are available so we need not worry about the revenue effect in each country. But with no individual transfers available, harmonisation is potentially Pareto improving if it increases taxes for the consumer with the higher marginal valuation of public good. Note that a necessary condition for conditional revenue neutrality to hold, given the Keen reform, is that e'q dt + E~) dT < 0, that is, global revenue at unchanged behaviour falls (since t' e qq d t + T'Eoo dT > 0). The Commission's 1985 proposals suggesting that the harmonising reforms would be more or less revenue neutral (with the exception of Denmark and Ireland) were based on the arbitrary assumption that there would be no change in the demand patterns. 14 Proposition 5 below suggests that revenue neutrality at unchanged behaviour is not sufficient for harmonisation to be potentially Pareto improving. A harmonising reform which is world revenue neutral at unchanged behaviour, that is, r
t
e q dt + E o d T = 0,
(5.18)
can be strictly potentially improving only when certain conditions hold. Defining A* = A +
I.t'eqq. + T'EQQ,] . . . . -0~-_-1. . . . . i
t
t
=
[
A2t
:
A22
] '
(5.19)
we have
Proposition 5. Suppose either kind of transfers (or both) can be deployed. Then, commodity tax harmonisation in the sense of (5.1)-(5.2) is potentially improving if (i) harmonisation is revenue neutral at unchanged behaviour, (ii) public good provision follows the Samuelson rule in both countries, and (iii) Det(A*) has same sign as Det(A). Proof: It is shown in the Appendix that ~4See, for example, Lee, Pearson and Smith (1988) for the effects of the 1985 proposed tax changes on the UK household spendings.
462
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
Det(A*)- Det(A), ,
du . . . . Det(A) .
[eq at + E~ dT)
Det(A*) + Det(A) (t'eqq dt + T'EQo d T ) .
(5.20)
Assuming harmonisation is revenue neutral at unchanged behaviour, the first term on the right-hand side vanishes. Therefore, recalling that t'eqq dt+ T'EQo dT > 0, global welfare increases as long as Det(A*) has the same sign as Det(A). QED. Equation (5.20), has a nice interpretation, showing the welfare effects of harmonisation to be a weighted average of the revenue effect with no behavioural response (e'qdt+ E~ dT), as calculated by the Commission, and the deadweight loss effect (t'eqq dt + T'EQe dT). Condition (i) here captures exactly the form of European Commission's 1985 proposals: tax changes will not lead to changes in the demand patterns. But revenue neutrality at unchanged behaviour (at both national and global levels) is not sufficient for the harmonising reform to be potentially Pareto improving. Even if we assume that the governments follow the Samuelson rule, since there is no a priori reason to assume that EU Member States follow the rules of optimal taxation, condition (iii) has to be satisfied as well.
6. Conclusions
In this paper, we have been interested in examining how robust the results in Keen (1987) are to the recognition that tax revenue is spent rather than returned to the consumer as a lump sum. The analysis shows that, if we assume conditional revenue neutrality, that is, revenue unchanged at constant world prices, for the world as a whole, harmonisation is potentially Pareto improving if we can use both transfers between consumers and transfers between governments (Proposition 2). Transfers between governments are needed to ensure that no country loses in revenue, leaving its public spending unaffected. Transfers between consumers then guarantee that both consumers benefit from the more efficient reallocation of consumption. When only consumer transfers are possible, harmonisation is welfare improving if it is not only conditionally revenue neutral for the world as a whole but it also conditionally increases revenue in whichever country has the higher MSCPF (Proposition 3). The last condition is needed to ensure that efficient reallocation of public goods takes place: from the low marginal valuation consumer to the high marginal valuation consumer. When only government transfers are available, and conditional revenue
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
463
neutrality for the world as a whole holds, then harmonisation is potentially improving when it increases revenue at unchanged behaviour in the country with the higher MSCPF (Proposition 4). Since government transfers can be deployed, there is no need to worry here about the revenue changes in each country. However, since transfers between individuals can not be used, we must ensure that taxes increases for the consumer with the highest marginal valuation of the public good. Thus, two points emerge here. First, as it was expected, it is unlikely to find very general conditions under which Pareto improving reforms are possible. Second, and more interestingly (since it has never been recognised in the tax reform literature before), the two kinds of transfers have different implications. Therefore, any arguments that rely on international transfers should be handled with care. 15 A well known criticism of this analysis is the need to use compensation transfers for an actual Pareto improvement. The Pareto principle cannot be used as a criterion for social choices in most real-world situations where policy changes produce both gainers and losers. In such cases one may apply the compensation principles suggested by Hicks (1939) and Kaldor (1939). This principle does not require the actual payment of compensation, otherwise it would satisfy the Pareto criterion. Of course, by considering hypothetical compensation we focus on the efficiency aspects of the policy change. Whether or not a transfer is actually carried out is considered to be an important but separate issue.16
Acknowledgements I am grateful to Mick Keen for his detailed comments and suggestions. I also thank Sajal Lahiri, Gareth Myles and Miguel-Angel Loprz Garcia, as well as an anonymous referee, for their comments. Remaining errors are mine.
Appendix Derivation of (5.20): Using (3.15) and (5.6), we write (3.20) as 15 An example of transfer between consumers could be repatriation of income to the migrant's family in the country of origin. t6 Note that there already exists a central institution in the Community with a budget for structural funds (see, for example, Structural Funds: 1992 Report, COM(93) 530).
464
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
dp=
B~i, B~2
[:
(%
][+ .
= ~, L B : , j
.
.
.
t eqq)dt .
.
.
.
.
.
.
.
7" Eoo ) d r
(E o
++ .
.
.
.
.
.
.
.
.
.
.
.
.
t
'
where y = (e'q + t'eqq) dt + (E~ + T'EQo ) d T .
(A.2)
Then, (3.21) becomes ,
du-y[e'q.-Trp-t
rBlll
eqq.]~-B2-] +t'eqq d t - p a ( d b - d # ) .
(A.3)
Then using the analogue for the foreign country, and defining db and d/3 to leave foreign utility unaffected, recalling that by assumption PG = - e , = E R, (A.3) becomes . . . . . [BIll du = -y[ea, + EQ. - 7rp - l l e -,'eqq. - T EQo.] [ ~ i - ] + t'eqq dt + T'E~2 Q d T .
(A.4)
Making use of the market-clearing condition (2.2), and partitioning [e ql ]eqq] = eqq., expression (A.4) gives d=y[t'eql + T'EQllt'eqq + T'EQQ][-B-1)-I LBzl j + t ,eqq dt + T'EQQ d T .
(A.5) Now using (3.11) and (3.12), one gets du=-T[All
[Bll1 Zlz][-/~2; j
+ T[Pc(~'o, +//Ol) - e, - E, Ipc(Tro# +//0#) - eq - E~]
[Bill
× [_Bzl] + t'eqq dt + T'EoQ d T . By definition FBtll
tAll ]AI2][-jD~; j = 1. So, using this and (3.18),
(A.6)
S. Delipalla / Journal of Public Economics 63 (l.997) 447-466
465
du = -3' + YBll[Pa(ZCol + 11ol) - el - Ei Jpa(Tro~ + Hop)
-- eq -- E~] "__
,
+ t eqq dt + T'EQo d T .
(A.7)
Using the definition of "y and combining terms, we have du = - (e'q dt + E 6 dT) + 7Blx[pa(Tro, + 11Ol)
- e 1 - E1[ pc(qro# +11o#) - e'q - E ~ l [ - - - ~ 1 q ~ :[] .
(A.8)
To derive a more neat expression for the last term on the right-hand side of (A~8), using the standard formula for calculating determinants (see, for example, Dhrymes (1978), p. 459, Proposition 32), expression (5.19) gives Det(A*) ~ Det(A22){pc(Trol + 1101) - - e~ - E 1 - [pG(~r0~ + H0~) - e'q - E ~ ] A ; ) A 2 , ) .
(A.9)
Using (A.9) in (A.8): Det(A*)
du = - (e'q dt + E ~ dT) + 3'B,a Det(A22) .
(A.10)
From (3.10), Det(A) = Det(A22)(A 11 - A12A2?A21 ) .
(A.11)
Since (A.11) and (3.16) imply Bll-
Det(A22) Det(A) '
then Det(A*) du = - (e'q dt + E ~ dT) + 7 Det(A)
Finally, using the definition of 7, we can write this as d/A =
Det(A*) - Det(A) Oet(A) (e'q dt + E ~ dT) Det(A*) + Det(A) (t'eqq dt + T'EQQ d T ) ,
which is (5.20) in the text.
(A.12)
466
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
References Atkinson, A.B. and N.H. Stern, 1974, Pigou, taxation and public goods, Review of Economic Studies 41, 119-128. Auerbach, A.J., 1985, The theory of excess burden and optimal taxation, in: A. Auerbach and M.S. Feldstein, eds., Handbook of Public Economics, Vol. 1, 61-127. Browning, E.K., 1976, The marginal cost of public funds, Journal of Political Economy 84, 283-298. Commission of the European Communities, 1993, Structural Funds: 1992 Report, COM(93), 530 (Brussels). Delipalla, S., 1994, Commodity tax harmonisation and public goods, Working paper 94-17, University of Wales Swansea. Dhrymes, P.J., 1978, Mathematics for Econometrics (Springer-Verlag, New York). Dixit, A.K. and V. Norman 1980, Theory of International Trade (Cambridge University Press). Haufler, A., 1993, Public goods, international trade, and tax competition, in Commodity Tax Harmonization in the European Community (Physica Verlag, Heidelberg). Hicks, J.R., 1939, The foundation of welfare economics, Economic Journal 49, 696-712. Kaldor, N., 1939, Welfare propositions of economics and interpersonal comparisons of utility, Economic Journal 49, 549-552. Kanbur, R. and M.J. Keen, 1993, Jeux sans fronti6res: Tax competition and tax coordination when countries differ in size, American Economic Review 83, 877-892. Keen, M.J., 1987, Welfare effects of commodity tax harmonisation, Journal of Public Economics 33, 107-14. Keen, M.J., 1989, Pareto-improving indirect tax harmonisation, European Economic Review 33, 1-12. Keen, M.J. and S. Lahiri, 1993, Domestic tax reform and international oligopoly, Journal of Public Economics 51, 55-74. Lahiri, S. and P. Raimondos, 1995, Public good provision and the welfare effects of indirect tax harmonisation, Discussion paper, University of Essex. Lockwood, B., 1995, Commodity tax harmonisation with public g o o d s - A n alternative perspective, Discussion paper, University of Exeter. Lee, C., M. Pearson and S. Smith, 1988, Fiscal harmonisation: An analysis of the Commission's proposals, IFS Report Series 28. Lop6z-Garcia, M., 1996, The origin principle and the welfare gains from indirect tax harmonisation, International Tax and Public Finance 3, 83-93. Mintz, J. and H. Tulkens, 1986, Commodity tax competition between member states of a federation: equilibrium and efficiency, Journal of Public Economics, 29, 133-172. Pigou, A.C., 1947, A study in Public Finance (Macmillan). Sinn, H-W, 1990, Tax harmonization and tax competition in Europe, European Economic Review 34, 489-504. Turunen-Red, A.H. and A.D. Woodland, 1990, Multilateral reforms of domestic taxes, Oxford Economic Papers 42, 160-186. Wildasin, D.E., 1979, Public good provision with optimal and non-optimal commodity taxation, Economics Letters 4, 59-64.
PUBLIC ELSEVIER
Journal of Public Economics 63 (1997) 447-466
ECONOMICS
Commodity tax harmonisation and public goods Sophia Delipalla Department of Economics, Keynes College, University of Kent at Canterbury, Canterbury CT2 7NP, UK Received October 1994; final version received January 1996
Abstract This paper examines the welfare effects of commodity tax harmonisation incorporating in the analysis the important feature that tax revenue is not returned to the consumer as a lump sum but it is used to finance a local public good. Only under certain conditions, commodity tax harmonisation is potentially welfare improving. Introducing both transfers between consumers and transfers between governments, it is shown, inter alia, that the analysis is sensitive to the kind of transfers assumed, suggesting that arguments that rely on international transfers should be handled with care.
Keywords: Tax harmonisation; Public goods; International transfers JEL classification: H21; H41; H87
1. Introduction
The European Commission's proposals for tax harmonisation have been a subject of concern t o both policy makers and academics. In 1987, the European Commission proposed that excise duties should be uniform, with tax rates approximately equal to the average community level, to facilitate the abolition of fiscal frontiers. Certainly, it was not o b v i o u s - given that a number of distortions exist in each Member S t a t e - why a movement towards the average community distortion be an improvement. Interestingly enough, Keen (1987) shows that a move towards an appropriately weighted average of pre-existing destination-based commodity taxes, with the weights 0047-2727/97/$17.00 ~) 1997 Elsevier Science S.A. All rights reserved PII S0047-2727(96)01599-X
448
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
reflecting the different demand responses in each country, generates a potential Pareto improvement. The intuition is simple. This particular reform has no effect on global demand leaving production decisions unaffected. The only consequence of harmonisation is the more efficient allocation of commodities between (home and foreign) consumers: from consumers with low marginal valuation to consumers with high marginal valuation. Keen (1989) establishes conditions under which such a harmonising reform would lead to a strict Pareto improvement without any need for compensation, if the initial situation is one in which each country uses its domestic tax structure as a protective device taken the taxes of the other country as given) In fact, harmonisation never happened. In 1989, because of the strong opposition of Member States, the harmonisation proposals were replaced by proposals for the imposition of minimum rates. Nevertheless, there still exist pressures towards some degree of harmonisation. Even the minimum tax rates reforms have enforced a degree of harmonisation. A minimum rate, for example, on the VAT which was binding for some Member States implied a convergence of tax rates in the EU. Most of the Member States though were allowed to maintain their current tax rates and high tax countries are still exposed to the forces of tax competition. Tax competition might itself bring about tax harmonisation. There will be pressures for effective commodity tax harmonisation. There will be pressures for effective commodity tax harmonisation from cross-border shopping. Since 1st January 1993 the tax frontiers were abolished and, although the destination principle still applies for registered traders, final consumers are taxed in the country of purchase. Sinn (1990) argues that the only way to limit cross-border shopping seems to be a harmonisation of tax rates. For these reasons, the welfare effects of a commodity tax harmonisation as analysed by Keen (1987, 1989) are still of policy interest. In particular, Keen (1987, 1989) and later studies such as Turunen-Red and Woodland (1990) and Keen and Lahiri (1993) looked at the welfare effects of multilateral domestic tax reforms in a free trade area but they ignored the budgetary implications of such reforms. The aim of this paper is to contribute to the theoretical literature by incorporating into the analysis public goods and so the revenue effects, extending the analysis in Keen (1987). In two recent papers, Lahiri and Raimondos (1995) and Lockwood (1995) also investigate this issue but they treat the public good in a different set up (discussed below). Following the analysis in Keen (1987, 1989), we assume the destination
1 Lop6z-Garcia (1994) establishes a parallelism between Keen's analysis and its counterpart when taxes are origin-based.
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
449
principle applies.2 We assume that monitoring by governments of all individual purchases is possible so all goods are taxed under the destination principle) Section 2 sets up a competition model of a world comprising two countries which use their tax revenue to finance the provision of a local public good. The public good is modelled as a government purchase of a privately produced commodity. For ease of exposition, the public good is assumed to be traded between countries; 4 an example of such a good could be military equipment. Section 3 derives the comparative statics results. In section 4 we derive the expression that characterises the optimal public good provision in an open economy. Then, section 5 addresses the issue of commodity tax harmonisation when countries face binding revenue constraints. Section 6 concludes.
2. The model
We consider two countries referred to as "home" and "foreign". All variables and functions referring to the home country will be in lower case letters and those for the foreign country in the corresponding upper case ones. The framework is as in Keen (1987, 1989) only here destination-based taxes are levied to finance public expenditure (rather than returned to the consumer as a lump sum). In each country, there are N + 1 commodities, N private goods and one public good labelled O. Note that good O is a local public good so there are no spillover effects between the two countries. There is a single representative consumer and all goods are tradeable. We model the home consumer using the expenditure function e(q*,r,u); this gives the total income necessary to achieve utility level u when the level of public good provision is equal to a scalar r and consumer prices for private goods are given by the N-vector q*. Similarly E(Q*, R, U) is the expenditure function for the foreign consumer. We write q* as a partitioned vector, with the two partition 2 The ideal would be to model cross-border shopping explicitly. But Kanbur and Keen (1993) show that modelling cross-border shopping is hard even in a single good framework. Our framework may be a convenient way of looking at the effects of commodity tax harmonisation in a general equilibrium setting. 3 Haufler (1993) - who looks at the welfare effects of more general tax changes and not a harmonising reform towards a certain target - assumes that, in a framework with two private goods and one public good, one private good is taxed under the destination principle and the other under the origin principle. 4 Lahiri and Raimondos (1995) assume that the public good is produced by the government and it is non-tradeable. Lockwood (1995) also treats the public good in the same fashion but he considers a very specific model with only two goods and complete specialisation in production,
450
s. Delipalla / Journal of Public Economics 63 (1997) 447-466
blocks being ql, the price of good 1, and the ( N - 1 ) - v e c t o r q. In the absence of tariffs and transportation costs, and with the exchange rate normalised at unity, under the destination principle arbitrage equalises producer prices in both countries. The world prices p* are given by the partitioned (N + 1)-vector with the partition blocks being P0, the producer price of the public good, and p, the N-vector of producer prices of private goods. Vector p is further partitioned into p~, the world price of good 1, and /~, the world prices of the remaining N - 1 private goods. The N-vector of specific taxes on private goods 6 is denoted by t*, in home country, with t* = q * - p , or
where t~ denotes the tax on good 1 and t is an ( N - 1 ) - v e c t o r of taxes. Similarly, for the foreign country. The production sectors are characterised by the profit functions ~'(p*) and Fl(p*) for the home and foreign country respectively. We assume perfect competition with decreasing returns to scale. On efficiency grounds, income from immobile and inelastically supplied factors of production is taxed at a 100 per cent. We also assume that one good is internationally mobile with a variable supply res~aonse; for example, labour that the consumer may sell home or abroad. We indicate the derivatives with respect to P0 and p~ by the subscripts 0 and 1 respectively, and the vector of derivatives with respect to prices of the N-1 private goods by the subscript /~ and q or Q as appropriate. Then assuming an equilibrium exists, we can write the market-clearing conditions for both countries taken together as
eq.( q*, r, u) + E e . ( Q * , R, U) - z g ( p * ) - He(p*) = ON
(2.2)
r + R = 7ro(p* ) + / / o ( P * ) •
(2.3)
and
The N market-clearing equations (2.2) represent the world market clearing conditions for all private goods and equation (2.3) for the public good. The home demand function eq.(q*, r, u) is partitioned into e 1 and the ( N - 1)-vector eq. The home supply function ~rp.(p*) is partitioned into 7r0 5This is without loss of generality since specific and ad vaiorem taxes are equivalent under perfect competition. 6Note that public sector's purchases of public good are untaxed. 7Mintz and Tulkens (1986) make the same assumption in a similar context. One can interpret labour services performed abroad as importation of leisure by the foreign country.
s. Delipalla / Journal of Public Economics 63 (1997) 447-466
451
and ~rp, with rrp further partitioned into ,r~ and the ( N - 1)-vector ~r#. The budget constraints of the private sector, are e ( q * , r, u) = - p o b
(2.4)
E ( Q * , R, U ) = po b ,
(2.5)
and
where b is a scalar denoting transfers between consumers of good O from h o m e to foreign country. It proves useful for later purposes to point out that it is important whether the international transfers are transfers between individuals or transfers between governments. Therefore, to develop some intuition, we use here both kind of transfers. Denoting by /3 the government transfer from h o m e to foreign country, and with prime denoting transposition, the budget constraints of the public sector in each country are po r = t*' eq.( q*, r, u) + ~r(p* ) - Po/3
(2.6)
po R = T * ' E e . ( Q * , R, U ) + H ( p * ) + Po/3 ,
(2.7)
and
that is, the governments raise revenue through commodity and rent taxation to finance the public good provision. We assume that 100% rent taxation is not enough to finance the public good provision and that any lump sum transfer between the government and the consumers is ruled out. ~ The system of equations (2.2)-(2.7) is separately homogeneous in p* and q*. Since the supply function is homogeneous (of degree zero) in producer prices and the demand function is homogeneous (of degree zero) in consumer prices alone in absence of income, one can normalise by fixing one producer price and one consumer price. Note that transfers b and/3 are considered as exogenous. Then, the revenue constraint is h o m o g e n e o u s (of degree zero) in prices alone, as well. Thus, it will not be restrictive to impose that one of the prices is predetermined, so set P0 = PG, where P c is fixed, and one good is untaxed, say t~ = 0. G o o d 1 is the arbitrarily untaxed good in both countries. 9 8 In the model there are only two purchasers of the public good, the two governments. However, they cannot make any use of their duopsony power. The demand of public good is determined by the budget constraints of the governments and there are no lump sum transfers between government and consumers. If such transfers were allowed, each government would be able to use its duopsony power by optimally allocating resources between consumers and itself. This observation is due to a referee. 9 By assuming 100% profit taxation, we gain an additional normalisation. See Auerbach (1985) for a discussion on numeraires and untaxed commodities. Note that we do not set Pc = 1, because it proves helpful for some intuition to have Pc in formulae.
452
s. Delipalla / Journal of Public Economics 63 (1997) 447-466
By Walras law, we can drop one equation as being implied by the rest; we drop the market-clearing equation for commodity 1. The system then becomes e q( q*, r, u) + E Q ( Q * , R , U ) - rr¢(p*) - I I p ( p * ) = ON_ 1
(2.8)
r + R = 1to(p* ) + H o ( p * )
(2.9)
e ( q * , r, u) = - p ~ b
(2.10)
E(Q*, R, U) = pcb
(2.11)
pG r = t ' e q ( q * , r, u) + 7r(p*) --Pal3 = t'x + 7r --PG/3
(2.12)
pGR=T'Eo(Q*,R,U)+H(p*)+pG/3=T'X+H+pc;/3,
(2.13)
where x = eq(q*, r, u) and X = E o ( Q * , R , U ) . The above system has N + 4 equations to solve for N + 4 unknowns (N relative prices p and u, U, r, R) given the two (N - 1)-vectors of taxes (t, T) and lump sum transfers b and/3. We assume that a solution with qi > 0 for all private goods exists, and in the next section we examine how changes in the policy instruments affect the equilibrium conditions.
3. Comparative statics To derive the welfare consequences of tax changes, we consider now a commodity tax reform {dt, dT} combined with transfer reforms db and d/3. Taking total differentials in the consumer's budget constraint (2.10), and using (2.1) and dt I = 0, we have: e . du
=
-
e'q .
(3.1)
dp - x ' dt - e r dr - p a db ,
where e. is the inverse of marginal utility of income and e r < 0 is the marginal rate of substitution (MRS) between the public good and lump sum income. Without loss of generality, we normalize the marginal utility of income in the initial equilibrium at unity, that is e u = 1. Perturbing the revenue constraint (2.12), recalling dp0 = 0, PG dr = t' dx + x' dt + Irp dp - P c d/3.
(3.2)
Substituting for x' dt in (3.1) using (3.2), and denoting by m* the vector of imports of private goods for the home country, that is, m* eq. - 77"p, we have =
du = - m * ' dp + t' dx - (PG + er) dr - p G ( d b + d/3).
(3.3)
Equation (3.3) shows that the effect on home welfare of an arbitrary tax
S, Delipalla / Journal of Public Economics 63 (1997) 447-466
453
reform consists of three terms. The first is the effect on the terms of trade: home country's terms of trade improve if, in the face of a slight change in the tax vector, the initial import vector (m*) is cheaper at the new world prices than at the old, that is, if m*' dp < 0 . The second term is the change in the deadweight loss (first order effect) resulting from marginal commodity tax changes; this is beneficial if the tax reform reduces the distortionary effect on the demand of the initial tax structure. The third term relates to the deviation of the public good provision from that implied by the Samuelson rule. In the present context, the Samuelson rule simply requires that Pc = -e~. Note that here the Samuelson rule is not generally optimal. The public good provision is financed by distortionary taxation and, moreover, our economy is not a closed one (see section 4 for more detail on this point). To evaluate tax reforms, we now need to relate the change in welfare, du and dU, directly to changes in tax instruments. To simplify the analysis, which becomes notationally very complex and unpleasantly difficult to conclude otherwise, we assume first that there are no income effects for the N - 1 taxed commodities; that is, good 1 picks up all the income effects 1° a n d equ = EQU = ON_ 1. Second, we assume that the demand for the N - 1 private goods is independent of the public good provision, that is, eqr = EQR = ON_ 1. After this simplification, we perturb the equilibrium conditions to derive an expression for the change in world prices and tax revenues in terms of the policy instruments. First, we perturb the market-clearing condition for the private goods (equation (2.8)). Using q* = p + t*, dt 1 = 0 and dp0 = 0, and introducing the d e f i n i t i o n [eql ]eqq] = eqq. and [7r~1 ] ~-~] = 7r~p, we get eqq dt + EQQ d T = (Tr¢p + H~p - eqq. -- EQQ,) d p .
(3.4)
Note that eqq and E o o are ( N - 1 ) x ( N - 1 ) matrices and eqq., EOQ. , "lr~p and II~p are [ ( N - 1 ) x N] matrices. Now perturbing the market-clearing condition for the public good (equation (2.9)), and recalling dp0 = 0, we have dr + d R = (Trop + Hop ) d p .
(3.5)
From the revenue constraint for the home country, equation (2.12), using (2.1) and recalling that dti = 0 and dp0 = 0, Pa dr = (e'q + t' e qq) dt + (Trp + t' e qq. ) dp - Pa dfl .
(3.6)
Using (3.6) and the analogue for the foreign country in expression (3.5), we obtain ~°This is an assumption used by Keen (1989, p. 5).
454
S. Delipalla / Journal of Public Economics 63 (1997) 447-466 (e'q + t'eqq) dt + (E6 + T'EoQ ) d T = [pG(Trop + Hop )
- (Tr'p + t'eqq. + 1I~ + T'EQQ.)] d p .
(3.7)
Stacking (3.7) and (3.4) together one gets
Ie'q + t'eqq] [ g ' e + T'Eo.o.]. L " ' e q ; " ' j d, + I d r = a dp
(3.8)
where
[pG(Trop + H~p)-'rr'p-t'eqq.-_Fl'p- T'EQQ.] A = ~_. . . . . . . . ~r:'p""q-'Hl3;"--'eqq'."--'f_,Q;'." . . . . . . . . ?
(3.9)
is an (N x N) matrix. Before we proceed, we need to consider matrix A more closely. For analytical convenience, we rewrite it as
(3.10)
A= [Azl:A22 j where, making use of (2.2), A 11 = P o ( % l A12
+//Ol) -
t
t'eql -- T ' E o l - el - E1 ,
t
¢
= pa(Tr0p + Hop ) - t eqq
__
¢
t
T'Ef)Q - eq - E o ,
(3.11) (3.12)
m21 = ~pl +//pl
- eql -
Eol ,
(3.13)
A 2 2 = 7rpp + / / p p
- eqq -
EOO .
(3.14)
We assume A to be non-singular and obtain"
(3.15)
A - l = [ nil i B12] where Bll
~ (All
B12 = -A
-- A12A;21A21)
-1 ,
;11A12(A22 - A21A
B21 = -A2-21A21nll
?11A12) - I ,
,
B22 = (A22 - A21A~11A12) -l . With
A -1
given by (3.15)-(3.19), expression (3.8) implies
11See Dhrymes (1978) for basic operations with partitioned matrices.
(3.16) (3.17)
(3.18) (3.19)
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
e'q + t'eqq EQ + T'EQQ dp= a-'{['"'e'q'q"-] dt + [ .... E'o-Q.... ] d T } .
455 (3.20)
Finally, substituting for dr and dp in (3.1), using (3.6) and (3.20), we obtain the following expression for the effect of an arbitrary tax reform on home welfare: du=-
{
er [ G , ] e'q+~-~(e'q+t'eqq)+ eq,'+~-~(%+t'eqq.) A-'
×[eq+t'eqq]~dt
I_e~q-- j j e q.
xdr-pc
PG (Tr'p +
qq, j
L . . . . EQ-Q''''~
( db + Pae, dE 1 .
(3.21)
Equation (3.21) and the analogue for the foreign country relate the welfare effects directly to the policy instruments, taxes and international transfers, and serve as a basis for the succeeding analysis.
4. Optimal commodity taxation and public good provision
We assume in this section that each country chooses its commodity taxes-and hence, through its revenue constraint, the level of the public good provision - so as to maximise its own national welfare, taking the other country's taxes as given. Then, commodity taxes are optimal, from the point of view of the country though not necessarily of the world as a whole, if the coefficient of dt in expression (3.21) is equal to zero. Thus, the ( N - 1 ) conditions that characterise the optimal commodity taxes in home country are e ' e'q+~(e'q+teqq)
=-
[ ' er eq.+~(vr'p+
I eqq,) ] A 1 [ e'q + t'eqq ] ' L---~;q--- j
(4.1) Collecting terms in (4.1) and post-multiplying by t, gives er[
Pc
,
(e'qt+t'eqqt)+(Tr'p+teqq,)A
[fe'qt
1[
, -1 [e'qt + t'eqqt] ] +eq,A [''"edqt''"J~"
y~!+t'eqqt
G
]~
JJ (4.2)
456
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
The analogue of (4.2) holds for the foreign country. Then follows Proposition 1: When the home country sets its commodity taxes and thus the " public good provision optimally, the condition that characterizes the optimal public good provision in an open economy is ol M R T = -~ M R S
(4.3)
where a = e'qt+teqqt+(Tr;+ ' t 'eqq.)A -1[[ 'e'qt+t'eqqt] ' " d q q t " " J and
A =e'qt + e;,A ,[e'qt + t'eqqt] i---G-c-- ] • We must stress that condition (4.3) characterizes the optimal public good provision under certain assumptions: there are no income effects and demand for taxed goods is independent of public good provision. Under these conditions, a special case of a well known result in public finance literature is that MRS must exceed MRT at an optimum (see Atkinson and Stern (1976), Browning (1976), Wildasin (1979)). But does this result hold when we hove an open economy? Condition (4.3) shows that following the Samuelson rule, incorrectly, would not necessarily lead to oversupply of the public good; it could lead to undersupply. What might reverse the conclusion drawn in the case of a closed (or a small open) economy 12 is that, now, financing an extra unit of public good by commodity taxation has an additional effect: a change in the tax rates affects the terms of trade through the change in world prices. If the terms of trade improve "enough" to outweigh the (negative) deadweight loss effect, Samuelson rule may underestimate the benefits of an extra unit of public good provided. We must stress though that we find hard to believe that the Member countries in the EU follow the rule given by (4.3), that is, that they are at a nationalistic optimum. This section's purpose was to help us with our intuition for the results that follow by showing that the Samuelson rule is not generally optimal in an open economy with distortionary taxation. Having established this, we proceed, in the next section, to the analysis of tax harmonisation and its welfare effects focusing on the case considered by Keen (1987), that is, starting from an arbitrary tax equilibrium, 12See Delipalla (1994) for a discussion on optimal public good provision in a small open economy.
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
457
5. Commodity tax reform from an arbitrary tax distorted equilibrium In this section we examine the effects of commodity tax harmonisation on welfare. We consider the reform dT
H-
,]
T
(5.1)
'
where H = (eqq + E o o ) - l ( e q q t + E o o T ) ,
(5.2)
a reform familiar from Keen (1987, 1989). Reform (5.1) requires both countries to converge towards the common target H, which is a loose interpretation of a weighted average of initial tax structures of the kind proposed by the European Commission. If eqq = EQQ, that is, the home and the foreign country face the same demand responses, it is simply the arithmetic mean of the initial tax rates. Let us examine now the effect of a small move of both taxes, t and T, towards H. Using (5.2) in expression (5.1), one gets
dt = (eqq q- EQQ)-l(eqqt + EQQT ) - t = (eqq d- EOQ)-IEQQ(T -- t)
(5.3)
d Z = - (eqq + Eao)-leqq(T - t ) .
(5.4)
and
Define -1
1 -1
S = eqq(eqq + E Q Q ) - I E Q Q = [eqq (eqq + EQQ)EQQ] = EQQ(eqq + E Q Q ) - l e q q .
(5.5)
Note S is a negative definite matrix since both eqq and EQQ a r e negative definite matrices, a3 Then making use of (5.5), we can easily see from (5.3) and (5.4) that for this particular reform
eqq dt + EQO d T = 0.
(5.6)
In Keen (1987, 1989) the harmonisation reform (5.1)-(5.2) ensures that harmonisation has no effect on total demand so that world prices are unaffected. Here tax revenue is not returned to the consumer as a lump sum; instead, it finances the public good provision. Thus, when taxes change, it is not only the change in total demand that matters but also the 13 It is assumed that there is enough substitutability in demand between the taxed goods and the untaxed (private) good so that eqq and EeQ are negative definite: see Dixit and Norman (1980), p. 130.
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
458
change in tax revenue and the implied change in the level of public good provided. Hence, the question is, would the result of Keen (1987) still hold in a more realistic setting when countries face binding constraints on the tax revenue required? For further analysis, using the particular feature (5.6) of the harmonisation reform, it is helpful to rewrite (3.21) as
e r "x , l+-~-~G)(e q +t'eqq)dt+t'eqqdt
du=- -
[ 'eq. + - -er t )1 -1 P G ( TI'p"k-t qq, A '
×[(e;+t'eqq)dt+(EQ+T'gQQ)DT]
-
-
( db
PG
(5.7)
Let us now call a reform "conditionally revenue neutral" if it is revenue neutral at constant p. That is, for the world as a whole,
(e'q + t'eqq) dt + (E~ + T'EQQ) dT = 0.
(5.8)
When this holds, from (3.20) the reform (5.1)-(5.2) implies dp = 0. With world prices constant, profit tax revenue is also unaffected. Since a conditionally revenue neutral reform implies that dp = 0 , conditional revenue neutrality here is sufficient for unconditional revenue neutrality. Then,
Proposition 2. Commodity tax harmonisation in the sense o f (5.1)-(5.2) is potentially improving if (i) it is conditionally revenue neutral for the worm as a whole, and (ii) both transfers between governments and transfers between individuals can be deployed. Proof: Using (5.8) and (5.6), expression (3.21) becomes
du=-{e'q+
er-~c(eq'+teqq)}dt-pG(db'
er
+ ~--~d/3) .
(5.9)
Using the analogue for the foreign country and choosing d/3 to leave utility in foreign country unchanged,
E R dfl = E ~ d T -
ER Pc (e'q + t'eqq) dt - P c d b ,
(5.10)
where use has been made of (5.8). Multiplying (5.10) by e,/E R, and then using it to substitute for e, d/3 in (5.9), expression (5.9) becomes
S. Delipalla / Journal o f Public Economics 63 (1997) 447-466
d u = - e ' q d t - E o d'T +
(e-~n) -1
(padb-E~dT).
459
(5.11)
Finally, it is easy to see that if we set Pc db = E~ dT, and make use of assumption (5.8), expression (5.11) becomes
du = t'eqq dt + T'EQo d T .
(5.12)
Using (5.3) and (5.4) and definition (5.5),
du = - ( T - t ) S ( T - t),
(5.13)
which is positive. QED. It is interesting that, according to Proposition 2, we have to be able to use both types of transfers for harmonisation to be potentially Pareto improving. Transfers between governments are needed to ensure that tax revenue is constant in both countries and transfers between individuals are needed to ensure that gain from reduced consumption inefficiency goes to both individuals. But what can one say when harmonisation is conditionally revenue neutral for the world as a whole and we can only use one kind of transfers? We look first at the case where only transfers between individuals are available, that is, set d/3 = 0. Then
Proposition 3. Suppose that only transfers between individuals can be deployed. Then, commodity tax harmonisation in the sense of (5.1)-(5.2)/s strictly potentially improving if (i) it is conditionally revenue neutral for the worm as a whole, and (ii) it conditionally increases revenue in whichever country has higher Marginal Social Cost of Public Funds (MSCPF). Proof. Since (5.8) combined with (5.6) imply dp = 0 , expression (5.7) becomes du .
. 1. + . P6
eq +
t'eqq) dt + t'eqq dt - P c db.
(5.14)
Then using its foreign analogue and defining db to leave utility in foreign country unchanged, (5.14) becomes
du = +
(er) (p~) 1 +-~a (e'q+ t'eqq) d t - 1 +
(E~ + T'EQQ) dT
t'eqq dt + T'EQQ d T .
Making use of (5.8), expression (5.15) becomes
(5.15)
460
S. Delipalla / Journal o f Public Economics 63 (1997) 447-466
du = -
(er
P-~c
E_~)
(eq -~ t'eqq) dt + t'eqq dt + T'EQQ d T
= (MSCPF h - MSCPFf)(e'q + t'eqq) dt + t'eqq dt + T'EQo d T , (5.16) where with MSCPF h and MSCPF: we denote the Marginal Social Cost of Public Funds for home and foreign country respectively. Since t'eqq dt + T'EQQ dT > 0, the result follows from assumption (ii). QED. Since the only available transfers now are transfers between individuals, conditional revenue neutrality for the world as a whole cannot ensure revenue neutrality for each country. Then harmonisation is potentially improving if r e v e n u e - and hence the level of public good provisionincreases in the country of the individual with the higher marginal valuation of the public good. Then, the transfers between individuals are needed to ensure that both individuals gain. If we now assume that can only use transfers between governments, that is, set db = 0, then,
Proposition 4. Suppose that only transfers between governments can be deployed. Then, commodity tax harmonisation in the sense of (5.1)-(5.2) is potentially improving if (i) it is conditionally revenue neutral for the worm as a whole, and (ii) it increases revenue at unchanged behaviour in whichever country has higher Marginal Social Cost of Public Funds (MSCPF). Proof. Recall from Proposition 2 that, setting d/3 so that foreign utility is unchanged, the effect on home welfare is given by (5.11). Setting db = 0 in (5.11), and using (5.8) then gives er \
,
d u = t 'eqq dt + T'EQQdT + 1----E~n)EQdT.
(5.17)
Since the sum of the first two terms is positive, home welfare increases if E~ d T > 0 and E R > er, that is, revenue rises at unchanged behaviour in the country with the highest MSCPF. QED. Note that when only transfers between individuals can be used, for harmonisation to be potentially Pareto improving we need conditional revenue increase in the country with the highest MSCPF; Proposition 3. When only transfers between governments can be used, we need an increase in revenue at unchanged behaviour in whichever country has the highest MSCPF. The reason is simple. In the first case government transfers are not
S, Delipalla / Journal of Public Economics 63 (1997) 447-466
461
available and it is important that the revenue effect will not be detrimental in both countries. Note that here the revenue effect depends on both the tax rate change (x' dt) and the effect on the consumer demand for taxed goods (t' dx). In the second case, government transfers are available so we need not worry about the revenue effect in each country. But with no individual transfers available, harmonisation is potentially Pareto improving if it increases taxes for the consumer with the higher marginal valuation of public good. Note that a necessary condition for conditional revenue neutrality to hold, given the Keen reform, is that e'q dt + E~) dT < 0, that is, global revenue at unchanged behaviour falls (since t' e qq d t + T'Eoo dT > 0). The Commission's 1985 proposals suggesting that the harmonising reforms would be more or less revenue neutral (with the exception of Denmark and Ireland) were based on the arbitrary assumption that there would be no change in the demand patterns. 14 Proposition 5 below suggests that revenue neutrality at unchanged behaviour is not sufficient for harmonisation to be potentially Pareto improving. A harmonising reform which is world revenue neutral at unchanged behaviour, that is, r
t
e q dt + E o d T = 0,
(5.18)
can be strictly potentially improving only when certain conditions hold. Defining A* = A +
I.t'eqq. + T'EQQ,] . . . . -0~-_-1. . . . . i
t
t
=
[
A2t
:
A22
] '
(5.19)
we have
Proposition 5. Suppose either kind of transfers (or both) can be deployed. Then, commodity tax harmonisation in the sense of (5.1)-(5.2) is potentially improving if (i) harmonisation is revenue neutral at unchanged behaviour, (ii) public good provision follows the Samuelson rule in both countries, and (iii) Det(A*) has same sign as Det(A). Proof: It is shown in the Appendix that ~4See, for example, Lee, Pearson and Smith (1988) for the effects of the 1985 proposed tax changes on the UK household spendings.
462
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
Det(A*)- Det(A), ,
du . . . . Det(A) .
[eq at + E~ dT)
Det(A*) + Det(A) (t'eqq dt + T'EQo d T ) .
(5.20)
Assuming harmonisation is revenue neutral at unchanged behaviour, the first term on the right-hand side vanishes. Therefore, recalling that t'eqq dt+ T'EQo dT > 0, global welfare increases as long as Det(A*) has the same sign as Det(A). QED. Equation (5.20), has a nice interpretation, showing the welfare effects of harmonisation to be a weighted average of the revenue effect with no behavioural response (e'qdt+ E~ dT), as calculated by the Commission, and the deadweight loss effect (t'eqq dt + T'EQe dT). Condition (i) here captures exactly the form of European Commission's 1985 proposals: tax changes will not lead to changes in the demand patterns. But revenue neutrality at unchanged behaviour (at both national and global levels) is not sufficient for the harmonising reform to be potentially Pareto improving. Even if we assume that the governments follow the Samuelson rule, since there is no a priori reason to assume that EU Member States follow the rules of optimal taxation, condition (iii) has to be satisfied as well.
6. Conclusions
In this paper, we have been interested in examining how robust the results in Keen (1987) are to the recognition that tax revenue is spent rather than returned to the consumer as a lump sum. The analysis shows that, if we assume conditional revenue neutrality, that is, revenue unchanged at constant world prices, for the world as a whole, harmonisation is potentially Pareto improving if we can use both transfers between consumers and transfers between governments (Proposition 2). Transfers between governments are needed to ensure that no country loses in revenue, leaving its public spending unaffected. Transfers between consumers then guarantee that both consumers benefit from the more efficient reallocation of consumption. When only consumer transfers are possible, harmonisation is welfare improving if it is not only conditionally revenue neutral for the world as a whole but it also conditionally increases revenue in whichever country has the higher MSCPF (Proposition 3). The last condition is needed to ensure that efficient reallocation of public goods takes place: from the low marginal valuation consumer to the high marginal valuation consumer. When only government transfers are available, and conditional revenue
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
463
neutrality for the world as a whole holds, then harmonisation is potentially improving when it increases revenue at unchanged behaviour in the country with the higher MSCPF (Proposition 4). Since government transfers can be deployed, there is no need to worry here about the revenue changes in each country. However, since transfers between individuals can not be used, we must ensure that taxes increases for the consumer with the highest marginal valuation of the public good. Thus, two points emerge here. First, as it was expected, it is unlikely to find very general conditions under which Pareto improving reforms are possible. Second, and more interestingly (since it has never been recognised in the tax reform literature before), the two kinds of transfers have different implications. Therefore, any arguments that rely on international transfers should be handled with care. 15 A well known criticism of this analysis is the need to use compensation transfers for an actual Pareto improvement. The Pareto principle cannot be used as a criterion for social choices in most real-world situations where policy changes produce both gainers and losers. In such cases one may apply the compensation principles suggested by Hicks (1939) and Kaldor (1939). This principle does not require the actual payment of compensation, otherwise it would satisfy the Pareto criterion. Of course, by considering hypothetical compensation we focus on the efficiency aspects of the policy change. Whether or not a transfer is actually carried out is considered to be an important but separate issue.16
Acknowledgements I am grateful to Mick Keen for his detailed comments and suggestions. I also thank Sajal Lahiri, Gareth Myles and Miguel-Angel Loprz Garcia, as well as an anonymous referee, for their comments. Remaining errors are mine.
Appendix Derivation of (5.20): Using (3.15) and (5.6), we write (3.20) as 15 An example of transfer between consumers could be repatriation of income to the migrant's family in the country of origin. t6 Note that there already exists a central institution in the Community with a budget for structural funds (see, for example, Structural Funds: 1992 Report, COM(93) 530).
464
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
dp=
B~i, B~2
[:
(%
][+ .
= ~, L B : , j
.
.
.
t eqq)dt .
.
.
.
.
.
.
.
7" Eoo ) d r
(E o
++ .
.
.
.
.
.
.
.
.
.
.
.
.
t
'
where y = (e'q + t'eqq) dt + (E~ + T'EQo ) d T .
(A.2)
Then, (3.21) becomes ,
du-y[e'q.-Trp-t
rBlll
eqq.]~-B2-] +t'eqq d t - p a ( d b - d # ) .
(A.3)
Then using the analogue for the foreign country, and defining db and d/3 to leave foreign utility unaffected, recalling that by assumption PG = - e , = E R, (A.3) becomes . . . . . [BIll du = -y[ea, + EQ. - 7rp - l l e -,'eqq. - T EQo.] [ ~ i - ] + t'eqq dt + T'E~2 Q d T .
(A.4)
Making use of the market-clearing condition (2.2), and partitioning [e ql ]eqq] = eqq., expression (A.4) gives d=y[t'eql + T'EQllt'eqq + T'EQQ][-B-1)-I LBzl j + t ,eqq dt + T'EQQ d T .
(A.5) Now using (3.11) and (3.12), one gets du=-T[All
[Bll1 Zlz][-/~2; j
+ T[Pc(~'o, +//Ol) - e, - E, Ipc(Tro# +//0#) - eq - E~]
[Bill
× [_Bzl] + t'eqq dt + T'EoQ d T . By definition FBtll
tAll ]AI2][-jD~; j = 1. So, using this and (3.18),
(A.6)
S. Delipalla / Journal of Public Economics 63 (l.997) 447-466
465
du = -3' + YBll[Pa(ZCol + 11ol) - el - Ei Jpa(Tro~ + Hop)
-- eq -- E~] "__
,
+ t eqq dt + T'EQo d T .
(A.7)
Using the definition of "y and combining terms, we have du = - (e'q dt + E 6 dT) + 7Blx[pa(Tro, + 11Ol)
- e 1 - E1[ pc(qro# +11o#) - e'q - E ~ l [ - - - ~ 1 q ~ :[] .
(A.8)
To derive a more neat expression for the last term on the right-hand side of (A~8), using the standard formula for calculating determinants (see, for example, Dhrymes (1978), p. 459, Proposition 32), expression (5.19) gives Det(A*) ~ Det(A22){pc(Trol + 1101) - - e~ - E 1 - [pG(~r0~ + H0~) - e'q - E ~ ] A ; ) A 2 , ) .
(A.9)
Using (A.9) in (A.8): Det(A*)
du = - (e'q dt + E ~ dT) + 3'B,a Det(A22) .
(A.10)
From (3.10), Det(A) = Det(A22)(A 11 - A12A2?A21 ) .
(A.11)
Since (A.11) and (3.16) imply Bll-
Det(A22) Det(A) '
then Det(A*) du = - (e'q dt + E ~ dT) + 7 Det(A)
Finally, using the definition of 7, we can write this as d/A =
Det(A*) - Det(A) Oet(A) (e'q dt + E ~ dT) Det(A*) + Det(A) (t'eqq dt + T'EQQ d T ) ,
which is (5.20) in the text.
(A.12)
466
S. Delipalla / Journal of Public Economics 63 (1997) 447-466
References Atkinson, A.B. and N.H. Stern, 1974, Pigou, taxation and public goods, Review of Economic Studies 41, 119-128. Auerbach, A.J., 1985, The theory of excess burden and optimal taxation, in: A. Auerbach and M.S. Feldstein, eds., Handbook of Public Economics, Vol. 1, 61-127. Browning, E.K., 1976, The marginal cost of public funds, Journal of Political Economy 84, 283-298. Commission of the European Communities, 1993, Structural Funds: 1992 Report, COM(93), 530 (Brussels). Delipalla, S., 1994, Commodity tax harmonisation and public goods, Working paper 94-17, University of Wales Swansea. Dhrymes, P.J., 1978, Mathematics for Econometrics (Springer-Verlag, New York). Dixit, A.K. and V. Norman 1980, Theory of International Trade (Cambridge University Press). Haufler, A., 1993, Public goods, international trade, and tax competition, in Commodity Tax Harmonization in the European Community (Physica Verlag, Heidelberg). Hicks, J.R., 1939, The foundation of welfare economics, Economic Journal 49, 696-712. Kaldor, N., 1939, Welfare propositions of economics and interpersonal comparisons of utility, Economic Journal 49, 549-552. Kanbur, R. and M.J. Keen, 1993, Jeux sans fronti6res: Tax competition and tax coordination when countries differ in size, American Economic Review 83, 877-892. Keen, M.J., 1987, Welfare effects of commodity tax harmonisation, Journal of Public Economics 33, 107-14. Keen, M.J., 1989, Pareto-improving indirect tax harmonisation, European Economic Review 33, 1-12. Keen, M.J. and S. Lahiri, 1993, Domestic tax reform and international oligopoly, Journal of Public Economics 51, 55-74. Lahiri, S. and P. Raimondos, 1995, Public good provision and the welfare effects of indirect tax harmonisation, Discussion paper, University of Essex. Lockwood, B., 1995, Commodity tax harmonisation with public g o o d s - A n alternative perspective, Discussion paper, University of Exeter. Lee, C., M. Pearson and S. Smith, 1988, Fiscal harmonisation: An analysis of the Commission's proposals, IFS Report Series 28. Lop6z-Garcia, M., 1996, The origin principle and the welfare gains from indirect tax harmonisation, International Tax and Public Finance 3, 83-93. Mintz, J. and H. Tulkens, 1986, Commodity tax competition between member states of a federation: equilibrium and efficiency, Journal of Public Economics, 29, 133-172. Pigou, A.C., 1947, A study in Public Finance (Macmillan). Sinn, H-W, 1990, Tax harmonization and tax competition in Europe, European Economic Review 34, 489-504. Turunen-Red, A.H. and A.D. Woodland, 1990, Multilateral reforms of domestic taxes, Oxford Economic Papers 42, 160-186. Wildasin, D.E., 1979, Public good provision with optimal and non-optimal commodity taxation, Economics Letters 4, 59-64.