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Optimal trade taxes in the presence of foreign ownership and equity exchanges
Journal
of International
Economics
36 (1994) 483-500.
North-Holland
Optimal trade taxes in the presence of foreign ownership and equity exchanges Shumpei
Takemori
and Masatoshi
Tsumagari”
Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, 108 Tokyo, Japan Received
February
1992, revised version
received
May 1993
This paper investigates the question of the optimal trade policies in the presence of foreign ownership, extending the framework of the pioneering studies by Brecher and Bhagwati. Trade in the ownership claims is explicitly modelled using a stochastic trade model. The paper concludes that the results of the above studies crucially depend on the policy not being expected at the time foreign investment takes place. Key words: Optimal
trade policy; Foreign
ownership
JEL classification: F 13
1. Introduction
Seminal works by Bhagwati and Brecher (1980) and Brecher and Bhagwati (1981) correctly point out that many standard normative propositions of trade theory are seriously challenged in the presence of foreign ownership in the domestic economy. We further investigate into this question, focusing on the issue of the optimal trade policy. Specifically, we extend their framework in one important aspect: instead of taking the presence of foreign ownership as a ‘fait accompli’, as in their studies, we explicitly model a trade in ownership claim which determines it. This extended framework, which incorporates two types of trade, enables us to study a policy question which is left out by their 1981 paper; namely, how a trade policy implemented by a country affects its welfare if the policy intention is revealed before the trade in ownership claims takes place. (We henceforth refer to this paper as B-B.) The model that we set out is the simplest stochastic model, which Correspondence to: S. Takemori, Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, 108 Tokyo, Japan. *We are grateful to Peter Petri for providing insights into our results. We also thank Eric Bond, Fumio Dei, Ron Jones, and Michihiro Ohyama for helpful comments. We are also grateful to the two anonymous referees for pointing out serious mistakes in an earlier draft and for their suggestions with regard to the organization of the paper. Naturally all errors are ours. The present study has benefited from the financial assistance of the Nomura Investment Trust Memorial Fund. 0022-1996/94/$07.00 0 1994 Elsevier SSDI 0022-1996(93)01300-4
Science
B.V. All rights
reserved
484
S. Takemori
and M. Tsumagari,
Optimal trade taxes
generates international trade in commodities and ownership claims, and is basically similar to those studied by Helpman and Razin (1978). There are two countries in the world, which produce two types of goods. The production level of one of these goods is constant and that of the other depends only on whether the country is in a good or bad state. However, since the agents of each country know the probability of the occurrence of these states, and at the worldwide level the randomness is idiosyncratic, they may pool away risks by an asset trade. The type of asset we assume is a firm’s equity, which entitles its owners to receive dividends when the product of the firm is sold at the market. There is an interval between the time at which the equity trade takes place and the time at which the commodity trade takes place. Since a trade policy has its effect only concurrently with the commodity trade, each agent must form an expectation on future trade policy and its effects at the time he participates in the equity trade. Under this setting we contrast the effects of the following two types of trade policies. (a) A trade policy that is not anticipated by agents at the time they participate in the equity trade. (This type of policy, which is henceforth called an ex post trade policy, is the one studied by B-B.) (b) A trade policy that is announced to agents prior to their participation in the equity trade. (This type of trade policy is henceforth called an ex ante trade policy.) Our main contributions are as follows: (1) In the case of an ex post trade policy, we reinterpret the results of B-B by deriving a slightly different formula of welfare change. The source of their paradoxical result, the optimality of an import subsidy, is revealed in this formula as the transfer of surplus that an import subsidy generates between domestic consumers and foreign equity holders: an import subsidy that depresses the domestic price below the level of the foreign price exploits foreign interests in the domestic industry to the benefit of home consumers. We also show that this same force makes the effect of an export subsidy even more adverse. (2) In the case of an ex ante trade policy, we show that the transfer of surplus described above is totally offset by an adverse movement in the equity terms of trade: reflecting the fall in return caused by an import subsidy, the price of the home assets falls, to the detriment of the home country. The case for an import subsidy is therefore diminished. This result suggests that the conclusions of B-B for commercial policy in the presence of foreign ownership depend crucially on the policy not being expected at the time foreign investment takes place. The organization of our paper is as follows. In section 2 we present our model and characterize the world equilibrium under perfect free trade. In section 3 we investigate the question of ex post optimal trade taxes. The question of ex ante optimal trade taxes is dealt with in section 4. Section 5 concludes our paper.
S. Takemori
and M. Tsumagari,
Optimal trade taxes
485
2. The model There are two countries, home and foreign, two commodities, X and Y and two periods, period 0 and period 1. In period 1, the two countries obtain the outputs of the two commodities, produced by numerous firms. (We assume that each firm produces only one type of commodity). The factors that produce these commodities are already sunk in the production process, so that only an exogenous productivity shock can cause a change in the production levels. The output of Y is fixed for the two countries. (There is no uncertainty involved in the production of Y) Let Y and Y*, respectively, be the outputs of Y in the home and foreign countries. (We henceforth denote by an asterisk the variables of the foreign country.) Define Y,=Y+Y*,
8, = YIYW,
as the total world output of Y and the home country’s production share. In the following analysis we fix Yw and take B, as a parameter. There is a country-specific stochasticity in the production of X: factors that produce X are sunk, but their productivity levels depend on the state in which a country finds itself. There are two states of the world, states 1 and 2, which have equal probability of occurrence, l/2. The outputs of X in these states take the following forms:
x,=x:,
x, = XT,
x, >x,,
in which Xi (XT) is the home (foreign) x,=x,+x,*,
output
px, =X,/X,,
(1) of X in state i. Let
i= 1,2,
be the world total output of X and the home country’s share of production. From (1) Xw is constant and bx, + bx2 = 1. In period 0, the output level of X is unknown to the agents. They know, however, the output level in each state, namely (l), as well as the probability of occurrence of these states. We assume that consumers’ preferences in the two countries can be represented by the same concave and homothetic utility function:
v = V[C(D,,
D,)],
V’ > 0, V” < 0,
(2)
in which D, and D, represent the consumption of commodities X and I: and C( .) is a linear homogeneous function which represents the real income of a country. CC(.) is henceforth called a real income function.] There are two types of trade in this economy. One is trade in equities, which takes place in period 0. Initially, the equities of firms that produce X and Y are owned by domestic agents. There is, however, an opportunity for
486
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agents of both countries to smooth out country-specific shocks by engaging in trade in the equities of firms that produce the risky product, X. This trade takes place in the following way: the agents of each country sell on the world equity market the equities of the domestic firms which they own at the beginning, and use the proceeds to buy the equivalent values of equities in foreign firms. The trade in equities must therefore fulfill the following wealth constraint:
4(1-%)=Q,,
(3)
in which 0,, represents the equities of the home firms owned by the home agents after the trade and 9r the equities of the foreign firms which they have purchased. (We normalize the total number of equities to be 1 for both home and foreign firms.) q is the relative price of the home equities, which is defined by taking the price of the foreign equity to be 1. The ownership of an equity in a firm entitles its owner to receive a cash dividend in period 1, when the state is realized and the output is sold on the world commodity market.’ Let P be the world price of X in terms of I: If the state of the world is 1, for example, home agents will receive a total of B,PX, in dividends from home firms, and B,PXT in dividends from foreign ones. Home agents will also receive Y from the non-stochastic sector. Therefore the following represents the budget constraint of home agents under free trade: PD,+D,~P(0,Xi+8,XT)+
Y
i=1,2.
We next characterize the equilibrium of the world economy under free trade. Due to our assumptions that X, and Yw are constant and that the tastes of these two countries are identical and homothetic, P is unrelated to the state of the world and the values of the parameters /Ix, and /I,. We assume that the agents perfectly foresee this in period 0. In each state the optimum consumption of goods X and Y are functions of price and nominal income Ii: Dj=Dj(P, Ii), j=X, I: Substituting these relations for D, and D, in function C( .), we obtain an indirect real income function. Furthermore, due to the fact that C(.) is linear homogeneous, it can be written in a separable form: c(P)I,. Therefore, the indirect utility function of the representative home consumer can be written in the following form:
v = V[c(P)I,], ‘Alternatively, we may assume that equity holders receive commodity X in kind, before it is sold at the commodity market. Under this assumption, the outcomes of trade policies are totally different from those stated in sections 3 and 4. (We are grateful to an anonymous referee for pointing out this fact.)
S. Takemori
Ii=P(e,Xi+B,X;)+
and M. Tsumagari,
I:
Optimal trade taxes
487
i=l,2.
Then, in period 0, the representative home agent maximizes the expected utility under the wealth constraint, taking 13, and 19, as instruments. More specifically, the representative home agent’s problem is defined as
max C Oh,&
V[C(P){P(B~Xi+efx~)+ Y}]
i=1,2
subject to q( 1 - (3,) = or.
(4)
The maximization problem of the representative foreign agent can be defined similarly. Due to the specifications of stochasticity and the assumption of concave and identical utility functions, the following symmetrical solutions constitute the equilibrium of the equity market:
eh=e,=+,
q= 1.
(5)
The above solution implies that the agents of the two countries can perfectly smooth out their incomes from the output of X. Given these shares, the equilibrium consumptions of the two countries are characterized by the following conditions:
D,= -
~[P+(x,+x:)+ Y],
0: = - g
[lJ)(x,+xi*)
+ Y*].
From the above equations and the world market equilibrium condition, we can verify that the home country’s consumption of X will exceed the part of the total world output X controlled by the home equity ownership, &Xi + XT), if and only if 8, > i. It should also be noted that the home trade patterns depend not only on the value of the parameter /I,,, but also on the state of nature. If &,=f, for example, the home country will consume exactly 50 percent of the X produced in the world in both states 1 and 2. Given X1 >X,, it will then export X in state 1 and import it in state 2. 3. Ex post optimum trade policy In this section we investigate how the home country’s trade its own welfare when the levels of equity ownership are given equilibrium levels [see (5)]. The exposition will be brief since has already been tackled by B-B. However, our derivation
JIE
K
policy affects at free trade the question of a slightly
488
S. Takemori
and M. Tsumagari,
Optimal trade taxes
different formula of welfare change sheds new light on their results, and makes the main results of the next section more understandable. First, let us discuss the treatment of trade taxes in our model. The country of origin of a product is defined by its production location, while the home government treats alike all products originating in one country, regardless of the percentage of the equities that the home country might hold in specific foreign firms. (To illustrate, under this rule, the U.S. government would treat both Volvo and Ford Europe as foreign producers, and GM and Honda U.S. as home producers.) An ad valorem trade tax, t, then creates a wedge between the home price of X, (1 + t)P, and the foreign price of X, P.* In state i the home X sector realizes a total revenue of (1 +t)PX,, of which the home country receives ~9,(1+ t)PX, in dividends. The total revenue of the foreign X sector is PXT, of which the home country receives O,PXT. The home country also receives revenue from the Y sector, and collects a tax revenue of tP(D,-Xi). In summary, the home budget constraint becomes (l+t)PD,+D,=(l+t)PO,Xi+PB,XT+Y+tP(D,-Xi), Therefore
we can express the indirect ~=
v[C((
utility
function
i=1,2. of the home country
as
1 + t)P)li],
Ii=(l+t)PO,Xi+PO,X~+Y+tP(D,-Xi),
i=l,2.
(6)
differentiating (6) with respect to t at t=O, and using Roy’s identity - c4W(m~ = D,, we obtain the following expression for the changes in the real income of the home country which result from a small change in t:
Then
dU. L =-[“,-e,Xi-e,X~]~-P(l-B,)Xi, dt f=,,
i=l,2,
in which
(Since v’c>O, dU,/dtl,=, has the same sign as dL$/dtl,=,.) Although equity ownership is not explicitly treated
by B-B (1981),
an
‘We assume that a trade policy is always applied to market X. At the end of the previous section it was stated that the home country might be either the exporter or the importer of X, depending on the value of /3, and the state of nature. Thus t>O is either an import tax (if D,> Xj) or an export subsidy (if D,XJ, or an export tax (if D, < Xi).
s. Takemori
and M.
TSUmAgAri,
Optimal
trade taxes
489
expression quite similar to (7) can be obtained from their basic equation (16).3 The first term on the right-hand side of (7) is the terms of trade effect: the change in the home country’s welfare that results from changes in the world price. (We can easily check that dP/dt is negative.) In contrast to the standard trade theory literature, in which the coefficient of this term shows a gap between home consumption and home production, in our model it shows a gap between home consumption and that part of world production that is owned by the home country through equity holdings. The second term in (7) which we will henceforth call the transfer effect, shows how the price wedge created by the trade tax generates a transfer of surplus between home consumers and foreign equity holders. Fig. 1 may be of some help. Suppose a small tax, t, is imposed on the import of X, then the domestic price, P,, becomes higher than the world price, P. In contrast to the standard literature, the loss in consumer surplus in area B is not completely offset by the home country’s gain in producer surplus, since foreign equity holders steal part of the surplus.4 (By protecting the domestic auto industry from imports, the U.S. government would shift part of the surplus of U.S. consumers to the shareholders of Honda U.S.) As is pointed out by B-B, the presence of foreign ownership may make import subsidies the favored policy of the home country, because of the transfer effect. The same force, however, would make export subsidies even more adverse.5 The simulations reported in fig. 2 also confirm this point. In this exercise we assume a Cobb-Douglas real income function, C(.), and find the optimum trade policy of the home country for the values of three parameters: (i) pxi, (ii) /?, and (iii) cx, which is the Cobb-Douglas parameter on the expenditure share of X. (See appendix A for the details.) Locus VT in these figures represent the combinations of /?,, and CI, which make the expression dU,/dt If= O in (7) equal to zero. For all combinations ‘On the assumption (which is in our model but not in theirs) that home consumption entirely of consumption by home residents, and using our notation, their basic equation be rewritten in the following form: dU dt,=,
consists (16) can
= -[D,-O,x]~+‘(Dx-x)>
where P, is the domestic price. Differentiating into the above equation, we obtain:
P,=(l
+I)P,
at r=O,
and substituting
the result
dU = -[u,-o,x]g-P(l-o,)x~ dt ,=o The differences between the above equation and (7) are: (a) the above equation is non-stochastic, and (b) it does not envisage the home ownership of foreign assets. 41n the neighborhood of a free trade equilibrium the lirst-order measure of the loss in consumer surplus, which is represented by the area A, is just offset by the gain in tax revenue. 5An export subsidy raises the home price above the world price or lowers the world price below the home price (t>O). Therefore it transfers the home consumers’ surplus to the foreign equity holders.
490
S. Takemori and M. Tsumagari, Optimal trade taxes
P
Pd
Import tax P
Xi
Quantity
Fig. 1
that fall in the region below (above) I’,, a negative (positive) t improves the home country’s welfare. Locus 7__, on the other hand, represents combinations of parameters that make the home country just self-sufficient in X. In the area above (below) Tp, the home country is an importer (exporter) of X. There are three regions in fig. 2: region (a), in which an import tariff is called for; region (b), in which an import subsidy is called for; and region (c), in which an export tax is called for. There is no region in which an export subsidy is called for, since loci V, and Tp do not intersect. 4. Ex ante optimum trade policy In the preceding section we implicitly assumed that the policy intervention in period 1 was a perfect surprise to the agents, so that the levels of equity ownership remained the same with or without trade policy intervention. In this section we investigate a different scenario, in which agents participate in the equity trade with full knowledge of the trade policy that the home country will take in period 1. Specifically, we assume that the events take place in the following sequences. In period 0, the home government announces the value of t that it will adopt after the realization of the state. The value of t can be positive, negative or zero. In any cases the government
5’. Takemori and M. Tsumagari, Optimal trade taxes
(1) &i = 0.2
a
1
0.8 0.6 0.4
(b)
o.2t$q, , 0
0.2
0.4
0.6
0.8
(2) fixi = 0.5
0.6-
TP
0.4(cl
0.2I
0
I
0.2
0.4
0.6
0.8
(3) /3xi = 0.8
0.6-
(c)
0.40.2 I
0
0.2 Fig. 2
0.4
I
0.6
0.8
491
492
S. Takemori
and M. Tsumagari,
Optimal trade taxes
commits itself to this policy. Agents engage in equity trade on the basis of their knowledge of the value of t, and their accurate calculations of the equilibrium price that will hold in the commodity market. In period 1, when the commodity trade actually takes place, the government faithfully carries out the trade policy that it announced in period 0. A slight modification of the analysis of the previous section allows us to incorporate the effects of the changes in the equity price on the home country’s welfare. For this purpose we will define a trade policy as improving the home country’s welfare if it increases its expected utility. First, we substitute the wealth constraint (3) into (6) and take an expectation: E[ vi] =d
1
V[C(( 1+ t)P)Ii],
i=1,2
Ii=(l+t)PB,Xi+Pq(l-_B,)XT+Y+tP(D,-XX,),
i=l,2.
(8)
Differentiating the above equation with respect to t at t=O, taking into account the fact that the home incomes in states 1 and 2 are the same if t = 0, we obtain: dUE ~ = -[O -0 E(X)-0 dt 1=0 x h
f
-P(l-8,)E(X) (
E(X*)]dP
1 - dd; , 1
dt
(9)
in which dUE dt
1 dE[y] _,,=1/)C
dt
(Vc>O). r=O
The first term on the right-hand side of (9) is once again the terms of trade effect, the coefficient of which is the gap between the home consumption of X and the average world supplies of X which are controlled by the home equity ownership. The second term should be understood as comprising two effects: (a) the transfer effect, P( 1 -&)E(X), minus (b) the equity terms of trade effect, P( 1- B,)E(X)(dq/dt). Let us focus on the second term first, and in order to do so, suppose that the first term is 0. (This requires /I,,= f.) Then the sign of the optimum trade policy will depend on the sign of (1 -(dq/dt)). dq/dt is positive, since a positive t will raise the domestic price and thus also raise the revenue from
S. Takemori
and M. Tsumagari,
Optimal
trade taxes
493
The home demand curve
The foreign supply curve
l/2
Of
Fig. 3
home output. The higher revenue will also lead to a higher equity price. The question then boils down to this: Will the equity price rise by a greater, equal, or smaller amount than the change in t? If it is greater, a positive t is called for, and if it is smaller, a negative t. As it turns out, the change in the equity price is exactly equal to the change in t. And this depends neither on the degree of risk aversion in the consumer’s preference nor on variances in the output of X. Hence if the two countries are symmetrical, nonintervention is optimal for the home country. Appendix B demonstrates this conclusion through algebra. Here we try a more intuitive explanation, using a diagram. In fig. 3 we denote the foreign supply of equity and the home demand for it, Of, in the horizontal axis and the relative price of the equity, q, in the vertical axis. Given P and t, the foreign offer of 8, is drawn as a downward-sloping curve, while the home demand is drawn as an upwardsloping curve. If t changes by a small negative value, dt, from zero, both curves shift down by dt. Why? Because these shifts are sufficient to make home and foreign investors indifferent between the two assets. Since (1 t)(PX,/q) is the earnings per share of the home equity in each state, and PX,* is the earnings per share of the foreign equity, the percentage change in the home earnings per share is given by dt +(dP/P) -dq and that of the foreign earnings per share by dP/P. Therefore the relative earnings per share of the two assets in each state are unchanged if dq=dt. In the resulting equilibrium dq is equal to dt and Of is constant. 8,, however, changes as the result of a trade policy; the changes being given by dB,=)dt. Hence, if a positive t is announced, the home country increases its equity share in the home industry of X. This, in turn, increases the dividends it receives by PXidOh=PXiidt. This increase is (not accidentally) equal to +
494
S. Takemori
and M. Tsumagari,
Optimal trade taxes
the loss the home country suffers from the negative transfer effect of t>O in period 1. Fig. 3 suggests that the equity terms of trade move exactly to offset the transfer effect because a trade policy has similar effects on both home and foreign equity holders. Since a positive (negative) t raises (depresses) the return on the home firms, both foreign and home equity holders of the home firms suffer to the same extent, and as a result, both the foreign supply curve and the home demand curve of the foreign asset shift down by the same magnitude. Since the second term disappears, (9) can be now rewritten as
E(X)-0
f
E(X*)]c
dt ’
(10)
Hence, the home trade policy should depend on the terms of trade effect alone: since dP/dt is negative, the home country should use a trade policy that creates a positive wedge (t>O) between its domestic price and the world price, if and only if the home consumption exceeds that part of average world production that is owned by the home country through equity holdings6 The above policy rules can be translated into the standard vocabularly of trade policy, such as import taxes or export subsidies, with the help of a simple conversion rule: a positive (negative) wedge implies a tax (subsidy) if the home country is the importer of commodity X, D,>Xi, and a subsidy (tax) if it is the exporter, D,
“We have restricted our discussions to policies that are not state-contingent. use of state-contingent policy, such as a combination of a positive t in one state in the other, the home country’s welfare can still be improved. Yet we have meaningful result on state-contingent policies. The far greater complexity of the makes it doubtful that a simple policy rule can be derived for this case.
Evidently, by the and a negative t not arrived at a algebra involved
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S. Takemori and M. Tsumagari, Optimal trade taxes
(1) fixi=O.2
Oy1 0.8 -
(a)
0.6VT
0.4(b)
0.2 0.2
0
(2)
&i =
0.5
0.4
0.8
0.6
By1 0.8-
(a)
0.6VT
Tp
0.4(c)
0.2 -
0.2
0 (3) fixi = 0.8
I 0.4
0.6
I 0.8
1
a
a1 0.8 0.6
0.2 t OW Fig. 4
J.I.E.
L
1
ff
496
S. Takemori and M. Tsumagari, Optimal trade taxes
expanded, while the area in which called for has shrunk. In addition, called for has now emerged. This is where D,(X, +X,)/2
an import subsidy or an export tax is an area in which an export subsidy is because there are a range of parameters both hold.
5. Concluding remarks In this paper we have shown that for a preannounced and precommitted commercial policy, a government should still be guided by the terms of trade effect alone since any transfer of surplus from foreign equity holders to home consumers that a surprise commercial policy can generate will be totally offset by adverse movements in the home asset price. Obviously, there is a problem of time inconsistency. For example, the home government might be tempted to announce a trade policy that would enhance the value of the home asset, and then reverse it in order to exploit foreign equity holders. This problem seems to be as present in the real world as in our model. For example, the U.S. government, which has attracted Japanese direct investment by its protectionist stance, should find it more advantageous to reverse the stance once the investment has settled there. How can we solve the times inconsistency problem? As far as theoretical modelling is concerned, a popular solution involves an extension of the model framework into a repeated game. Under such an extension, a subgame perfect equilibrium may be found, where the government faithfully carries out the policy that it has announced at the betinning of the period. Nonetheless, in the real world, governments are still capable of behaving opportunistically in the matter of trade policies. Our trade model can easily be extracted to incorporate the production process, which uses factors such as labor. The simplest way to do this is to assume the following: two sectors m an economy employ two types of factors of production - one mobile, labor, and the other sector-specific, capital. Then the ownership claim to the sector-specific factor is internationally traded in an equity market. Under this setting, most of the results of the present study need only slight modifications in order to remain valid. For example, the basic equations of the welfare changes, (7), for ex post optimum policy and (9), for ex ante optimum policy, are virtually the same. The basic messages of our paper can also survive a relaxation of the special assumption of stochasticity that the outputs of good X in the countries are perfectly negatively correlated. Our analysis of ex post trade policy does not rely on this assumption. As to the analysis of ex ante trade policy, we can still expect a negative domestic price wedge to depress the home equity price, thus eroding a part of the gains by the transfer effect; we cannot state, however, whether or not the gains by the transfer effect would be completely offset by the change in the equity price.
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S. Takemori and M. Tsumagari, Optimal trade taxes
Appendix A In this appendix we discuss the derivation of fig. 2. Let us assume real income function in (2) takes the following Cobb-Douglas form: C(D,,D,)=D”,D;-“,
O
1.
(A.1)
Then utility maximization, given each country’s respective implies the following demand functions for X of the countries: D,
that the
budget constraints, home and foreign
= __-(l:t)P[(l+t)Pd,Xi+PO,X:+Y+~P(D,-X,)l,
(A.21
D;=;[(l+t)P(l-o,)Xi+P(l-B,)X:+Y*]. The market-clearing
condition
is naturally
D,+D;=X,. For t=O we can solve from this and (A.2), the equilibrium
price
p=----- UYlV
(1 -cr)X,’ Then at t=O we can derive D,-f(Xi+Xi*)=(l-cr)X,(B,-:),
(A.3)
P(l -$)xi=z
(A.4)
On the other we obtain
hand,
dP dt 2=o Substituting
2(1-a)
YWPX,.
by totally
differentiating
= _ ~YwC~+2(l-4&1 2(1-M)X,
(A.3)-(A.5)
the market-clearing
condition,
(A.5)
.
into (7), we obtain
(A.61 Hence the sign of the optimum
t depends
on the sign of the large bracket
on
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S. Takemori and M. Tsumagari, Optimal trade taxes
the right-hand side of the above equation. The I’, locus in fig. 2 shows the combinations of the parameters that make the large bracket term equal to zero. Above (below) the V, locus, [.I is positive (negative) and a positive (negative) t is called for. Also we can derive D,-Xi=X,[tcr+(l-CI)By-_BXi].
(A.7)
Therefore the sign of the above expression depends on the sign of the bracket on the right-hand side. The T, locus in fig. 2 represents combinations of parameters that render the above expression equal to zero. Above (below) this locus, the home country is the importer (exporter) of X.
Appendix B
In this appendix we derive the change in the relative equity price resulting from the the announcement of a trade policy by the home government. With the presence of a home trade tax or subsidy, the maximization problem of home consumers (4) should be rewritten as follows: max 2 Bh i=l,Z
V[C[(
(B.1)
1 +t)P]Zi]
where Ii=P[(l+t)B,Xi+(l-B,)qX~]+Y+tP(D,-Xi),
i=l,2,
in which we make use of the wealth constraint q( l-6,) = 0,. On the other hand, the maximization problem of foreign consumers is given by max 1 &l i=l,Z
V[c(P)r:],
(B.2)
in which
and in which we also make use of the above wealth constraint. The first-order condition of (B.1) is given by
+T,
v’[C[(l +t)P]li]C[(l
+t)P]P[(l
+t)Xi-qXT]=O.
(B.3)
The first-order condition of (B.2) is given by i=$. z V'[C[P]Zf]C[P]P[qXT-(1
+ t)Xi] =O.
(B.4)
We totally differentiate (B.3) and (B.4) and evaluate at t=O. We also make
S. Takemori
use of the equilibrium we get from (B.3):
and M. Tsumagari,
conditions
- 8PRo’
Optimal
at t=O, namely
+[2PRa2-(X,+X,)]
499
trade taxes
(5). Then after rearranging,
2
= -[~PRc~+(X,+X,)],
0
in which R = - V”c[P]/V’ is a measure of consumers’ c2 =4(X, -X2)* is the variance in the endowments. Similarly from (B.4) we obtain
risk aversion,
and
8PRa2
Solving
(B.5) and (B.6) together,
de,, 1 dt -2,
we obtain
dq z=l.
Hence the claim of section also calculate
4 is proved.
This solution can be illustrated rewrite (B.5) as
Using
by fig. 3. Using
8PRa2 d& = [2PRa2 +(X1 +X,)1
the wealth
constraint,
we can
the wealth constraint,
we can
dq - [2PRa2 +(X1 +X2)] dt.
(B.7)
Letting de,=0 in (B.7), we can see that the home demand curve for Qf shifts by dq =dt at the original equilibrium point e,=i. Similarly, we can rewrite (B.6) as 8PRa2 d&=[2PRo2-(X,
+X2)]
dq-[2PRa2-(X,
+X2)]
dt.
(B.8)
Letting de,=0 in (B.8), we can see that the foreign offer curve for 8, also shifts by dq =dt at the original equilibrium point 0,= i. By these shifts in the two curves, the equilibrium of is unchanged and the equilibrium dq is equal to dt.
500
S. Takemori and M. Tsumagari, Optimal trade taxes
References Bhagwati, J. and R. Brecher, 1980, National Welfare in an open economy in the presence of foreign-owned factors of production, Journal of International Economics 10, no. 1, 103-I 15. Brecher, R. and J. Bhagwati, 1981, Foreign ownership and the theory of trade and welfare, Journal of Political Economy 89, no. 3, 4977511. Helpman E. and A. Razin, 1978, A theory of international trade under uncertainty (Academic Press, New York).
of International
Economics
36 (1994) 483-500.
North-Holland
Optimal trade taxes in the presence of foreign ownership and equity exchanges Shumpei
Takemori
and Masatoshi
Tsumagari”
Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, 108 Tokyo, Japan Received
February
1992, revised version
received
May 1993
This paper investigates the question of the optimal trade policies in the presence of foreign ownership, extending the framework of the pioneering studies by Brecher and Bhagwati. Trade in the ownership claims is explicitly modelled using a stochastic trade model. The paper concludes that the results of the above studies crucially depend on the policy not being expected at the time foreign investment takes place. Key words: Optimal
trade policy; Foreign
ownership
JEL classification: F 13
1. Introduction
Seminal works by Bhagwati and Brecher (1980) and Brecher and Bhagwati (1981) correctly point out that many standard normative propositions of trade theory are seriously challenged in the presence of foreign ownership in the domestic economy. We further investigate into this question, focusing on the issue of the optimal trade policy. Specifically, we extend their framework in one important aspect: instead of taking the presence of foreign ownership as a ‘fait accompli’, as in their studies, we explicitly model a trade in ownership claim which determines it. This extended framework, which incorporates two types of trade, enables us to study a policy question which is left out by their 1981 paper; namely, how a trade policy implemented by a country affects its welfare if the policy intention is revealed before the trade in ownership claims takes place. (We henceforth refer to this paper as B-B.) The model that we set out is the simplest stochastic model, which Correspondence to: S. Takemori, Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, 108 Tokyo, Japan. *We are grateful to Peter Petri for providing insights into our results. We also thank Eric Bond, Fumio Dei, Ron Jones, and Michihiro Ohyama for helpful comments. We are also grateful to the two anonymous referees for pointing out serious mistakes in an earlier draft and for their suggestions with regard to the organization of the paper. Naturally all errors are ours. The present study has benefited from the financial assistance of the Nomura Investment Trust Memorial Fund. 0022-1996/94/$07.00 0 1994 Elsevier SSDI 0022-1996(93)01300-4
Science
B.V. All rights
reserved
484
S. Takemori
and M. Tsumagari,
Optimal trade taxes
generates international trade in commodities and ownership claims, and is basically similar to those studied by Helpman and Razin (1978). There are two countries in the world, which produce two types of goods. The production level of one of these goods is constant and that of the other depends only on whether the country is in a good or bad state. However, since the agents of each country know the probability of the occurrence of these states, and at the worldwide level the randomness is idiosyncratic, they may pool away risks by an asset trade. The type of asset we assume is a firm’s equity, which entitles its owners to receive dividends when the product of the firm is sold at the market. There is an interval between the time at which the equity trade takes place and the time at which the commodity trade takes place. Since a trade policy has its effect only concurrently with the commodity trade, each agent must form an expectation on future trade policy and its effects at the time he participates in the equity trade. Under this setting we contrast the effects of the following two types of trade policies. (a) A trade policy that is not anticipated by agents at the time they participate in the equity trade. (This type of policy, which is henceforth called an ex post trade policy, is the one studied by B-B.) (b) A trade policy that is announced to agents prior to their participation in the equity trade. (This type of trade policy is henceforth called an ex ante trade policy.) Our main contributions are as follows: (1) In the case of an ex post trade policy, we reinterpret the results of B-B by deriving a slightly different formula of welfare change. The source of their paradoxical result, the optimality of an import subsidy, is revealed in this formula as the transfer of surplus that an import subsidy generates between domestic consumers and foreign equity holders: an import subsidy that depresses the domestic price below the level of the foreign price exploits foreign interests in the domestic industry to the benefit of home consumers. We also show that this same force makes the effect of an export subsidy even more adverse. (2) In the case of an ex ante trade policy, we show that the transfer of surplus described above is totally offset by an adverse movement in the equity terms of trade: reflecting the fall in return caused by an import subsidy, the price of the home assets falls, to the detriment of the home country. The case for an import subsidy is therefore diminished. This result suggests that the conclusions of B-B for commercial policy in the presence of foreign ownership depend crucially on the policy not being expected at the time foreign investment takes place. The organization of our paper is as follows. In section 2 we present our model and characterize the world equilibrium under perfect free trade. In section 3 we investigate the question of ex post optimal trade taxes. The question of ex ante optimal trade taxes is dealt with in section 4. Section 5 concludes our paper.
S. Takemori
and M. Tsumagari,
Optimal trade taxes
485
2. The model There are two countries, home and foreign, two commodities, X and Y and two periods, period 0 and period 1. In period 1, the two countries obtain the outputs of the two commodities, produced by numerous firms. (We assume that each firm produces only one type of commodity). The factors that produce these commodities are already sunk in the production process, so that only an exogenous productivity shock can cause a change in the production levels. The output of Y is fixed for the two countries. (There is no uncertainty involved in the production of Y) Let Y and Y*, respectively, be the outputs of Y in the home and foreign countries. (We henceforth denote by an asterisk the variables of the foreign country.) Define Y,=Y+Y*,
8, = YIYW,
as the total world output of Y and the home country’s production share. In the following analysis we fix Yw and take B, as a parameter. There is a country-specific stochasticity in the production of X: factors that produce X are sunk, but their productivity levels depend on the state in which a country finds itself. There are two states of the world, states 1 and 2, which have equal probability of occurrence, l/2. The outputs of X in these states take the following forms:
x,=x:,
x, = XT,
x, >x,,
in which Xi (XT) is the home (foreign) x,=x,+x,*,
output
px, =X,/X,,
(1) of X in state i. Let
i= 1,2,
be the world total output of X and the home country’s share of production. From (1) Xw is constant and bx, + bx2 = 1. In period 0, the output level of X is unknown to the agents. They know, however, the output level in each state, namely (l), as well as the probability of occurrence of these states. We assume that consumers’ preferences in the two countries can be represented by the same concave and homothetic utility function:
v = V[C(D,,
D,)],
V’ > 0, V” < 0,
(2)
in which D, and D, represent the consumption of commodities X and I: and C( .) is a linear homogeneous function which represents the real income of a country. CC(.) is henceforth called a real income function.] There are two types of trade in this economy. One is trade in equities, which takes place in period 0. Initially, the equities of firms that produce X and Y are owned by domestic agents. There is, however, an opportunity for
486
S. Takemori and M. Tsumagari, Optimal trade taxes
agents of both countries to smooth out country-specific shocks by engaging in trade in the equities of firms that produce the risky product, X. This trade takes place in the following way: the agents of each country sell on the world equity market the equities of the domestic firms which they own at the beginning, and use the proceeds to buy the equivalent values of equities in foreign firms. The trade in equities must therefore fulfill the following wealth constraint:
4(1-%)=Q,,
(3)
in which 0,, represents the equities of the home firms owned by the home agents after the trade and 9r the equities of the foreign firms which they have purchased. (We normalize the total number of equities to be 1 for both home and foreign firms.) q is the relative price of the home equities, which is defined by taking the price of the foreign equity to be 1. The ownership of an equity in a firm entitles its owner to receive a cash dividend in period 1, when the state is realized and the output is sold on the world commodity market.’ Let P be the world price of X in terms of I: If the state of the world is 1, for example, home agents will receive a total of B,PX, in dividends from home firms, and B,PXT in dividends from foreign ones. Home agents will also receive Y from the non-stochastic sector. Therefore the following represents the budget constraint of home agents under free trade: PD,+D,~P(0,Xi+8,XT)+
Y
i=1,2.
We next characterize the equilibrium of the world economy under free trade. Due to our assumptions that X, and Yw are constant and that the tastes of these two countries are identical and homothetic, P is unrelated to the state of the world and the values of the parameters /Ix, and /I,. We assume that the agents perfectly foresee this in period 0. In each state the optimum consumption of goods X and Y are functions of price and nominal income Ii: Dj=Dj(P, Ii), j=X, I: Substituting these relations for D, and D, in function C( .), we obtain an indirect real income function. Furthermore, due to the fact that C(.) is linear homogeneous, it can be written in a separable form: c(P)I,. Therefore, the indirect utility function of the representative home consumer can be written in the following form:
v = V[c(P)I,], ‘Alternatively, we may assume that equity holders receive commodity X in kind, before it is sold at the commodity market. Under this assumption, the outcomes of trade policies are totally different from those stated in sections 3 and 4. (We are grateful to an anonymous referee for pointing out this fact.)
S. Takemori
Ii=P(e,Xi+B,X;)+
and M. Tsumagari,
I:
Optimal trade taxes
487
i=l,2.
Then, in period 0, the representative home agent maximizes the expected utility under the wealth constraint, taking 13, and 19, as instruments. More specifically, the representative home agent’s problem is defined as
max C Oh,&
V[C(P){P(B~Xi+efx~)+ Y}]
i=1,2
subject to q( 1 - (3,) = or.
(4)
The maximization problem of the representative foreign agent can be defined similarly. Due to the specifications of stochasticity and the assumption of concave and identical utility functions, the following symmetrical solutions constitute the equilibrium of the equity market:
eh=e,=+,
q= 1.
(5)
The above solution implies that the agents of the two countries can perfectly smooth out their incomes from the output of X. Given these shares, the equilibrium consumptions of the two countries are characterized by the following conditions:
D,= -
~[P+(x,+x:)+ Y],
0: = - g
[lJ)(x,+xi*)
+ Y*].
From the above equations and the world market equilibrium condition, we can verify that the home country’s consumption of X will exceed the part of the total world output X controlled by the home equity ownership, &Xi + XT), if and only if 8, > i. It should also be noted that the home trade patterns depend not only on the value of the parameter /I,,, but also on the state of nature. If &,=f, for example, the home country will consume exactly 50 percent of the X produced in the world in both states 1 and 2. Given X1 >X,, it will then export X in state 1 and import it in state 2. 3. Ex post optimum trade policy In this section we investigate how the home country’s trade its own welfare when the levels of equity ownership are given equilibrium levels [see (5)]. The exposition will be brief since has already been tackled by B-B. However, our derivation
JIE
K
policy affects at free trade the question of a slightly
488
S. Takemori
and M. Tsumagari,
Optimal trade taxes
different formula of welfare change sheds new light on their results, and makes the main results of the next section more understandable. First, let us discuss the treatment of trade taxes in our model. The country of origin of a product is defined by its production location, while the home government treats alike all products originating in one country, regardless of the percentage of the equities that the home country might hold in specific foreign firms. (To illustrate, under this rule, the U.S. government would treat both Volvo and Ford Europe as foreign producers, and GM and Honda U.S. as home producers.) An ad valorem trade tax, t, then creates a wedge between the home price of X, (1 + t)P, and the foreign price of X, P.* In state i the home X sector realizes a total revenue of (1 +t)PX,, of which the home country receives ~9,(1+ t)PX, in dividends. The total revenue of the foreign X sector is PXT, of which the home country receives O,PXT. The home country also receives revenue from the Y sector, and collects a tax revenue of tP(D,-Xi). In summary, the home budget constraint becomes (l+t)PD,+D,=(l+t)PO,Xi+PB,XT+Y+tP(D,-Xi), Therefore
we can express the indirect ~=
v[C((
utility
function
i=1,2. of the home country
as
1 + t)P)li],
Ii=(l+t)PO,Xi+PO,X~+Y+tP(D,-Xi),
i=l,2.
(6)
differentiating (6) with respect to t at t=O, and using Roy’s identity - c4W(m~ = D,, we obtain the following expression for the changes in the real income of the home country which result from a small change in t:
Then
dU. L =-[“,-e,Xi-e,X~]~-P(l-B,)Xi, dt f=,,
i=l,2,
in which
(Since v’c>O, dU,/dtl,=, has the same sign as dL$/dtl,=,.) Although equity ownership is not explicitly treated
by B-B (1981),
an
‘We assume that a trade policy is always applied to market X. At the end of the previous section it was stated that the home country might be either the exporter or the importer of X, depending on the value of /3, and the state of nature. Thus t>O is either an import tax (if D,> Xj) or an export subsidy (if D,
s. Takemori
and M.
TSUmAgAri,
Optimal
trade taxes
489
expression quite similar to (7) can be obtained from their basic equation (16).3 The first term on the right-hand side of (7) is the terms of trade effect: the change in the home country’s welfare that results from changes in the world price. (We can easily check that dP/dt is negative.) In contrast to the standard trade theory literature, in which the coefficient of this term shows a gap between home consumption and home production, in our model it shows a gap between home consumption and that part of world production that is owned by the home country through equity holdings. The second term in (7) which we will henceforth call the transfer effect, shows how the price wedge created by the trade tax generates a transfer of surplus between home consumers and foreign equity holders. Fig. 1 may be of some help. Suppose a small tax, t, is imposed on the import of X, then the domestic price, P,, becomes higher than the world price, P. In contrast to the standard literature, the loss in consumer surplus in area B is not completely offset by the home country’s gain in producer surplus, since foreign equity holders steal part of the surplus.4 (By protecting the domestic auto industry from imports, the U.S. government would shift part of the surplus of U.S. consumers to the shareholders of Honda U.S.) As is pointed out by B-B, the presence of foreign ownership may make import subsidies the favored policy of the home country, because of the transfer effect. The same force, however, would make export subsidies even more adverse.5 The simulations reported in fig. 2 also confirm this point. In this exercise we assume a Cobb-Douglas real income function, C(.), and find the optimum trade policy of the home country for the values of three parameters: (i) pxi, (ii) /?, and (iii) cx, which is the Cobb-Douglas parameter on the expenditure share of X. (See appendix A for the details.) Locus VT in these figures represent the combinations of /?,, and CI, which make the expression dU,/dt If= O in (7) equal to zero. For all combinations ‘On the assumption (which is in our model but not in theirs) that home consumption entirely of consumption by home residents, and using our notation, their basic equation be rewritten in the following form: dU dt,=,
consists (16) can
= -[D,-O,x]~+‘(Dx-x)>
where P, is the domestic price. Differentiating into the above equation, we obtain:
P,=(l
+I)P,
at r=O,
and substituting
the result
dU = -[u,-o,x]g-P(l-o,)x~ dt ,=o The differences between the above equation and (7) are: (a) the above equation is non-stochastic, and (b) it does not envisage the home ownership of foreign assets. 41n the neighborhood of a free trade equilibrium the lirst-order measure of the loss in consumer surplus, which is represented by the area A, is just offset by the gain in tax revenue. 5An export subsidy raises the home price above the world price or lowers the world price below the home price (t>O). Therefore it transfers the home consumers’ surplus to the foreign equity holders.
490
S. Takemori and M. Tsumagari, Optimal trade taxes
P
Pd
Import tax P
Xi
Quantity
Fig. 1
that fall in the region below (above) I’,, a negative (positive) t improves the home country’s welfare. Locus 7__, on the other hand, represents combinations of parameters that make the home country just self-sufficient in X. In the area above (below) Tp, the home country is an importer (exporter) of X. There are three regions in fig. 2: region (a), in which an import tariff is called for; region (b), in which an import subsidy is called for; and region (c), in which an export tax is called for. There is no region in which an export subsidy is called for, since loci V, and Tp do not intersect. 4. Ex ante optimum trade policy In the preceding section we implicitly assumed that the policy intervention in period 1 was a perfect surprise to the agents, so that the levels of equity ownership remained the same with or without trade policy intervention. In this section we investigate a different scenario, in which agents participate in the equity trade with full knowledge of the trade policy that the home country will take in period 1. Specifically, we assume that the events take place in the following sequences. In period 0, the home government announces the value of t that it will adopt after the realization of the state. The value of t can be positive, negative or zero. In any cases the government
5’. Takemori and M. Tsumagari, Optimal trade taxes
(1) &i = 0.2
a
1
0.8 0.6 0.4
(b)
o.2t$q, , 0
0.2
0.4
0.6
0.8
(2) fixi = 0.5
0.6-
TP
0.4(cl
0.2I
0
I
0.2
0.4
0.6
0.8
(3) /3xi = 0.8
0.6-
(c)
0.40.2 I
0
0.2 Fig. 2
0.4
I
0.6
0.8
491
492
S. Takemori
and M. Tsumagari,
Optimal trade taxes
commits itself to this policy. Agents engage in equity trade on the basis of their knowledge of the value of t, and their accurate calculations of the equilibrium price that will hold in the commodity market. In period 1, when the commodity trade actually takes place, the government faithfully carries out the trade policy that it announced in period 0. A slight modification of the analysis of the previous section allows us to incorporate the effects of the changes in the equity price on the home country’s welfare. For this purpose we will define a trade policy as improving the home country’s welfare if it increases its expected utility. First, we substitute the wealth constraint (3) into (6) and take an expectation: E[ vi] =d
1
V[C(( 1+ t)P)Ii],
i=1,2
Ii=(l+t)PB,Xi+Pq(l-_B,)XT+Y+tP(D,-XX,),
i=l,2.
(8)
Differentiating the above equation with respect to t at t=O, taking into account the fact that the home incomes in states 1 and 2 are the same if t = 0, we obtain: dUE ~ = -[O -0 E(X)-0 dt 1=0 x h
f
-P(l-8,)E(X) (
E(X*)]dP
1 - dd; , 1
dt
(9)
in which dUE dt
1 dE[y] _,,=1/)C
dt
(Vc>O). r=O
The first term on the right-hand side of (9) is once again the terms of trade effect, the coefficient of which is the gap between the home consumption of X and the average world supplies of X which are controlled by the home equity ownership. The second term should be understood as comprising two effects: (a) the transfer effect, P( 1 -&)E(X), minus (b) the equity terms of trade effect, P( 1- B,)E(X)(dq/dt). Let us focus on the second term first, and in order to do so, suppose that the first term is 0. (This requires /I,,= f.) Then the sign of the optimum trade policy will depend on the sign of (1 -(dq/dt)). dq/dt is positive, since a positive t will raise the domestic price and thus also raise the revenue from
S. Takemori
and M. Tsumagari,
Optimal
trade taxes
493
The home demand curve
The foreign supply curve
l/2
Of
Fig. 3
home output. The higher revenue will also lead to a higher equity price. The question then boils down to this: Will the equity price rise by a greater, equal, or smaller amount than the change in t? If it is greater, a positive t is called for, and if it is smaller, a negative t. As it turns out, the change in the equity price is exactly equal to the change in t. And this depends neither on the degree of risk aversion in the consumer’s preference nor on variances in the output of X. Hence if the two countries are symmetrical, nonintervention is optimal for the home country. Appendix B demonstrates this conclusion through algebra. Here we try a more intuitive explanation, using a diagram. In fig. 3 we denote the foreign supply of equity and the home demand for it, Of, in the horizontal axis and the relative price of the equity, q, in the vertical axis. Given P and t, the foreign offer of 8, is drawn as a downward-sloping curve, while the home demand is drawn as an upwardsloping curve. If t changes by a small negative value, dt, from zero, both curves shift down by dt. Why? Because these shifts are sufficient to make home and foreign investors indifferent between the two assets. Since (1 t)(PX,/q) is the earnings per share of the home equity in each state, and PX,* is the earnings per share of the foreign equity, the percentage change in the home earnings per share is given by dt +(dP/P) -dq and that of the foreign earnings per share by dP/P. Therefore the relative earnings per share of the two assets in each state are unchanged if dq=dt. In the resulting equilibrium dq is equal to dt and Of is constant. 8,, however, changes as the result of a trade policy; the changes being given by dB,=)dt. Hence, if a positive t is announced, the home country increases its equity share in the home industry of X. This, in turn, increases the dividends it receives by PXidOh=PXiidt. This increase is (not accidentally) equal to +
494
S. Takemori
and M. Tsumagari,
Optimal trade taxes
the loss the home country suffers from the negative transfer effect of t>O in period 1. Fig. 3 suggests that the equity terms of trade move exactly to offset the transfer effect because a trade policy has similar effects on both home and foreign equity holders. Since a positive (negative) t raises (depresses) the return on the home firms, both foreign and home equity holders of the home firms suffer to the same extent, and as a result, both the foreign supply curve and the home demand curve of the foreign asset shift down by the same magnitude. Since the second term disappears, (9) can be now rewritten as
E(X)-0
f
E(X*)]c
dt ’
(10)
Hence, the home trade policy should depend on the terms of trade effect alone: since dP/dt is negative, the home country should use a trade policy that creates a positive wedge (t>O) between its domestic price and the world price, if and only if the home consumption exceeds that part of average world production that is owned by the home country through equity holdings6 The above policy rules can be translated into the standard vocabularly of trade policy, such as import taxes or export subsidies, with the help of a simple conversion rule: a positive (negative) wedge implies a tax (subsidy) if the home country is the importer of commodity X, D,>Xi, and a subsidy (tax) if it is the exporter, D,
“We have restricted our discussions to policies that are not state-contingent. use of state-contingent policy, such as a combination of a positive t in one state in the other, the home country’s welfare can still be improved. Yet we have meaningful result on state-contingent policies. The far greater complexity of the makes it doubtful that a simple policy rule can be derived for this case.
Evidently, by the and a negative t not arrived at a algebra involved
495
S. Takemori and M. Tsumagari, Optimal trade taxes
(1) fixi=O.2
Oy1 0.8 -
(a)
0.6VT
0.4(b)
0.2 0.2
0
(2)
&i =
0.5
0.4
0.8
0.6
By1 0.8-
(a)
0.6VT
Tp
0.4(c)
0.2 -
0.2
0 (3) fixi = 0.8
I 0.4
0.6
I 0.8
1
a
a1 0.8 0.6
0.2 t OW Fig. 4
J.I.E.
L
1
ff
496
S. Takemori and M. Tsumagari, Optimal trade taxes
expanded, while the area in which called for has shrunk. In addition, called for has now emerged. This is where D,
an import subsidy or an export tax is an area in which an export subsidy is because there are a range of parameters both hold.
5. Concluding remarks In this paper we have shown that for a preannounced and precommitted commercial policy, a government should still be guided by the terms of trade effect alone since any transfer of surplus from foreign equity holders to home consumers that a surprise commercial policy can generate will be totally offset by adverse movements in the home asset price. Obviously, there is a problem of time inconsistency. For example, the home government might be tempted to announce a trade policy that would enhance the value of the home asset, and then reverse it in order to exploit foreign equity holders. This problem seems to be as present in the real world as in our model. For example, the U.S. government, which has attracted Japanese direct investment by its protectionist stance, should find it more advantageous to reverse the stance once the investment has settled there. How can we solve the times inconsistency problem? As far as theoretical modelling is concerned, a popular solution involves an extension of the model framework into a repeated game. Under such an extension, a subgame perfect equilibrium may be found, where the government faithfully carries out the policy that it has announced at the betinning of the period. Nonetheless, in the real world, governments are still capable of behaving opportunistically in the matter of trade policies. Our trade model can easily be extracted to incorporate the production process, which uses factors such as labor. The simplest way to do this is to assume the following: two sectors m an economy employ two types of factors of production - one mobile, labor, and the other sector-specific, capital. Then the ownership claim to the sector-specific factor is internationally traded in an equity market. Under this setting, most of the results of the present study need only slight modifications in order to remain valid. For example, the basic equations of the welfare changes, (7), for ex post optimum policy and (9), for ex ante optimum policy, are virtually the same. The basic messages of our paper can also survive a relaxation of the special assumption of stochasticity that the outputs of good X in the countries are perfectly negatively correlated. Our analysis of ex post trade policy does not rely on this assumption. As to the analysis of ex ante trade policy, we can still expect a negative domestic price wedge to depress the home equity price, thus eroding a part of the gains by the transfer effect; we cannot state, however, whether or not the gains by the transfer effect would be completely offset by the change in the equity price.
497
S. Takemori and M. Tsumagari, Optimal trade taxes
Appendix A In this appendix we discuss the derivation of fig. 2. Let us assume real income function in (2) takes the following Cobb-Douglas form: C(D,,D,)=D”,D;-“,
O
1.
(A.1)
Then utility maximization, given each country’s respective implies the following demand functions for X of the countries: D,
that the
budget constraints, home and foreign
= __-(l:t)P[(l+t)Pd,Xi+PO,X:+Y+~P(D,-X,)l,
(A.21
D;=;[(l+t)P(l-o,)Xi+P(l-B,)X:+Y*]. The market-clearing
condition
is naturally
D,+D;=X,. For t=O we can solve from this and (A.2), the equilibrium
price
p=----- UYlV
(1 -cr)X,’ Then at t=O we can derive D,-f(Xi+Xi*)=(l-cr)X,(B,-:),
(A.3)
P(l -$)xi=z
(A.4)
On the other we obtain
hand,
dP dt 2=o Substituting
2(1-a)
YWPX,.
by totally
differentiating
= _ ~YwC~+2(l-4&1 2(1-M)X,
(A.3)-(A.5)
the market-clearing
condition,
(A.5)
.
into (7), we obtain
(A.61 Hence the sign of the optimum
t depends
on the sign of the large bracket
on
498
S. Takemori and M. Tsumagari, Optimal trade taxes
the right-hand side of the above equation. The I’, locus in fig. 2 shows the combinations of the parameters that make the large bracket term equal to zero. Above (below) the V, locus, [.I is positive (negative) and a positive (negative) t is called for. Also we can derive D,-Xi=X,[tcr+(l-CI)By-_BXi].
(A.7)
Therefore the sign of the above expression depends on the sign of the bracket on the right-hand side. The T, locus in fig. 2 represents combinations of parameters that render the above expression equal to zero. Above (below) this locus, the home country is the importer (exporter) of X.
Appendix B
In this appendix we derive the change in the relative equity price resulting from the the announcement of a trade policy by the home government. With the presence of a home trade tax or subsidy, the maximization problem of home consumers (4) should be rewritten as follows: max 2 Bh i=l,Z
V[C[(
(B.1)
1 +t)P]Zi]
where Ii=P[(l+t)B,Xi+(l-B,)qX~]+Y+tP(D,-Xi),
i=l,2,
in which we make use of the wealth constraint q( l-6,) = 0,. On the other hand, the maximization problem of foreign consumers is given by max 1 &l i=l,Z
V[c(P)r:],
(B.2)
in which
and in which we also make use of the above wealth constraint. The first-order condition of (B.1) is given by
+T,
v’[C[(l +t)P]li]C[(l
+t)P]P[(l
+t)Xi-qXT]=O.
(B.3)
The first-order condition of (B.2) is given by i=$. z V'[C[P]Zf]C[P]P[qXT-(1
+ t)Xi] =O.
(B.4)
We totally differentiate (B.3) and (B.4) and evaluate at t=O. We also make
S. Takemori
use of the equilibrium we get from (B.3):
and M. Tsumagari,
conditions
- 8PRo’
Optimal
at t=O, namely
+[2PRa2-(X,+X,)]
499
trade taxes
(5). Then after rearranging,
2
= -[~PRc~+(X,+X,)],
0
in which R = - V”c[P]/V’ is a measure of consumers’ c2 =4(X, -X2)* is the variance in the endowments. Similarly from (B.4) we obtain
risk aversion,
and
8PRa2
Solving
(B.5) and (B.6) together,
de,, 1 dt -2,
we obtain
dq z=l.
Hence the claim of section also calculate
4 is proved.
This solution can be illustrated rewrite (B.5) as
Using
by fig. 3. Using
8PRa2 d& = [2PRa2 +(X1 +X,)1
the wealth
constraint,
we can
the wealth constraint,
we can
dq - [2PRa2 +(X1 +X2)] dt.
(B.7)
Letting de,=0 in (B.7), we can see that the home demand curve for Qf shifts by dq =dt at the original equilibrium point e,=i. Similarly, we can rewrite (B.6) as 8PRa2 d&=[2PRo2-(X,
+X2)]
dq-[2PRa2-(X,
+X2)]
dt.
(B.8)
Letting de,=0 in (B.8), we can see that the foreign offer curve for 8, also shifts by dq =dt at the original equilibrium point 0,= i. By these shifts in the two curves, the equilibrium of is unchanged and the equilibrium dq is equal to dt.
500
S. Takemori and M. Tsumagari, Optimal trade taxes
References Bhagwati, J. and R. Brecher, 1980, National Welfare in an open economy in the presence of foreign-owned factors of production, Journal of International Economics 10, no. 1, 103-I 15. Brecher, R. and J. Bhagwati, 1981, Foreign ownership and the theory of trade and welfare, Journal of Political Economy 89, no. 3, 4977511. Helpman E. and A. Razin, 1978, A theory of international trade under uncertainty (Academic Press, New York).