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Welfare comparison of trade situations
Journal of International
Economics 30 (1991) 49-68. North-Holland
Welfare comparison
of trade situations
Kar-yiu Wang* Unirersity
of Washington,
Seattle,
WA 98195, USA
Received April 1989, revised version received June 1990
This paper applies the compensation principle to compare the welfare levels of a small, many-household open economy in different trade situations. Two types of trade situations, free and restricted trade, and two types of compensation schemes, lump-sum transfers and consumption taxes, are considered and compared. For each type of trade situation, necessary and sufftcient welfare-improving conditions are derivedwhen losers are compensated using either lump-sum transfers or consumption taxes. Important differences are noted between the results that are based on compensation and the familiar results based on a well-behaved social utility function.
1. Introduction It has been widely recognized that it is difficult to compare situations facing a many-individual economy from its national welfare point of view. Three different approaches to welfare comparison have been suggested in the literature, but none of them is universally accepted. First, we have the social welfare approach in which a Bergson-Samuelson social welfare function is defined in terms of the utility levels of different individuals. [See, for example, Boadway and Bruce (1984) and Halvorsen and Ruby (1983) for a detailed discussion of the merits and demerits of this approach.] In the second approach, which can be called the social utility approach, all aggregate consumption bundles are ranked with respect to a well-behaved social utility function.’ The advantage of this approach is that the economy can be regarded as a single consumer, so axioms of revealed preference can be applied. Some very general conditions for welfare improvement in the presence of goods trade were derived by Ohyama (1972), and an exact measure of welfare change was developed by Grinols and Wong (1990). Last, we have the compensation approach in which the transition from one situation to another situation is said to be preferable if all losers can be *Thanks are due to Jagdish Bhagwati, Avinash Dixit, Robert Feenstra, Earl Grinols. Robert
Halvorsenand two anonymousrefereesfor helpful comments. The author is solely responsible for any remaining shortcomings and errors. ‘Samuelson (1956) showed that a social utility function exists if a social welfare function exists and is always maximized with optimal income distribution. 0022-1996/91/SO3.50 0 1991-Elsevier
Science Publishers B.V. (North-Holland)
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of trade situations
compensated while at least one individual can be made better off. Although it has been criticized for, among other things, assuming hypothetical, timeless, and costless compensation schemes, the compensation approach has the advantage of requiring no interpersonal comparison, and it is still adopted frequently in the literature [for example, Dixit and Norman (1986) Kemp and Wan (1986) and Diewert, Turunen-Red and Woodland (1984)]. The purpose of this paper is to take the compensation approach to compare the welfare impacts of different trade situations on a small open economy. There are four reasons for this paper. First, many compensation criteria were developed with an implicit or explicit assumption of a closed economy. Recent contributions have been made by Boadway (1974). Foster (1976), Bruce and Harris (1982), and Boadway and Bruce (1984). This paper extends some of their results to an open economy. Since trade opportunities provide more consumption possibilities to an open economy, we can hope to get more results about ranking two situations. Second, the paper derives necessary and sufficient conditions for welfare improvement when the economy shifts from one trade situation to another and when compensation is allowed. The shift in the trade situation may be due to changes in external shocks, such as the world’s technologies, preferences, and endowments, or due to changes in government policies. The results are general in the sense that previous theory of the gains from trade can be considered as special cases [Samuelson (1962), Kemp (1962) Kemp and Wan (1972), and Dixit and Norman (1980), among others] because autarky can be treated as a special trade situation with prohibitive tariffs. Another reason for analyzing the welfare impacts of a shift of trade situation is due to the fact that usually only trade situations, not autarky, are observed in the world. Third, while it is recognized that comparing trade situations is important, most papers carry out the comparison with respect to a well-behaved social utility function [Ohyama (1972), Grossman (1984), and many others]. Since the existence of a social utility function requires interpersonal comparison and depends on some strong assumptions, it is important to see how two’ trade situations can be compared using other criteria. Necessary and sufficient conditions for welfare improvement based on the compensation principle are compared with welfare improvement conditions based on a social utility function, and we will show that in some cases, two situations can be ranked uniquely using either the compensation approach or the social utility approach, but in some other cases, the ranking is ambiguous. While a direct comparison of these two approaches is not the major purpose of this paper, our results do bring out the point that a rise in the social utility level or the social welfare level does not guarantee a Pareto improvement through compensation. Fourth, in deriving conditions for welfare improvement, the paper separa-
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51
tely examines two ways of compensating the losers: lump-sum transfers and commodity consumption taxes. Using commodity taxes for compensation was first suggested by Dixit and Norman (1980). Whereas Kemp and Wan (1986), and Dixit and Norman (1984, 1986) analyzed how an economy can benefit from trade when lump-sum transfers or commodity taxes are available for compensating the losers, this paper extends their work and compares the use of these two compensation schemes for Pareto improvement as the economy shifts from one trade situation to another. Two types of trade situations will be compared separately in the paper: free trade and restricted trade. Under each type of trade situation, necessary and sufficient conditions for welfare improvement through transfer compensation, and those for welfare improvement through commodity-tax compensation, will be derived. The paper will then apply these conditions to examine the welfare impacts of shocks such as an improvement in the terms of trade, more trade in goods and factors, changes in tariff rates, and so on. A comparison of these conditions with those under the social-utility approach will be made. The rest of the paper is organized as follows. Section 2 describes the use of lump-sum transfers or consumption taxes for compensation and defines two criteria for welfare improvement as the economy shifts from one trade situation to another. Section 3 applies the criteria to compare two free-trade situations and derives necessary and sufficient conditions for welfare improvements. Section 4 analyzes the cases in which trade is restricted in at least one of the trade situations. Section 5 applies the conditions for welfare improvement to analyze the impacts of shocks like a change in the terms of trade, more trade in goods and factors, and changes in tariff rates. The tinal section gives some concluding remarks.
2. The model Consider a small open economy in which there are I tradable goods, J tradable primary factors, H individuals and N firms. All markets are competitive. Not necessarily all goods and factors are traded, but it is assumed that the number of goods and factors that are traded and locally produced is not less than the number of non-traded goods and factors. This assumption is made to guarantee that given the technologies of the economy, the prices of non-traded goods and factors are dependent upon the prices of traded goods and factors, but not on the preferences and income distribution of the economy.’ For meaningful comparative-static analysis, such depen*See Diewert and Woodland (1977) (1984). Ethier and Svensson factor mobility.
for an analysis.A recent survey is provided (1986) established similar results in the presence of goods
in Ethier trade and
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of‘ trade situations
dence is assumed to be unique in the sense that given the domestic prices of traded goods and factors, there exists a unique set of the prices of non-traded goods and factors. The preferences and endowments of the economy are assumed to be fixed. A (economic) situation faced by the economy is a specification of (i) the government’s tariffs on trading goods and factors, (ii) the economic conditions of the rest of the world summarized by the prevailing world prices of tradable goods and factors, and (iii) domestic technologies. The economy shifts from an initial trade situation s to the tinal trade situation S due to a change in one or more of the following (unless stated otherwise): (i) world prices, (ii) trade taxes, and (iii) domestic technologies. Note that autarky can be regarded as a trade situation with prohibitive tariffs. Define the following (column) vectors (lower-case letters for variables in situation s and upper-case letters for those in situation S): q E E: (r E Et) E world commodity (factor) prices; p E E!+(w E EC ) 3 domestic producer commodity (factor) prices; pc E E:(w’ E Et) z domestic consumer commodity (factor) prices; x,, E E’+(v,, E E: ) = individual h’s consumption of goods (supply of factor services); yn E E!+(v, E Et) = firm n’s supply of goods (demand for factor services); m E E!+(k E E:) = import of goods (inflow of factors).
In equilibrium, p-q and r - w are the specific trade taxes imposed by the government, while pc -p and w-w’ are the specific consumption taxes. The preferences of individual h are described by a continuous, quasiconcave, and strictly monotonic utility function, u,(x,, -v,,). Denote his expenditure function as e,(p, w, u,,). He receives a transfer bh from the government, implying that with non-satiation, b, = e,(p, w, uh) =p ‘xk - w * vhr where (I,, - yh) now denotes the optimal consumption choice. The aggregate consumption of goods equals x =xhXh and the aggregate factor supply equals v = I,, Y,,. The production possibility set of firm n is assumed to be compact and convex. Possibilities of inaction and free disposal are allowed. No transport costs, external economies and diseconomies are assumed. The firm chooses optimal inputs and outputs to maximize its profit p*y.- w. Y,. The aggregate output is denoted as u=cnu.. Equilibrium of factor markets means En Y,= v+k. Assuming constant returns to scale and perfect competition, the firm’s maximum profit is zero, implying p .y - w. (v + k) = 0. Two alternative income redistribution policies of the government are considered in this paper. A lump-sum transfer policy is described by the Hvector of distribution b=(b,, . . . , b,)T. The net transfer to all individuals equals & bh = &,(PC ’ xh - wc * vh) =p' . x - wc. Y. Alternatively, income can be redistributed using consumption taxes of specific rates w-p) on goods and
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(w- wc) on factors consumed by nationals.3 There is a third policy of the government, namely trade restriction with tariffs, which also has income distributional effects, but it is not used for such a purpose in this paper. Existence and uniqueness of equilibrium can be analyzed using the standard arguments.4 With non-satiation in consumption and zero-profit production, the net revenue of the government from the transfer and tax policies, which is the consumption tax revenue plus tariff revenue less transfers to individuals, equals the trade balance, because
= --p.x+w.v+(p-q).m+(w-r).k = -p.y+w.v+w.k-q.m-r.k = -q-m-r+k.
(1)
The policies of transfers, consumption taxes, and trade restriction are said to be feasible if and only if the government’s net revenue is non-negative, i.e.
+[(p’-p).x+(w-w’)*v]+[(p-q).m+(w-r)*k]zO.
(2)
For simplicity, we assume that if the above government revenue is positive, it is distributed to individuals in the form of poll grants or is disposed of freely.5 This guarantees that, in equilibrium, we have a balanced government budget and, thus, a balanced trade. As noted by Boadway (1974) and Foster (1976), strong compensation tests that assume a given aggregate consumption bundle, and weak compensation tests in which income or purchasing power is redistributed, can be distinguished. Boadway and Bruce (1984, p. 97) showed that a welfare improvement that passes a strong compensation test will also pass a weak
‘Using the terminology of Brecher and Choudhri (1990) the consumption taxes considered here are taxes by nationality. They also considered location-based commodity taxes and showed that the latter taxes cannot compensate losers in an economy when free movements of factors are allowed. ?See, for example, Arrow and Hahn (1971) and Grandmont and McFadden (1972). ‘Distributing the revenue in the form of poll grants is. in fact, the fourth policy of the government and it may alkct the income and consumption of individuals, and even production of firms. Thus, we should bear in mind that in specifying the equilibrium point, how the government spends the revenue has already been assumed implicitly.
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compensation compensation
K.-Y.
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test, but not vice versa. Thus, this paper focuses on weak tests only. Two weak compensation tests are suggested below:
incomplete weak compensation test (IWCT). Situation
S is said to be IWCT preferable to situation s if in situation S, through income redistribution, all individuals can be made no worse off, with some better off, than what they actually are in situation s. Complete weak compensation tests (CWCT). Situation S is said to be CWCT
preferable to situation s if in situation S, through income redistribution, all individuals can be made no worse off, with some better off, than what they could be through income redistribution in situation s. The IWCT is defined along the spirit of Boadway (1974). Foster (1976) and Bruce and Harris (1982) for closed economies, and that of Krueger and Sonneschein (1967), and Diewert, Turunen-Red and Woodland (1984) for open economies.6 The test is useful for examining the welfare impacts of exogenous shocks, but because of the possibility of the Scitovsky reversal [Scitovsky (1942)], the test may give inconsistency in policy recommendation. The CWCT is consistent (and transitive) and good for checking government policies, but it is more restrictive (or less complete) and hence is more difficult to pass. By the definitions, passing the CWCT implies passing the IWCT, but not vice versa, and if the IWCT can be passed independent of the initial income distribution, the CWCT is passed as well. The IWCT test is analogous to the Hicks criterion and the CWCT is analogous to the Samuelson criterion for welfare improvement.
3. Free-trade situations This section derives necessary and sufficient conditions for welfare improvement when distortions like trade restrictions and domestic taxes are absent in both situations. Thus, in this section we assume that q=p=p’, r=w=w’, and similar conditions for situation S before any compensation. The economy experiences exogenous changes in the prevailing world prices or domestic technologies. For convenience, we assume that there are initially no lump-sum transfers or consumption taxes in both situations before any compensation is made, but this assumption is not crucial and can be relaxed without affecting the results. For compensation in situation S, consider first the use of lump-sum 6Krueger and Sonnenschein (1967) define the criterion of ‘potential gain’ as the one that ‘compares the set of possibilities at a new set of prices with the actually chosen (emphasis added) at the former prices’.
K.-Y.
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Wang,
Welfare comparison
of trcide situations
55
Note that in the present framework, transfers do not affect and factor prices. Suppose that the consumption bundle of h in situation s is (x,, -v,,) and that in situation S before
compensation is (X,,, - I’,,). If (A?,‘,,, - Q) is the minimum-expenditure consumption bundle for the individual when facing P and W to reach utility compensating variation level then his CV, equals n,(x,, - v,), (P.X,,- W. If,,)-(P.XbW. Q). His compensation variation then equals in magnitude the minimum government transfer B,, he has to receive in order to remain as well off as before, B,,= - CV,,. Thus, the total government transfer required to make every individual as well off as before equals -ch CV,. Now we are ready to state a necessary and sufficient condition for welfare improvement. Proposition 1. Given free trade, if income can be redistributed by using lump-sum transfers, the situation S is IWCT preferable to situation s if and only if the aggregate compensating variation is positive. Proof. The proposition follows nearly immediately the definition of feasibility of the government income redistribution policy. If situation S is IWCT preferable to situation s, then the lump-sum transfer policy to make some individuals better off, with none worse off, is feasible. This means that the above defined sum of transfers paid to individuals is negative, or that the aggregate compensating variation is positive. On the other hand, if the aggregate compensating variation is positive, the compensation policy is feasible. 0
The necessary part of Proposition 1 was proved by Foster (1976) using a different method. What is new in the proposition is that for a small open economy, a positive aggregate compensating variation is also a sufficient condition for welfare improvement, as the consumption possibility frontier of the economy can be represented by a hyperplane in the commodity space. We have thus extended a result in Boadway and Bruce (1984) that for a closed economy a positive aggregate compensating variation implies a welfare improvement if the production possibility frontier of the economy is linear. Two more results concerning the lump-sum compensation policy can be introduced. Lemma 1. if, under free trade, there is a rise in national income evaluated at final prices, i.e. ‘For the details about the mechanism of income redistribution using lump-sum transfers, see, for example, Chipman and Moore (1972). Grandmont and McFadden (1972). and Kemp and Wan (1986).
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K.-Y. K’ong, Welfure comparison of‘ trade siruations
P.X-
w. V>P.x--
w.v,
(3)
then the aggregate compensating variation is positive. Proof. Using the notation in the previous proof and by the detinition of minimum expenditure function, for individual h, P. X,,- W* V, s P*‘x,W. vk, where (X,,, - V,,) is the minimum-expenditure consumption bundle at prices P and W to reach the utility level of u,(x,, -v,,). Aggregating over the individuals, P.x’W. V’sP*xWe v. The aggregate compensating variation CV equals (P.XW. V)-(P-X’W. V’), and is positive if (3) holds. IJ
Note that Lemma 1 remains valid even if there are consumption long as P and W are replaced by consumer prices PC and WC.
taxes, as
Proposition 2. Given free trade, if (3) holds and if income can be redistributed by using lump-sum transfers, rhen situation S is I WCT preferable to situation s. Proof.
The proposition
is obvious from Proposition
1 and Lemma 1.
0
Note that if the preferences of all individuals are such that consumption substitution does not exist at the initial equilibrium point, then the consumption bundle (X,,, - I’,,) is the same as (x,,, - v,,) for all individuals and (3) holds if and only if the aggregate compensating variation is positive. In that case, (3) is a necessary and sufficient condition for welfare improvement. However, if consumption substitution exists for at least one individual, (3) is just a sufficient, but not a necessary, condition for welfare improvement.’ We now examine compensation by using consumption taxes. Consumption taxes are imposed so that in situation S the initial prices faced by consumers are restored without disturbing the prices faced by producers. Thus, the consumers will choose the same consumption bundles and are as well off as before. However, for welfare improvement, some individuals must be made better off. This requires that the tax revenue be positive and be distributed to some or all individuals. Two ways of distributing the revenue have been suggested. First, if the Weymark (1979) condition is satisfied, then some of the consumption prices can be changed marginally to benefit some individuals without affecting the utility of the others.’ An alternative method is to aChipman and Moore (1978) showed that in order for an increase- in the real national income to imply an improvement in potential welfare in all conceivable situations, it was necessary for individuals’ preferences to be identical and homothetic. ‘The Weymark condition can be stated as: ‘There exists at least one commodity, either pure or a Hicksian composite, such that in the initial situation some individuals are net buyers of it and none are net sellers, or vice versa.’ Dixit and Norman (1986) slightly modified it to avoid boundary problems.
K.-Y. H’ong. Welfare comparison of trdde siruarions
give each individual a poll grant in such a way that the sum of grants is not greater than the consumption tax revenue.” Both distributing the revenue are allowed in this paper. It should be noted consumption tax policy is inefficient in the sense that it introduces between the consumers’ prices and producers’ prices.
57
the poll ways of that the a wedge
Proposition 3. Suppose that free trade exists and income can be redistributed by using consumption taxes (p-P) and ( W-w). Situation S is I WCT preferable to situation s if and only if there is a rise in the national income as given by (3).” Proof. Suppose that (3) holds and that the government imposes specific taxes (P-P) on consumption goods and (W-w) on factor services in situation S. Facing prices that are the same as those in situation s, individuals will choose the same consumption bundle and enjoy the same utility levels as before. Condition (3) implies that the consumition tax revenue is positive: (p-P).x+(W-w)*v= -P.x+ W*v> -P*X+ W* Y=O, where the fact that p*x-w.v=P.XW. Y=O and (3) have been used. The revenue is distributed as described above to make some individuals better off. Next note that if situation S is IWCT preferable to situation s under the above income redistribution consumption tax policy, the revenue must be positive: (p-P)*x+(W-w).v>O. Since pax-w.v=P*XW. Y=O, (3) is immediately implied. 0
tiropositions 2 and 3 show that under certain conditions a rise in national income as given by (3) is a sufficient and necessary condition for welfare improvement in the IWCT sense, whether income is redistributed through lump-sum transfers or consumption taxes. The result is very much similar to the welfare improvement condition for a consumer facing exogenous prices, or that of a small open economy with a well-behaved social utility function. We are able to show that it holds even when a social utility function does not exist and when compensation is required. 4. Welfare change under restricted trade
We now turn to the trade situations in which trade is restricted by tariffs (subsidies being negative tariffs) on trading goods and factors. The economy “For more details of how the tax revenue is distributed to achieve Pareto improvement, see Dixit and Norman (1984, 1986). “An anonymous referee pointed out a limitation of the necessary part of the proposition [that S is IWCT preferred to s with consumption taxes implies (3)] and of the consumption tax policy under consideration. There may be cases in which any attempt to restore prices to their initial levels. as required by the policy, will generate negative revenue; yet all individuals may already be better off without any compensation.
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shifts from situations s to S due to a change in the world prices, tariff rates, or technologies. In both situations, lump-sum transfers and consumption taxes may exist before any compensation, i.e. the transfer to individual h is bh=pc.xh-wC.v,,, and there are specific consumption taxes (PC-p) and w’). Feasibility condition (2) is assumed. Note that in the special case in (wwhich no initial transfers and consumption taxes are present, (2) states that the tariff revenue is non-negative. This type of trade is called ‘trade under self-financing tariffs’ by Ohyama (1972) or ‘natural trade’ by Deardorff (1982). Furthermore, in both situations and before any compensation, trade balance evaluated at world prices is zero. Let us consider the use of consumption taxes for compensation. In situation S, the government imposes specific consumption taxes pc - P and W- wc on goods and factors, respectively. Individual h continues to receive a transfer bb =pc *x,, - we. v,,. Thus, he faces the same prices, receives the same incomes, consumes the same bundle (x,, -v,), and is as well off as in situation s. Since producers’ prices are not distributed by the consumption taxes, the production remains unchanged. This means that both before and after the imposition of consumption taxes, the output, Y, and the inputs remain unchanged, i.e. K’+ v= K+ V, where K’ is the post-compensation import of foreign factors. Define M’zx - Y. By (I), the government revenue equals the trade balance, -Q. M’ - R. K’. If we can show that the revenue is positive, and it is distributed by changing the tax rates slightly if the Weymark condition holds, or by giving some individuals appropriate poll grants, then the final situation is IWCT preferable to the initial situation. Proposition 4. Suppose that trade is restricted by non-prohibitive tariffs and is and balanced before any compensation. Using consumption taxes (p-P) (W-w) for compensation, situation S is I WCT preferable to situatipn s if and only if there is a rise in the national income at international prices, i.e. Q*X-R.
V>Q.x--R.v.
(4)
Proof.
The pre-compensation trade is balanced, i.e. -Q *MRearranging terms gives Q. Y = Q. X+ R. K. The post-compensation ment revenue, which equals the trade balance, reduces to -Q.M’-R.K’=
-Q-x+Q-
Y-R.
K’
[M’rx’-
= -Q.x+Q.X+Q.K-R.K’
=-Q.x+Q.X+Q.v-R. Thus, the government
R *K= 0.
govern-
Y-j
[Q.Y=Q.X+R*K-j V
[V-tK=v+K’].
revenue is positive if and only if condition
(4) is
K.-Y. Wang, Welfare
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comparisonof trade siruations
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2 A,
>
0
Good
1
Fig. 1
satisfied. The rest of the proof follows the definition compensation policy. 0
of feasibility
of a
It is interesting to compare the necessary and sufficient condition in (4) under the compensation approach with a similar condition when a social utility function is assumed. In condition (4) national income is evaluated at the final world prices. This follows the idea of Little and Mirrlees (1969), and Bhagwati and Hansen (1973), who argued that world prices, rather than domestic prices, better reflect the potential welfare of a small trade-distorted economy. However, under the social utility approach, whether distortions are present, welfare improvement usually requires a rise in national income evaluated at domestic consumer prices. [See, for example, Ohyama (1972, pp. 43-47).] Let us now turn to the use of lump-sum transfers for income redistribution. The first result that we are going to establish is that in the presence of distortions, a positive aggregate compensating variation, is neither a necessary nor sufficient condition for welfare improvement. When the distortion is in the form of a divergence between consumption and production prices, the necessary part was pointed out by Boadway (1974) and Foster (1976). A similar result holds in the presence of import tariffs and it can be proved by considering a hypothetical two-good economy shown in fig. 1. SS is the Scitovsky contour through the consumption point C, in the initial situation. QQ represents the final world price line through production point G. The
K.-Y. Wang, Welfare comparison of trade situations
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production is assumed to be independent of any compensation policies. In the final situation, in the presence of a tariff on the imported good 2, the consumption point is given at C, and the domestic price ratio given by the (negative of the) slope of line Pip,. (Neglect line P2Pz, and points Cz and D, for the time being.) Then D,, a point at which Pi!‘, touches contour SS, is the consumption point with the minimum total expenditure to make every individual as well off as before. D, is below and to the left of QQ, implying the existence of a trade surplus and a feasible lump-sum transfer policy. However, the aggregate compensating variation is negative because C, is below line P,P,. We can also show that a positive compensating variation is not a sufIIcient condition for welfare improvement. To do this, consider again fig. 1, but assume that given the world price line QQ through production point G in the final situation,. C, is the consumption point, and line P2P, is the domestic price line touching the Scitovsky contour SS at point D,. Since line P,P, also represents the minimum total expenditure to reach the initial utility levels of all individuals, and since C2 is above the line, the compensating variation is positive. However, because point D, is above and to the right of line QQ, consuming the bundle of goods represented by point D, will lead to a trade deficit and a government budget deficit, and thus the lump-sum transfer policy is not feasible. Moreover, the figure shows the case in which condition (4) holds, because point CO is below the world price line QQ. This means that even (4) is in general not a sufficient condition for welfare improvement. We now give the following sutlicient condition for welfare improvement: Proposition 5. If (i) (4) is given, (ii) trade is balanced before any compensation, and (iii) final domestic consumer prices are a linear combination of final world prices and initial domestic consumer prices: P’=aQ+bp’
and
W’=aR+bw’,
(5)
where a, b 20 with at least one of them positive, then situation S is I WCT preferable to situation s when income is redistributed by using lump-sum transfers. Proof. Suppose that in situation S individual h, when facing consumer prices PC and WC, receives a transfer PC* Xk- WC* V;, from the government and chooses a consumption bundle (Xh, - I’& where u,,(XI, - Vh)= u,,(x,, -Y,,). He is as well off as before. Denote the corresponding aggregate consumption bundle by (X’, - V’). By the definition of the minimum
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of trade situations
expenditure
function, P’*X’- WC. V’s P’*x- W’.v and p’*x- w’.vs Substitute the values of PC and WC in (5) into the first inequality, multiply the second inequality by b, and add up the two give a(Q.X’-RV’)~u(Q.x-RRV). If a>O, then inequalities to Q.X’-R. V’sQ.x-R-v. If a=O, then b>O and Pc=bpc and WC=bwC, implying (with uniqueness in consumption) that X=x, Y’=v and Q*X’-R* V’=Q.x-R-v. In either case, the result together with (4) gives:
p”X’-
wc. I”.
Q-X-R.
V>Q.X’-R.
I”.
(6)
Since the transfers do not affect producer prices, firms’ outputs and inputs remain unchanged, implying that V+ K= V’+K’, where K’ is the posttransfer inflow of foreign capital. By (l), the government revenue reduces to
> -Q..X+
R. V+Q* Y- R*( V+K)
[condition (6)]
= -Q.M_R.K
=o
[zero pre-compensation trade balance].
The trade surplus then implies that the transfer policy is feasible and that situation S is IWCT preferable to situation s. 0 A corollary of the proposition is that (4) is a sufficient condition for welfare improvement in two special cases: (i) free trade in the final situation, a= 1 and b=O, and (ii) no change in the consumer prices, a=0 and b= 1. Two more special cases will be introduced below. 5. Applications This section analyzes how the above propositions can be applied to show the welfare impacts of some trade conditions. Some of the results are analogous to the results in the literature when a social utility function is assumed [see, for example, Ohyama (1972) and the reference cited below], meaning that there are cases in which we can both make every individual better off through compensation, and reach a higher social utility level. However, there are cases in which the two approaches are contradictory, showing that a higher social utility level may not be sufficient to make every individual better off. Assume first that free trade exists with no domestic taxes. The world prices
K.-Y. W’ong. Welfare comparison of trade situations
6’
are identical to domestic consumer and producer prices. The national income levels in situation s and situation S are related to each other in the following ways: Q-X-R.
V=Q.
Y-R-
=Q. Y-R.
V+Q.M V-R.K+Q.M+R.K
zQ.y-R.v-R.k+Q.M+R.K =Q.x--R*v+Q.(M-m)+R*(K-k).
(7)
The inequality is due to profit maximization and convexity of technologies. Condition (7) immediately gives the following proposition. Proposition 6. open economy,
Given free
trade, if the following condition holds for a small
Q*(M-m)+R*(K-k)>O,
(8)
then the final situation is IWCT preferable to the initial situation, and compensation can be made by using either lump-sum transfers or consumption taxes. Proof.
It follows Propositions
2 and 3 and condition (7).
0
It is well known in the literature that condition (8) implies a higher social utility level. Proposition 6 shows that given condition (8), some individuals can be made better off, with none worse off, and either lump-sum taxes or consumption taxes can be used to compensate losers. The proposition has several interesting applications. First, more trade, in the sense of a higher value of import evaluated at final prices, is better than less trade. Second, if there are fixed amounts of foreign factors in the economy, at least in the short run [as analyzed, using a social utility function, in Bhagwati and Tironi (1980), Bhagwati and Brecher (1980), and Brecher and Bhagwati (1981)], then K=k and the sufficient condition (8) for welfare improvement is equivalent to Q. (M - m) > 0. Another application of Proposition 6 is to show that ‘trade in more goods/ factors is better than less’, as given in the following proposition. Proposition 7. Given free trade and exogenous/y determined world prices, trade in more goods and factors (in the sense that some goods and factors that were not tradable are now tradable, while .those that were tradable are still
K.-Y. Wang, Welfare
comparison
of trade situations
63
tradable) is CWCT preferable to less, and compensation can be made by using either lump-sum transfers or consumption taxes. Proof.
We first show that trade in more goods and factors is IWCT preferable to less. Partition the vectors of consumption in the initial situation into two parts, x =(x’~,x”~)~ and v=(v’~, v”~)~, where the primed variables refer to the goods and factors that are traded in both situations, and the double-primed variables refer to the goods and factors that are non-traded in the initial situation but traded in the final situation. Partition all other vectors in a similar way. Because trade is balanced in both situations, Q*M+ R* K= Q’.m‘+ R’*k’=O, and because there is no trade in the double-primed goods and factors in the initial situation, m”=O and k”=O. Thus, a weak version of condition (8) holds: Q-(M-m)+R*(K-k)= -Q” *m” -R” *k” = 0. Proposition 6 then implies that through either lump-sum transfers or consumption taxes, every individual can be made at least not worse off. In fact, some individuals can be made better off if production and/or consumption substitution is possible. Then note that the above result does not depend on the initial consumption point and thus not on the initial income distribution. Thus, this policy of trade liberalization passes the CWCT as well. 0 Another application of Proposition 6 is to determine the welfare effect of an improvement in the terms of trade. Proposition 8. Given free trade, if there is an improvement in the terms of trade of a small open economy in the sense that
Q.m+ R*kcO,
(9)
then there is a welfare improvement in the IWCT sense, and compensation can be made by using either lump-sum transfers or consumption taxes. Proof. Because of a balanced trade, Q *M+ R *K=O. If condition (9) is given, condition (8) holds. Proposition 6 then implies Proposition 8. IJ
Special forms of condition (9) have appeared in the literature. For example, when there is pure exchanges of goods, it can be reduced to an improvement in the commodity terms of trade, Q-m
(10)
as in Kemp (1962) and Krueger and Sonnenschein (1967). When there is only
K.-Y. Wong, Welfare comparison of trade situations
64
movement of factors but autarky in trade, as considered in Wong (1983, 1986),” the correct condition for welfare improvement should be an improvement in thefactor terms of trade, as follows: . R.k
(11)
Another point about Proposition 8 is that (9) passes the IWCT. but not necessarily the CWCT, a point noted by Kemp (1962) and Krueger and Sonnenschein (1967). We now turn to the cases in which trade is restricted. As shown in the previous section, both the IWCT and CWCT for welfare improvement are more difficult to pass under restricted trade than under free trade. Before we derive sufficient conditions for welfare improvement, let us first prove the following lemma. Lemma 2. Gicen fixed technologies, if the final domestic producer prices are a linear combination of the final world prices and initial domestic producer prices, i.e. P=cQ+dp
and
W=cR+dw,
(12)
for c, dz 0 with at least one of them positive, then Q. Y-R,
V-R.KlQ.y-Rev-R.k.
(13)
Owing to profit maximization of the firms, P* Y-W. V- W* Kz W-v- W.k and p.y-w-v-w.kzp. Y-w. V-w.K. Substitute the values of P and W given in (12) into the first inequality, multiply the second inequality by d, and add up the two inequalities to give Proof P-y-
c(Q. Y-R.
V-R.K)zc(Q.y-Rev-R.k).
If c>O, (14) implies (13). If c=O, and d>O, then P=dp, Y=y and V+K=v+k, and (13) is again implied. 0
(14) W=dw,
implying
Proposition 9. For a small tariff-ridden economy with given technologies, if conditions (5), (12) and (8) hold, then situation S is IWCT preferable to situation s whether lump-sum transfers or consumption taxes are used for compensation. Proof.
By Lemma
2, condition
(12) implies (13) which in turn implies
‘*Wang (1983, 1986) also considered factor movements in the presence of goods trade. The results were proved with the assumption of the existence of a social utility function.
K.-Y.
Wang,
Welfare
comparison
of trade situations
condition (7). Given conditions (7) and (8), condition (4) holds. Proposition is then implied by Propositions 4 and 5. 0
65
9
What Proposition 9 means is that if there is an improvement in the external terms of trade as given by condition (8), and if conditions (5) and (12) are satisfied, then there is an improvement in welfare in the IWCT sense, and compensation can be made by using either lump-sum transfers or ‘consumption taxes. Four special cases in which (12) holds can be mentioned. The first two were noted in the previous section: free trade in the final situation, c= 1, d=O and unchanged domestic prices, c=O and d =O. The third case is a small, tariff-ridden economy with two traded goods and a fixed supply of factors. Suppose that there is an improvement in the terms of trade as described by condition (8). It can be shown that if no consumption taxes exist in either situation, there exists a scalar 1 li.20 which satisfies condition ( 12).13 Thus, by Proposition 9, the improvement in the terms of trade is welfare improving. Kemp (1969, pp. 268-270) showed this result using a social utility function. We show that it also holds if compensation is needed. In fact, this result also holds if there exist consumption taxes as long as the ad valorem rates are uniform across commodities and factors. However, this result can hardly be generalized to a multi-good economy. The fourth case in which condition (12) holds is given in the following proposition. Proposition 10. For a small, tarin-ridden open economy with fixed technologies and uniform ad valorem consumption tax rates across commodities and factors, a proportional reduction in tariff passes the CWCT for welfare improvement, whether lump-sum transfers or consumption taxes are used for compensation. Proof.
We first show that the final domestic (consumer and producer) prices are a linear combination of the world prices and the initial domestic prices. To economize the use of notation, let us consider trade in goods first. Define t (T) as the diagonal J x J matrix whose elements are the ad valorem tariff rates on the goods before (after) the reduction in tariff. The elements in t or T may be different and may be positive (for taxes), negative (for subsidies), or zero (for free trade in the commodity). Using the above notation, we have p=(l+r)Q and P=(I+ T)Q, where I is the identity matrix. A proportional reduction in tariff means that T=,b, where I> i.>O. Thus, l3Let good 2 be the importable and good 1 be the exportable. Denote the constant ad valorem tariff rate as r. The relationship between domestic prices and world prices is p1 =q, and p2 =( 1 +r)q,. Suppose that there is a decrease in the world price of good 2 so that the final price is Qz= 4q2, where I > q5>0, while the world price of good 1 remains unchanged, Q, =q,. Then condition (8) holds. Condition (12) holds, too, with 1= (1 + r - 4 - &)/( 1 + r - 4).
66
K.-Y.
P=(f+
oQ=(r+j_l)Q=(l
Wang, Welfare comparison
-i.)Q+i.(l+r)Q=(
of‘ trade situations
1 -i.)Q+i.p,
which means that
P is a linear combination of Q and p. Similar arguments can be used to show that W=( 1 -i.)R+Lw. Thus, condition (12) holds, and Lemma 2 then implies
condition (13) which in turn implies (7). Because consumption tax rates are uniform across commodities and factors, condition (12) implies condition (5). Since trade is balanced both before and after the change in tariff, Q*M+ R. K=Q.m+ R.k=O, recalling that world prices are unchanged. Thus, condition (8) with a weak inequality is satisfied. Conditions (7) and (S), and production substitution possibilities imply an increase in national income. By Proposition 9, a proportional reduction in tariffs is IWCT preferable to the initial situation. Since the above result does not depend on the initial equilibrium point and income distribution, a proportional reduction in tariffs is CWCT preferable too. 0 The proportional reduction in tariffs is a piecemeal policy suggested by several people. l4 For example, Diewert, Turunen-Red and Woodland (1984) showed that it passes the IWCT in a many-individual economy without any consumption taxes. We showed that it passes the CWCT as well, and consumption taxes may exist, as long as the ad valorem tax rates are uniform across commodities and factors. The proposition can easily be extended to imply the well-known propositions (at least for a small economy) that ‘restricted trade is better than no trade’, ‘free trade is better than no trade’, and ‘free trade is the optima1 policy’.
6. Concluding remarks This paper shows how two trade situations can be compared from the welfare point of view of a many-individual economy without relying on a social utility function or a social welfare function. We suggest two criteria for comparing welfare. The IWCT, which does not require income redistribution in the initial situation, is useful in examining whether an exogenous shock, such as a change in the external terms of trade, or an internal policy, such as a change in the tariff, is beneficial, but the CWCT is a consistent test for any trade policy recommendation. Two types of trade situations are considered: free trade and restricted trade. A change in the trade situation may be due to a change in world prices, trade policies, or domestic technologies. In each type of trade situation, necessary and sufficient conditions for welfare improvement are derived, either in the IWCT or CWCT sense.
“See Woodland (1982, ch. 11) for a recent survey.
K.-Y. Wong, Welfare comparison of trade situations
67
We extend some welfare improvement conditions for closed economies to welfare improvement conditions for open economies. We also compare some of these conditions with the conditions derived when a social utility function is assumed. As pointed out in the introduction to this paper, there are three approaches to welfare comparison: social welfare function, social utility function, and the compensation principle. The choice of an approach unavoidably involves value judgment. This paper does not compare the merits and demerits of these three approaches. However, it may be appropriate to point out that a rise in the social utility level or the social welfare level does not necessarily mean a (potential) Pareto improvement.‘5 This paper gives some conditions under which both the social-utility and the compensation approaches give the same welfare ranking, and some conditions under which they do not. 15A related point is that welfare comparison using a well-behaved social utility function or a social welfare function is complete but welfare comparison based on the Pareto criterion is not.
References Arrow, K.J. and F.H. Hahn. 1971, General competitive analysis (Holden-Day, San Francisco). Bhagwati, J.N., 1968, The gains from trade once again. Oxford Economic Papers 20, 137-148. Bhagwati. J.N. and R.A. Brecher, 1980. National welfare in an open economy in the presence of foreign-owned factors of production, Journal of International Economics 10, 103-t 15. Bhagwati, J.N. and B. Hansen. 1973, Should growth rates be evaluated at interntional prices?, in: J. Bhagwati and R. Eckaus, eds., Development and planning: Essays in honour of Par1 Rosenstern-Rodan (MIT Press, Cambridge). Bhagwati, J.N. and E. Tironi, 1980, Tariff change. foreign capital and immiserization: A theoretical analysis, Journal of Development Economics 7. 71-83. Boadway, R.W., 1974, The welfare foundations of cost-benefit analysis, Economic Journal 84, 926-939. Boadway, R.W. and N. Bruce. 1984, Welfare economics (Basil Blackwell Inc., New York). Brecher. R.A. and J.N. Bhagwati, 1981, Foreign ownership and the theory of trade and welfare, Journal of Political Economy 84, 497-511. Brecher, R.A. and E.U. Choudhri, 1990, Gains from international factor movements without lump-sum compensation: Taxation by location versus nationality, Canadian Journal of Economics 23, 44-59. Bruce. N. and R.G. Harris. 1982, Cost-benefit criteria and the compensation principle in evaluating small projects. Journal of Political Economy 90, 755-776. Chipman, J.S. and J.C. Moore, 1972, Social utility and the gains from trade, Journal of International Economics 2. 157-172. Chipman, J.S. and J.C. Moore, 1978,The new welfare economics 1939-1974, International Economic Review 19, 547-584. Deardorff. A.V., 1982, The general validity of the Heckscher-Ohlin theorem, American Economic Review 72, 683694. Diewert, W.E. and A.D. Woodland, 1977, Frank Knight’s theorem in linear programming revisited, Econometrics 45. 375-398. Diewert, W.E., A.H. Turunen-Red and A.D. Woodland, 1984, Productivity and pareto improving changes in taxes and tariffs, Mimeo. (University of British Columbia). Dixit, A. and V. Norman. 1980, Theory of intenational trade (James Nisbet and Co. Ltd., Digswell Place, Welwyn). Dixit, A. and V. Norman. 1984, Pareto-benelicial distribution of aggregate economic gains without lump-sum transfers, Mimeo.
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Wang,
Welfure
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of trade situations
Dixit. A. and V. Norman, 1986. Trade gains without lump-sum compensation, Journal of International Economics 21, I1 t-122. Ethier, W.J., 1984, Higher dimensional issues in trade theory, in: R.W. Jones and P.B. Kenen. eds.. Handbook of international economics, Vol. 1 (North-Holland. Amsterdam) 131-184. Ethier, W.J. and L.E.O. Svensson, 1986, The theorems of international trade with factor mobility, Journal of International Economics 20, 21-42. Foster, E., 1976, The welfare foundations of cost-benelit analysis - A comment, Economic Journal 86, 353-358. Grandmont, J.M. and D. McFadden, 1972, A technical note on classical gains from trade, Journal of International Economics 2, 109126. Grinols. E.L. and K.Y. Wong, 1990, An exact measure of welfare change, Canadian Journal of Economics (forthcoming). Grossman, G.M., 1984, The gains from international factor movements, Journal of International Economics 17. 73-83. Halvorsen, R. and M.G. Ruby, 1983, Benefit-cost analysis of air-pollution control (Lexington Books, Lexington). Kemp, M.C., 1962, The gain from international trade. Economic Journal 72, 303-319. Kemp, M.C., 1969, The pure theory of international trade and investment (Prentice-Hall, Englewood Cliffs, NJ). Kemp, M.C. and H.Y. Wan, 1972, The gains from free trade, International Economic Review 13, 509-522. Kemp, M.C. and H.Y. Wan, 1986. Trade gains with and without lump-sum compensation, Journal of International Economics 21.99-l 10. Krueger, A.O. and H. Sonnenschein, 1967, The terms of trade, the gains from trade and price divergence, International Economic Review 8, 121-127. Little, I.M.D. and J.A. Mirrlees, 1969, Manual of industrial project analysis in developing countries, Vol. 2 (Organisation of Economic Cooperation and Development, Paris). Ohyama. M., 1972, Trade and welfare in general equilibrium, Keio Economic Studies 2, 37-73. Samuelson, P.A., 1939, The gains from international trade, Canadian Journal of Economics and Political Science 5, 195-205. Samuelson, P.A., 1956, Social indilTerence curves, Quarterly Journal of Economics 70, l-22. Samuelson, P.A., 1962, The gains from international trade once again, Economic Journal 72, 820-829. Scitovsky, T., 1942, A reconsideration of the theory of tariffs, Review of Economic Studies 9, 89-110. Weymark, J.A., 1979, A reconciliation of recent results in optimal taxation theory, Journal of Public Economics 12, 171-189. Wong, K.Y., 1983, On choosing trade in goods and international capital and labor mobility: A theoretical analysis, Journal of International Economics 14, 223-250. Wang, K.Y., 1986, The economic analysis of international migration: A generalization, Canadian Journal of Economics 19.357-362. Woodland, A.D., 1982, International trade and resource allocation (North-Holland, Amsterdam).
Economics 30 (1991) 49-68. North-Holland
Welfare comparison
of trade situations
Kar-yiu Wang* Unirersity
of Washington,
Seattle,
WA 98195, USA
Received April 1989, revised version received June 1990
This paper applies the compensation principle to compare the welfare levels of a small, many-household open economy in different trade situations. Two types of trade situations, free and restricted trade, and two types of compensation schemes, lump-sum transfers and consumption taxes, are considered and compared. For each type of trade situation, necessary and sufftcient welfare-improving conditions are derivedwhen losers are compensated using either lump-sum transfers or consumption taxes. Important differences are noted between the results that are based on compensation and the familiar results based on a well-behaved social utility function.
1. Introduction It has been widely recognized that it is difficult to compare situations facing a many-individual economy from its national welfare point of view. Three different approaches to welfare comparison have been suggested in the literature, but none of them is universally accepted. First, we have the social welfare approach in which a Bergson-Samuelson social welfare function is defined in terms of the utility levels of different individuals. [See, for example, Boadway and Bruce (1984) and Halvorsen and Ruby (1983) for a detailed discussion of the merits and demerits of this approach.] In the second approach, which can be called the social utility approach, all aggregate consumption bundles are ranked with respect to a well-behaved social utility function.’ The advantage of this approach is that the economy can be regarded as a single consumer, so axioms of revealed preference can be applied. Some very general conditions for welfare improvement in the presence of goods trade were derived by Ohyama (1972), and an exact measure of welfare change was developed by Grinols and Wong (1990). Last, we have the compensation approach in which the transition from one situation to another situation is said to be preferable if all losers can be *Thanks are due to Jagdish Bhagwati, Avinash Dixit, Robert Feenstra, Earl Grinols. Robert
Halvorsenand two anonymousrefereesfor helpful comments. The author is solely responsible for any remaining shortcomings and errors. ‘Samuelson (1956) showed that a social utility function exists if a social welfare function exists and is always maximized with optimal income distribution. 0022-1996/91/SO3.50 0 1991-Elsevier
Science Publishers B.V. (North-Holland)
50
K.-Y.
Wang. Welfare
comparison
of trade situations
compensated while at least one individual can be made better off. Although it has been criticized for, among other things, assuming hypothetical, timeless, and costless compensation schemes, the compensation approach has the advantage of requiring no interpersonal comparison, and it is still adopted frequently in the literature [for example, Dixit and Norman (1986) Kemp and Wan (1986) and Diewert, Turunen-Red and Woodland (1984)]. The purpose of this paper is to take the compensation approach to compare the welfare impacts of different trade situations on a small open economy. There are four reasons for this paper. First, many compensation criteria were developed with an implicit or explicit assumption of a closed economy. Recent contributions have been made by Boadway (1974). Foster (1976), Bruce and Harris (1982), and Boadway and Bruce (1984). This paper extends some of their results to an open economy. Since trade opportunities provide more consumption possibilities to an open economy, we can hope to get more results about ranking two situations. Second, the paper derives necessary and sufficient conditions for welfare improvement when the economy shifts from one trade situation to another and when compensation is allowed. The shift in the trade situation may be due to changes in external shocks, such as the world’s technologies, preferences, and endowments, or due to changes in government policies. The results are general in the sense that previous theory of the gains from trade can be considered as special cases [Samuelson (1962), Kemp (1962) Kemp and Wan (1972), and Dixit and Norman (1980), among others] because autarky can be treated as a special trade situation with prohibitive tariffs. Another reason for analyzing the welfare impacts of a shift of trade situation is due to the fact that usually only trade situations, not autarky, are observed in the world. Third, while it is recognized that comparing trade situations is important, most papers carry out the comparison with respect to a well-behaved social utility function [Ohyama (1972), Grossman (1984), and many others]. Since the existence of a social utility function requires interpersonal comparison and depends on some strong assumptions, it is important to see how two’ trade situations can be compared using other criteria. Necessary and sufficient conditions for welfare improvement based on the compensation principle are compared with welfare improvement conditions based on a social utility function, and we will show that in some cases, two situations can be ranked uniquely using either the compensation approach or the social utility approach, but in some other cases, the ranking is ambiguous. While a direct comparison of these two approaches is not the major purpose of this paper, our results do bring out the point that a rise in the social utility level or the social welfare level does not guarantee a Pareto improvement through compensation. Fourth, in deriving conditions for welfare improvement, the paper separa-
K.-Y.
Wong, Welfirr
compaiison of trade situations
51
tely examines two ways of compensating the losers: lump-sum transfers and commodity consumption taxes. Using commodity taxes for compensation was first suggested by Dixit and Norman (1980). Whereas Kemp and Wan (1986), and Dixit and Norman (1984, 1986) analyzed how an economy can benefit from trade when lump-sum transfers or commodity taxes are available for compensating the losers, this paper extends their work and compares the use of these two compensation schemes for Pareto improvement as the economy shifts from one trade situation to another. Two types of trade situations will be compared separately in the paper: free trade and restricted trade. Under each type of trade situation, necessary and sufficient conditions for welfare improvement through transfer compensation, and those for welfare improvement through commodity-tax compensation, will be derived. The paper will then apply these conditions to examine the welfare impacts of shocks such as an improvement in the terms of trade, more trade in goods and factors, changes in tariff rates, and so on. A comparison of these conditions with those under the social-utility approach will be made. The rest of the paper is organized as follows. Section 2 describes the use of lump-sum transfers or consumption taxes for compensation and defines two criteria for welfare improvement as the economy shifts from one trade situation to another. Section 3 applies the criteria to compare two free-trade situations and derives necessary and sufficient conditions for welfare improvements. Section 4 analyzes the cases in which trade is restricted in at least one of the trade situations. Section 5 applies the conditions for welfare improvement to analyze the impacts of shocks like a change in the terms of trade, more trade in goods and factors, and changes in tariff rates. The tinal section gives some concluding remarks.
2. The model Consider a small open economy in which there are I tradable goods, J tradable primary factors, H individuals and N firms. All markets are competitive. Not necessarily all goods and factors are traded, but it is assumed that the number of goods and factors that are traded and locally produced is not less than the number of non-traded goods and factors. This assumption is made to guarantee that given the technologies of the economy, the prices of non-traded goods and factors are dependent upon the prices of traded goods and factors, but not on the preferences and income distribution of the economy.’ For meaningful comparative-static analysis, such depen*See Diewert and Woodland (1977) (1984). Ethier and Svensson factor mobility.
for an analysis.A recent survey is provided (1986) established similar results in the presence of goods
in Ethier trade and
52
K.-Y.
Wang. Welfare compurison
of‘ trade situations
dence is assumed to be unique in the sense that given the domestic prices of traded goods and factors, there exists a unique set of the prices of non-traded goods and factors. The preferences and endowments of the economy are assumed to be fixed. A (economic) situation faced by the economy is a specification of (i) the government’s tariffs on trading goods and factors, (ii) the economic conditions of the rest of the world summarized by the prevailing world prices of tradable goods and factors, and (iii) domestic technologies. The economy shifts from an initial trade situation s to the tinal trade situation S due to a change in one or more of the following (unless stated otherwise): (i) world prices, (ii) trade taxes, and (iii) domestic technologies. Note that autarky can be regarded as a trade situation with prohibitive tariffs. Define the following (column) vectors (lower-case letters for variables in situation s and upper-case letters for those in situation S): q E E: (r E Et) E world commodity (factor) prices; p E E!+(w E EC ) 3 domestic producer commodity (factor) prices; pc E E:(w’ E Et) z domestic consumer commodity (factor) prices; x,, E E’+(v,, E E: ) = individual h’s consumption of goods (supply of factor services); yn E E!+(v, E Et) = firm n’s supply of goods (demand for factor services); m E E!+(k E E:) = import of goods (inflow of factors).
In equilibrium, p-q and r - w are the specific trade taxes imposed by the government, while pc -p and w-w’ are the specific consumption taxes. The preferences of individual h are described by a continuous, quasiconcave, and strictly monotonic utility function, u,(x,, -v,,). Denote his expenditure function as e,(p, w, u,,). He receives a transfer bh from the government, implying that with non-satiation, b, = e,(p, w, uh) =p ‘xk - w * vhr where (I,, - yh) now denotes the optimal consumption choice. The aggregate consumption of goods equals x =xhXh and the aggregate factor supply equals v = I,, Y,,. The production possibility set of firm n is assumed to be compact and convex. Possibilities of inaction and free disposal are allowed. No transport costs, external economies and diseconomies are assumed. The firm chooses optimal inputs and outputs to maximize its profit p*y.- w. Y,. The aggregate output is denoted as u=cnu.. Equilibrium of factor markets means En Y,= v+k. Assuming constant returns to scale and perfect competition, the firm’s maximum profit is zero, implying p .y - w. (v + k) = 0. Two alternative income redistribution policies of the government are considered in this paper. A lump-sum transfer policy is described by the Hvector of distribution b=(b,, . . . , b,)T. The net transfer to all individuals equals & bh = &,(PC ’ xh - wc * vh) =p' . x - wc. Y. Alternatively, income can be redistributed using consumption taxes of specific rates w-p) on goods and
K.-Y.
Wong. Welfare
comparison
of wade situations
53
(w- wc) on factors consumed by nationals.3 There is a third policy of the government, namely trade restriction with tariffs, which also has income distributional effects, but it is not used for such a purpose in this paper. Existence and uniqueness of equilibrium can be analyzed using the standard arguments.4 With non-satiation in consumption and zero-profit production, the net revenue of the government from the transfer and tax policies, which is the consumption tax revenue plus tariff revenue less transfers to individuals, equals the trade balance, because
= --p.x+w.v+(p-q).m+(w-r).k = -p.y+w.v+w.k-q.m-r.k = -q-m-r+k.
(1)
The policies of transfers, consumption taxes, and trade restriction are said to be feasible if and only if the government’s net revenue is non-negative, i.e.
+[(p’-p).x+(w-w’)*v]+[(p-q).m+(w-r)*k]zO.
(2)
For simplicity, we assume that if the above government revenue is positive, it is distributed to individuals in the form of poll grants or is disposed of freely.5 This guarantees that, in equilibrium, we have a balanced government budget and, thus, a balanced trade. As noted by Boadway (1974) and Foster (1976), strong compensation tests that assume a given aggregate consumption bundle, and weak compensation tests in which income or purchasing power is redistributed, can be distinguished. Boadway and Bruce (1984, p. 97) showed that a welfare improvement that passes a strong compensation test will also pass a weak
‘Using the terminology of Brecher and Choudhri (1990) the consumption taxes considered here are taxes by nationality. They also considered location-based commodity taxes and showed that the latter taxes cannot compensate losers in an economy when free movements of factors are allowed. ?See, for example, Arrow and Hahn (1971) and Grandmont and McFadden (1972). ‘Distributing the revenue in the form of poll grants is. in fact, the fourth policy of the government and it may alkct the income and consumption of individuals, and even production of firms. Thus, we should bear in mind that in specifying the equilibrium point, how the government spends the revenue has already been assumed implicitly.
54
compensation compensation
K.-Y.
Wang,
Weljhre
comparison
of trade situations
test, but not vice versa. Thus, this paper focuses on weak tests only. Two weak compensation tests are suggested below:
incomplete weak compensation test (IWCT). Situation
S is said to be IWCT preferable to situation s if in situation S, through income redistribution, all individuals can be made no worse off, with some better off, than what they actually are in situation s. Complete weak compensation tests (CWCT). Situation S is said to be CWCT
preferable to situation s if in situation S, through income redistribution, all individuals can be made no worse off, with some better off, than what they could be through income redistribution in situation s. The IWCT is defined along the spirit of Boadway (1974). Foster (1976) and Bruce and Harris (1982) for closed economies, and that of Krueger and Sonneschein (1967), and Diewert, Turunen-Red and Woodland (1984) for open economies.6 The test is useful for examining the welfare impacts of exogenous shocks, but because of the possibility of the Scitovsky reversal [Scitovsky (1942)], the test may give inconsistency in policy recommendation. The CWCT is consistent (and transitive) and good for checking government policies, but it is more restrictive (or less complete) and hence is more difficult to pass. By the definitions, passing the CWCT implies passing the IWCT, but not vice versa, and if the IWCT can be passed independent of the initial income distribution, the CWCT is passed as well. The IWCT test is analogous to the Hicks criterion and the CWCT is analogous to the Samuelson criterion for welfare improvement.
3. Free-trade situations This section derives necessary and sufficient conditions for welfare improvement when distortions like trade restrictions and domestic taxes are absent in both situations. Thus, in this section we assume that q=p=p’, r=w=w’, and similar conditions for situation S before any compensation. The economy experiences exogenous changes in the prevailing world prices or domestic technologies. For convenience, we assume that there are initially no lump-sum transfers or consumption taxes in both situations before any compensation is made, but this assumption is not crucial and can be relaxed without affecting the results. For compensation in situation S, consider first the use of lump-sum 6Krueger and Sonnenschein (1967) define the criterion of ‘potential gain’ as the one that ‘compares the set of possibilities at a new set of prices with the actually chosen (emphasis added) at the former prices’.
K.-Y.
transfers.’ commodity individual
Wang,
Welfare comparison
of trcide situations
55
Note that in the present framework, transfers do not affect and factor prices. Suppose that the consumption bundle of h in situation s is (x,, -v,,) and that in situation S before
compensation is (X,,, - I’,,). If (A?,‘,,, - Q) is the minimum-expenditure consumption bundle for the individual when facing P and W to reach utility compensating variation level then his CV, equals n,(x,, - v,), (P.X,,- W. If,,)-(P.XbW. Q). His compensation variation then equals in magnitude the minimum government transfer B,, he has to receive in order to remain as well off as before, B,,= - CV,,. Thus, the total government transfer required to make every individual as well off as before equals -ch CV,. Now we are ready to state a necessary and sufficient condition for welfare improvement. Proposition 1. Given free trade, if income can be redistributed by using lump-sum transfers, the situation S is IWCT preferable to situation s if and only if the aggregate compensating variation is positive. Proof. The proposition follows nearly immediately the definition of feasibility of the government income redistribution policy. If situation S is IWCT preferable to situation s, then the lump-sum transfer policy to make some individuals better off, with none worse off, is feasible. This means that the above defined sum of transfers paid to individuals is negative, or that the aggregate compensating variation is positive. On the other hand, if the aggregate compensating variation is positive, the compensation policy is feasible. 0
The necessary part of Proposition 1 was proved by Foster (1976) using a different method. What is new in the proposition is that for a small open economy, a positive aggregate compensating variation is also a sufficient condition for welfare improvement, as the consumption possibility frontier of the economy can be represented by a hyperplane in the commodity space. We have thus extended a result in Boadway and Bruce (1984) that for a closed economy a positive aggregate compensating variation implies a welfare improvement if the production possibility frontier of the economy is linear. Two more results concerning the lump-sum compensation policy can be introduced. Lemma 1. if, under free trade, there is a rise in national income evaluated at final prices, i.e. ‘For the details about the mechanism of income redistribution using lump-sum transfers, see, for example, Chipman and Moore (1972). Grandmont and McFadden (1972). and Kemp and Wan (1986).
56
K.-Y. K’ong, Welfure comparison of‘ trade siruations
P.X-
w. V>P.x--
w.v,
(3)
then the aggregate compensating variation is positive. Proof. Using the notation in the previous proof and by the detinition of minimum expenditure function, for individual h, P. X,,- W* V, s P*‘x,W. vk, where (X,,, - V,,) is the minimum-expenditure consumption bundle at prices P and W to reach the utility level of u,(x,, -v,,). Aggregating over the individuals, P.x’W. V’sP*xWe v. The aggregate compensating variation CV equals (P.XW. V)-(P-X’W. V’), and is positive if (3) holds. IJ
Note that Lemma 1 remains valid even if there are consumption long as P and W are replaced by consumer prices PC and WC.
taxes, as
Proposition 2. Given free trade, if (3) holds and if income can be redistributed by using lump-sum transfers, rhen situation S is I WCT preferable to situation s. Proof.
The proposition
is obvious from Proposition
1 and Lemma 1.
0
Note that if the preferences of all individuals are such that consumption substitution does not exist at the initial equilibrium point, then the consumption bundle (X,,, - I’,,) is the same as (x,,, - v,,) for all individuals and (3) holds if and only if the aggregate compensating variation is positive. In that case, (3) is a necessary and sufficient condition for welfare improvement. However, if consumption substitution exists for at least one individual, (3) is just a sufficient, but not a necessary, condition for welfare improvement.’ We now examine compensation by using consumption taxes. Consumption taxes are imposed so that in situation S the initial prices faced by consumers are restored without disturbing the prices faced by producers. Thus, the consumers will choose the same consumption bundles and are as well off as before. However, for welfare improvement, some individuals must be made better off. This requires that the tax revenue be positive and be distributed to some or all individuals. Two ways of distributing the revenue have been suggested. First, if the Weymark (1979) condition is satisfied, then some of the consumption prices can be changed marginally to benefit some individuals without affecting the utility of the others.’ An alternative method is to aChipman and Moore (1978) showed that in order for an increase- in the real national income to imply an improvement in potential welfare in all conceivable situations, it was necessary for individuals’ preferences to be identical and homothetic. ‘The Weymark condition can be stated as: ‘There exists at least one commodity, either pure or a Hicksian composite, such that in the initial situation some individuals are net buyers of it and none are net sellers, or vice versa.’ Dixit and Norman (1986) slightly modified it to avoid boundary problems.
K.-Y. H’ong. Welfare comparison of trdde siruarions
give each individual a poll grant in such a way that the sum of grants is not greater than the consumption tax revenue.” Both distributing the revenue are allowed in this paper. It should be noted consumption tax policy is inefficient in the sense that it introduces between the consumers’ prices and producers’ prices.
57
the poll ways of that the a wedge
Proposition 3. Suppose that free trade exists and income can be redistributed by using consumption taxes (p-P) and ( W-w). Situation S is I WCT preferable to situation s if and only if there is a rise in the national income as given by (3).” Proof. Suppose that (3) holds and that the government imposes specific taxes (P-P) on consumption goods and (W-w) on factor services in situation S. Facing prices that are the same as those in situation s, individuals will choose the same consumption bundle and enjoy the same utility levels as before. Condition (3) implies that the consumition tax revenue is positive: (p-P).x+(W-w)*v= -P.x+ W*v> -P*X+ W* Y=O, where the fact that p*x-w.v=P.XW. Y=O and (3) have been used. The revenue is distributed as described above to make some individuals better off. Next note that if situation S is IWCT preferable to situation s under the above income redistribution consumption tax policy, the revenue must be positive: (p-P)*x+(W-w).v>O. Since pax-w.v=P*XW. Y=O, (3) is immediately implied. 0
tiropositions 2 and 3 show that under certain conditions a rise in national income as given by (3) is a sufficient and necessary condition for welfare improvement in the IWCT sense, whether income is redistributed through lump-sum transfers or consumption taxes. The result is very much similar to the welfare improvement condition for a consumer facing exogenous prices, or that of a small open economy with a well-behaved social utility function. We are able to show that it holds even when a social utility function does not exist and when compensation is required. 4. Welfare change under restricted trade
We now turn to the trade situations in which trade is restricted by tariffs (subsidies being negative tariffs) on trading goods and factors. The economy “For more details of how the tax revenue is distributed to achieve Pareto improvement, see Dixit and Norman (1984, 1986). “An anonymous referee pointed out a limitation of the necessary part of the proposition [that S is IWCT preferred to s with consumption taxes implies (3)] and of the consumption tax policy under consideration. There may be cases in which any attempt to restore prices to their initial levels. as required by the policy, will generate negative revenue; yet all individuals may already be better off without any compensation.
58
K.-Y.
Wong,
Welfare
comparison
of trade siruarions
shifts from situations s to S due to a change in the world prices, tariff rates, or technologies. In both situations, lump-sum transfers and consumption taxes may exist before any compensation, i.e. the transfer to individual h is bh=pc.xh-wC.v,,, and there are specific consumption taxes (PC-p) and w’). Feasibility condition (2) is assumed. Note that in the special case in (wwhich no initial transfers and consumption taxes are present, (2) states that the tariff revenue is non-negative. This type of trade is called ‘trade under self-financing tariffs’ by Ohyama (1972) or ‘natural trade’ by Deardorff (1982). Furthermore, in both situations and before any compensation, trade balance evaluated at world prices is zero. Let us consider the use of consumption taxes for compensation. In situation S, the government imposes specific consumption taxes pc - P and W- wc on goods and factors, respectively. Individual h continues to receive a transfer bb =pc *x,, - we. v,,. Thus, he faces the same prices, receives the same incomes, consumes the same bundle (x,, -v,), and is as well off as in situation s. Since producers’ prices are not distributed by the consumption taxes, the production remains unchanged. This means that both before and after the imposition of consumption taxes, the output, Y, and the inputs remain unchanged, i.e. K’+ v= K+ V, where K’ is the post-compensation import of foreign factors. Define M’zx - Y. By (I), the government revenue equals the trade balance, -Q. M’ - R. K’. If we can show that the revenue is positive, and it is distributed by changing the tax rates slightly if the Weymark condition holds, or by giving some individuals appropriate poll grants, then the final situation is IWCT preferable to the initial situation. Proposition 4. Suppose that trade is restricted by non-prohibitive tariffs and is and balanced before any compensation. Using consumption taxes (p-P) (W-w) for compensation, situation S is I WCT preferable to situatipn s if and only if there is a rise in the national income at international prices, i.e. Q*X-R.
V>Q.x--R.v.
(4)
Proof.
The pre-compensation trade is balanced, i.e. -Q *MRearranging terms gives Q. Y = Q. X+ R. K. The post-compensation ment revenue, which equals the trade balance, reduces to -Q.M’-R.K’=
-Q-x+Q-
Y-R.
K’
[M’rx’-
= -Q.x+Q.X+Q.K-R.K’
=-Q.x+Q.X+Q.v-R. Thus, the government
R *K= 0.
govern-
Y-j
[Q.Y=Q.X+R*K-j V
[V-tK=v+K’].
revenue is positive if and only if condition
(4) is
K.-Y. Wang, Welfare
Good
comparisonof trade siruations
59
2 A,
>
0
Good
1
Fig. 1
satisfied. The rest of the proof follows the definition compensation policy. 0
of feasibility
of a
It is interesting to compare the necessary and sufficient condition in (4) under the compensation approach with a similar condition when a social utility function is assumed. In condition (4) national income is evaluated at the final world prices. This follows the idea of Little and Mirrlees (1969), and Bhagwati and Hansen (1973), who argued that world prices, rather than domestic prices, better reflect the potential welfare of a small trade-distorted economy. However, under the social utility approach, whether distortions are present, welfare improvement usually requires a rise in national income evaluated at domestic consumer prices. [See, for example, Ohyama (1972, pp. 43-47).] Let us now turn to the use of lump-sum transfers for income redistribution. The first result that we are going to establish is that in the presence of distortions, a positive aggregate compensating variation, is neither a necessary nor sufficient condition for welfare improvement. When the distortion is in the form of a divergence between consumption and production prices, the necessary part was pointed out by Boadway (1974) and Foster (1976). A similar result holds in the presence of import tariffs and it can be proved by considering a hypothetical two-good economy shown in fig. 1. SS is the Scitovsky contour through the consumption point C, in the initial situation. QQ represents the final world price line through production point G. The
K.-Y. Wang, Welfare comparison of trade situations
60
production is assumed to be independent of any compensation policies. In the final situation, in the presence of a tariff on the imported good 2, the consumption point is given at C, and the domestic price ratio given by the (negative of the) slope of line Pip,. (Neglect line P2Pz, and points Cz and D, for the time being.) Then D,, a point at which Pi!‘, touches contour SS, is the consumption point with the minimum total expenditure to make every individual as well off as before. D, is below and to the left of QQ, implying the existence of a trade surplus and a feasible lump-sum transfer policy. However, the aggregate compensating variation is negative because C, is below line P,P,. We can also show that a positive compensating variation is not a sufIIcient condition for welfare improvement. To do this, consider again fig. 1, but assume that given the world price line QQ through production point G in the final situation,. C, is the consumption point, and line P2P, is the domestic price line touching the Scitovsky contour SS at point D,. Since line P,P, also represents the minimum total expenditure to reach the initial utility levels of all individuals, and since C2 is above the line, the compensating variation is positive. However, because point D, is above and to the right of line QQ, consuming the bundle of goods represented by point D, will lead to a trade deficit and a government budget deficit, and thus the lump-sum transfer policy is not feasible. Moreover, the figure shows the case in which condition (4) holds, because point CO is below the world price line QQ. This means that even (4) is in general not a sufficient condition for welfare improvement. We now give the following sutlicient condition for welfare improvement: Proposition 5. If (i) (4) is given, (ii) trade is balanced before any compensation, and (iii) final domestic consumer prices are a linear combination of final world prices and initial domestic consumer prices: P’=aQ+bp’
and
W’=aR+bw’,
(5)
where a, b 20 with at least one of them positive, then situation S is I WCT preferable to situation s when income is redistributed by using lump-sum transfers. Proof. Suppose that in situation S individual h, when facing consumer prices PC and WC, receives a transfer PC* Xk- WC* V;, from the government and chooses a consumption bundle (Xh, - I’& where u,,(XI, - Vh)= u,,(x,, -Y,,). He is as well off as before. Denote the corresponding aggregate consumption bundle by (X’, - V’). By the definition of the minimum
K.-Y.
Wong,
Welfare
comparison
61
of trade situations
expenditure
function, P’*X’- WC. V’s P’*x- W’.v and p’*x- w’.vs Substitute the values of PC and WC in (5) into the first inequality, multiply the second inequality by b, and add up the two give a(Q.X’-RV’)~u(Q.x-RRV). If a>O, then inequalities to Q.X’-R. V’sQ.x-R-v. If a=O, then b>O and Pc=bpc and WC=bwC, implying (with uniqueness in consumption) that X=x, Y’=v and Q*X’-R* V’=Q.x-R-v. In either case, the result together with (4) gives:
p”X’-
wc. I”.
Q-X-R.
V>Q.X’-R.
I”.
(6)
Since the transfers do not affect producer prices, firms’ outputs and inputs remain unchanged, implying that V+ K= V’+K’, where K’ is the posttransfer inflow of foreign capital. By (l), the government revenue reduces to
> -Q..X+
R. V+Q* Y- R*( V+K)
[condition (6)]
= -Q.M_R.K
=o
[zero pre-compensation trade balance].
The trade surplus then implies that the transfer policy is feasible and that situation S is IWCT preferable to situation s. 0 A corollary of the proposition is that (4) is a sufficient condition for welfare improvement in two special cases: (i) free trade in the final situation, a= 1 and b=O, and (ii) no change in the consumer prices, a=0 and b= 1. Two more special cases will be introduced below. 5. Applications This section analyzes how the above propositions can be applied to show the welfare impacts of some trade conditions. Some of the results are analogous to the results in the literature when a social utility function is assumed [see, for example, Ohyama (1972) and the reference cited below], meaning that there are cases in which we can both make every individual better off through compensation, and reach a higher social utility level. However, there are cases in which the two approaches are contradictory, showing that a higher social utility level may not be sufficient to make every individual better off. Assume first that free trade exists with no domestic taxes. The world prices
K.-Y. W’ong. Welfare comparison of trade situations
6’
are identical to domestic consumer and producer prices. The national income levels in situation s and situation S are related to each other in the following ways: Q-X-R.
V=Q.
Y-R-
=Q. Y-R.
V+Q.M V-R.K+Q.M+R.K
zQ.y-R.v-R.k+Q.M+R.K =Q.x--R*v+Q.(M-m)+R*(K-k).
(7)
The inequality is due to profit maximization and convexity of technologies. Condition (7) immediately gives the following proposition. Proposition 6. open economy,
Given free
trade, if the following condition holds for a small
Q*(M-m)+R*(K-k)>O,
(8)
then the final situation is IWCT preferable to the initial situation, and compensation can be made by using either lump-sum transfers or consumption taxes. Proof.
It follows Propositions
2 and 3 and condition (7).
0
It is well known in the literature that condition (8) implies a higher social utility level. Proposition 6 shows that given condition (8), some individuals can be made better off, with none worse off, and either lump-sum taxes or consumption taxes can be used to compensate losers. The proposition has several interesting applications. First, more trade, in the sense of a higher value of import evaluated at final prices, is better than less trade. Second, if there are fixed amounts of foreign factors in the economy, at least in the short run [as analyzed, using a social utility function, in Bhagwati and Tironi (1980), Bhagwati and Brecher (1980), and Brecher and Bhagwati (1981)], then K=k and the sufficient condition (8) for welfare improvement is equivalent to Q. (M - m) > 0. Another application of Proposition 6 is to show that ‘trade in more goods/ factors is better than less’, as given in the following proposition. Proposition 7. Given free trade and exogenous/y determined world prices, trade in more goods and factors (in the sense that some goods and factors that were not tradable are now tradable, while .those that were tradable are still
K.-Y. Wang, Welfare
comparison
of trade situations
63
tradable) is CWCT preferable to less, and compensation can be made by using either lump-sum transfers or consumption taxes. Proof.
We first show that trade in more goods and factors is IWCT preferable to less. Partition the vectors of consumption in the initial situation into two parts, x =(x’~,x”~)~ and v=(v’~, v”~)~, where the primed variables refer to the goods and factors that are traded in both situations, and the double-primed variables refer to the goods and factors that are non-traded in the initial situation but traded in the final situation. Partition all other vectors in a similar way. Because trade is balanced in both situations, Q*M+ R* K= Q’.m‘+ R’*k’=O, and because there is no trade in the double-primed goods and factors in the initial situation, m”=O and k”=O. Thus, a weak version of condition (8) holds: Q-(M-m)+R*(K-k)= -Q” *m” -R” *k” = 0. Proposition 6 then implies that through either lump-sum transfers or consumption taxes, every individual can be made at least not worse off. In fact, some individuals can be made better off if production and/or consumption substitution is possible. Then note that the above result does not depend on the initial consumption point and thus not on the initial income distribution. Thus, this policy of trade liberalization passes the CWCT as well. 0 Another application of Proposition 6 is to determine the welfare effect of an improvement in the terms of trade. Proposition 8. Given free trade, if there is an improvement in the terms of trade of a small open economy in the sense that
Q.m+ R*kcO,
(9)
then there is a welfare improvement in the IWCT sense, and compensation can be made by using either lump-sum transfers or consumption taxes. Proof. Because of a balanced trade, Q *M+ R *K=O. If condition (9) is given, condition (8) holds. Proposition 6 then implies Proposition 8. IJ
Special forms of condition (9) have appeared in the literature. For example, when there is pure exchanges of goods, it can be reduced to an improvement in the commodity terms of trade, Q-m
(10)
as in Kemp (1962) and Krueger and Sonnenschein (1967). When there is only
K.-Y. Wong, Welfare comparison of trade situations
64
movement of factors but autarky in trade, as considered in Wong (1983, 1986),” the correct condition for welfare improvement should be an improvement in thefactor terms of trade, as follows: . R.k
(11)
Another point about Proposition 8 is that (9) passes the IWCT. but not necessarily the CWCT, a point noted by Kemp (1962) and Krueger and Sonnenschein (1967). We now turn to the cases in which trade is restricted. As shown in the previous section, both the IWCT and CWCT for welfare improvement are more difficult to pass under restricted trade than under free trade. Before we derive sufficient conditions for welfare improvement, let us first prove the following lemma. Lemma 2. Gicen fixed technologies, if the final domestic producer prices are a linear combination of the final world prices and initial domestic producer prices, i.e. P=cQ+dp
and
W=cR+dw,
(12)
for c, dz 0 with at least one of them positive, then Q. Y-R,
V-R.KlQ.y-Rev-R.k.
(13)
Owing to profit maximization of the firms, P* Y-W. V- W* Kz W-v- W.k and p.y-w-v-w.kzp. Y-w. V-w.K. Substitute the values of P and W given in (12) into the first inequality, multiply the second inequality by d, and add up the two inequalities to give Proof P-y-
c(Q. Y-R.
V-R.K)zc(Q.y-Rev-R.k).
If c>O, (14) implies (13). If c=O, and d>O, then P=dp, Y=y and V+K=v+k, and (13) is again implied. 0
(14) W=dw,
implying
Proposition 9. For a small tariff-ridden economy with given technologies, if conditions (5), (12) and (8) hold, then situation S is IWCT preferable to situation s whether lump-sum transfers or consumption taxes are used for compensation. Proof.
By Lemma
2, condition
(12) implies (13) which in turn implies
‘*Wang (1983, 1986) also considered factor movements in the presence of goods trade. The results were proved with the assumption of the existence of a social utility function.
K.-Y.
Wang,
Welfare
comparison
of trade situations
condition (7). Given conditions (7) and (8), condition (4) holds. Proposition is then implied by Propositions 4 and 5. 0
65
9
What Proposition 9 means is that if there is an improvement in the external terms of trade as given by condition (8), and if conditions (5) and (12) are satisfied, then there is an improvement in welfare in the IWCT sense, and compensation can be made by using either lump-sum transfers or ‘consumption taxes. Four special cases in which (12) holds can be mentioned. The first two were noted in the previous section: free trade in the final situation, c= 1, d=O and unchanged domestic prices, c=O and d =O. The third case is a small, tariff-ridden economy with two traded goods and a fixed supply of factors. Suppose that there is an improvement in the terms of trade as described by condition (8). It can be shown that if no consumption taxes exist in either situation, there exists a scalar 1 li.20 which satisfies condition ( 12).13 Thus, by Proposition 9, the improvement in the terms of trade is welfare improving. Kemp (1969, pp. 268-270) showed this result using a social utility function. We show that it also holds if compensation is needed. In fact, this result also holds if there exist consumption taxes as long as the ad valorem rates are uniform across commodities and factors. However, this result can hardly be generalized to a multi-good economy. The fourth case in which condition (12) holds is given in the following proposition. Proposition 10. For a small, tarin-ridden open economy with fixed technologies and uniform ad valorem consumption tax rates across commodities and factors, a proportional reduction in tariff passes the CWCT for welfare improvement, whether lump-sum transfers or consumption taxes are used for compensation. Proof.
We first show that the final domestic (consumer and producer) prices are a linear combination of the world prices and the initial domestic prices. To economize the use of notation, let us consider trade in goods first. Define t (T) as the diagonal J x J matrix whose elements are the ad valorem tariff rates on the goods before (after) the reduction in tariff. The elements in t or T may be different and may be positive (for taxes), negative (for subsidies), or zero (for free trade in the commodity). Using the above notation, we have p=(l+r)Q and P=(I+ T)Q, where I is the identity matrix. A proportional reduction in tariff means that T=,b, where I> i.>O. Thus, l3Let good 2 be the importable and good 1 be the exportable. Denote the constant ad valorem tariff rate as r. The relationship between domestic prices and world prices is p1 =q, and p2 =( 1 +r)q,. Suppose that there is a decrease in the world price of good 2 so that the final price is Qz= 4q2, where I > q5>0, while the world price of good 1 remains unchanged, Q, =q,. Then condition (8) holds. Condition (12) holds, too, with 1= (1 + r - 4 - &)/( 1 + r - 4).
66
K.-Y.
P=(f+
oQ=(r+j_l)Q=(l
Wang, Welfare comparison
-i.)Q+i.(l+r)Q=(
of‘ trade situations
1 -i.)Q+i.p,
which means that
P is a linear combination of Q and p. Similar arguments can be used to show that W=( 1 -i.)R+Lw. Thus, condition (12) holds, and Lemma 2 then implies
condition (13) which in turn implies (7). Because consumption tax rates are uniform across commodities and factors, condition (12) implies condition (5). Since trade is balanced both before and after the change in tariff, Q*M+ R. K=Q.m+ R.k=O, recalling that world prices are unchanged. Thus, condition (8) with a weak inequality is satisfied. Conditions (7) and (S), and production substitution possibilities imply an increase in national income. By Proposition 9, a proportional reduction in tariffs is IWCT preferable to the initial situation. Since the above result does not depend on the initial equilibrium point and income distribution, a proportional reduction in tariffs is CWCT preferable too. 0 The proportional reduction in tariffs is a piecemeal policy suggested by several people. l4 For example, Diewert, Turunen-Red and Woodland (1984) showed that it passes the IWCT in a many-individual economy without any consumption taxes. We showed that it passes the CWCT as well, and consumption taxes may exist, as long as the ad valorem tax rates are uniform across commodities and factors. The proposition can easily be extended to imply the well-known propositions (at least for a small economy) that ‘restricted trade is better than no trade’, ‘free trade is better than no trade’, and ‘free trade is the optima1 policy’.
6. Concluding remarks This paper shows how two trade situations can be compared from the welfare point of view of a many-individual economy without relying on a social utility function or a social welfare function. We suggest two criteria for comparing welfare. The IWCT, which does not require income redistribution in the initial situation, is useful in examining whether an exogenous shock, such as a change in the external terms of trade, or an internal policy, such as a change in the tariff, is beneficial, but the CWCT is a consistent test for any trade policy recommendation. Two types of trade situations are considered: free trade and restricted trade. A change in the trade situation may be due to a change in world prices, trade policies, or domestic technologies. In each type of trade situation, necessary and sufficient conditions for welfare improvement are derived, either in the IWCT or CWCT sense.
“See Woodland (1982, ch. 11) for a recent survey.
K.-Y. Wong, Welfare comparison of trade situations
67
We extend some welfare improvement conditions for closed economies to welfare improvement conditions for open economies. We also compare some of these conditions with the conditions derived when a social utility function is assumed. As pointed out in the introduction to this paper, there are three approaches to welfare comparison: social welfare function, social utility function, and the compensation principle. The choice of an approach unavoidably involves value judgment. This paper does not compare the merits and demerits of these three approaches. However, it may be appropriate to point out that a rise in the social utility level or the social welfare level does not necessarily mean a (potential) Pareto improvement.‘5 This paper gives some conditions under which both the social-utility and the compensation approaches give the same welfare ranking, and some conditions under which they do not. 15A related point is that welfare comparison using a well-behaved social utility function or a social welfare function is complete but welfare comparison based on the Pareto criterion is not.
References Arrow, K.J. and F.H. Hahn. 1971, General competitive analysis (Holden-Day, San Francisco). Bhagwati, J.N., 1968, The gains from trade once again. Oxford Economic Papers 20, 137-148. Bhagwati. J.N. and R.A. Brecher, 1980. National welfare in an open economy in the presence of foreign-owned factors of production, Journal of International Economics 10, 103-t 15. Bhagwati, J.N. and B. Hansen. 1973, Should growth rates be evaluated at interntional prices?, in: J. Bhagwati and R. Eckaus, eds., Development and planning: Essays in honour of Par1 Rosenstern-Rodan (MIT Press, Cambridge). Bhagwati, J.N. and E. Tironi, 1980, Tariff change. foreign capital and immiserization: A theoretical analysis, Journal of Development Economics 7. 71-83. Boadway, R.W., 1974, The welfare foundations of cost-benefit analysis, Economic Journal 84, 926-939. Boadway, R.W. and N. Bruce. 1984, Welfare economics (Basil Blackwell Inc., New York). Brecher. R.A. and J.N. Bhagwati, 1981, Foreign ownership and the theory of trade and welfare, Journal of Political Economy 84, 497-511. Brecher, R.A. and E.U. Choudhri, 1990, Gains from international factor movements without lump-sum compensation: Taxation by location versus nationality, Canadian Journal of Economics 23, 44-59. Bruce. N. and R.G. Harris. 1982, Cost-benefit criteria and the compensation principle in evaluating small projects. Journal of Political Economy 90, 755-776. Chipman, J.S. and J.C. Moore, 1972, Social utility and the gains from trade, Journal of International Economics 2. 157-172. Chipman, J.S. and J.C. Moore, 1978,The new welfare economics 1939-1974, International Economic Review 19, 547-584. Deardorff. A.V., 1982, The general validity of the Heckscher-Ohlin theorem, American Economic Review 72, 683694. Diewert, W.E. and A.D. Woodland, 1977, Frank Knight’s theorem in linear programming revisited, Econometrics 45. 375-398. Diewert, W.E., A.H. Turunen-Red and A.D. Woodland, 1984, Productivity and pareto improving changes in taxes and tariffs, Mimeo. (University of British Columbia). Dixit, A. and V. Norman. 1980, Theory of intenational trade (James Nisbet and Co. Ltd., Digswell Place, Welwyn). Dixit, A. and V. Norman. 1984, Pareto-benelicial distribution of aggregate economic gains without lump-sum transfers, Mimeo.
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comparison
of trade situations
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