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International Economics, Robert A. Mundell, New York: Macmillan, 1968, pp. 54 - 64.
Tariff Preferences and the Terms of Trade
The impact of tariff preferences on resource allocation and welfare has been the subject of notable theoretical advances in the past decade,2 but there is a gap in the literature on the closely related question of their effect on the terms of trade, changes in which might significantly affect the distribution of the gains and losses among members and between the preference area as a whole and the rest of the world. The purpose of this chapter is to fill part of this gap by establishing what appear to be the main propositions valid for an arbitrary number of countries, and to contrast the results with those which derive from the traditional theory of nondiscriminatory tariffs.
We make three simplifying assumptions: (1) initial tariffs are low, (2) the contemplated tariff reductions are small, and (3) all exports are gross substitutes in world consumption in the sense that a rise in the price of any country's exports, all other prices remaining constant, creates an excess demand for the exports of every other country.3 The significance of these assumptions will be dealt with later.
Consider a three-country system in which A and B denote the prospective member countries and C denotes the rest of the world. The problem is to deduce the changes in the world (relative) prices of the exports of the three countries when the tariff concessions are initiated. The simplest approach to the solution is to investigate, for each tariff reduction in isolation, the changes in the balances of trade on the tentative supposition that international prices remain constant.
Let us examine first the reduction in A's tariff on B's exports. At constant international prices the price of B's goods in A falls by the amount of the tariff reduction. This price effect, assuming for now that all goods are substitutes in A's consumption,4 shifts demand in A away from home goods and C's goods onto B's goods, occasioning an improvement in B's balance and a worsening of C's balance. It can also be shown, however, that A's balance worsens, since the difference between the improvement in B's balance and the worsening of C's balance must equal the change in A's balance (by Cournot's law that the sum of all balances is identically zero), and because the improvement in B's balance must exceed the worsening of C 's balance by the reduced spending in A on home goods (by Walras' law that all excess demands sum to zero within any country).5 The price effect thus induces an improvement in B's balance and deteriorations in A's and C's balances.
The price effect, however, is partially offset by the budgetary effect -A's government experiences a budget deficit equal to the reduced tariff proceeds, and this deficit must be corrected by decreased government spending or increased taxes. The final result therefore depends on whether or not the change in spending due to the method by which the government restores balance in its budget is sufficient to offset the initial price effect. In principle either result is possible, depending on which taxes are increased or how the government reduces spending, but there is a strong presumption that the initial price effect will dominate. For example, if income taxes are raised, the reduced level of disposable income of the community means that consumers in A will spend less on all goods (in the absence of inferior commodities), but this budgetary effect is exactly equal, for small tariff changes, to the income effect implicit within the initial price effect,6 leaving only pure substitution terms that work in the same direction as the original price effect. Only in exceptional cases where reduction in government spending is the method used to balance the budget and where it is heavily biased against one of the goods can the budgetary effect dominate. In what follows we shall ignore these exceptional cases.
The tariff reduction, then, tends to improve B's balance and worsen A's and C's balances at constant international prices. The latter must therefore move, if equilibrium is to be restored, in a direction that worsens B's balance and improves the balances of A and C. Figure 4-1 provides a method of determining this direction.
The lines AA', BB', and CC' trace the loci of the world prices of A and B, relative to the world prices of C, which permit equilibrium (before the tariff changes) in the balances of A, B, and C, respectively. The following character
istics of these curves are implied by the assumption that all goods are substitutes in world markets:
1. AA' and BB' have positive slopes.7 This follows because a rise in A's price (relative to C's price) must be associated with a rise in B's price (relative to C's price) along any isobalance line, since a corresponding price rise in A's price worsens A's and improves B's balance, while a corresponding price rise in B's price worsens B's and improves A's balance. Similarly, CC' has a negative slope because a rise in A's price (relative to C 's price) would improve C 's balance and must therefore be associated, along C's isobalance schedule, with a fall in B's price that would worsen C 's balance [the asymmetrical position of C's curve derives from the (unimportant) assumption that C's goods serve as numéraire].
2. The slope of AA' must exceed, and the slope of BB' must fall short of the slope of a line from O to Q. This follows because a movement along this line is a proportionate movement of B's and A's prices, and is therefore the same (in a "homogeneous" price system) as a corresponding price movement of C 's price. Any point on OQ must therefore be a point of balance-of-payments surplus for A and B and balance-of-payments deficit for C, while any point along OQ-extended must be a point of surplus for C and deficit for A and B.
3. When the system is not in equilibrium at the point Q, the situations of deficit or surplus in the balances of the three countries must be those indicated by the inequalities in the six sectors.
The diagram can now be used to establish the direction of change in the terms of trade. From the initial equilibrium Q the tariff reduction in A causes the three schedules to shift. At constant international prices, that is, at the point Q, the tariff reduction causes B's balance to be in surplus and A's and C 's balances to be in deficit, so world prices must move in a direction which worsens B's balance and improves those of A and C. In other words, the new point of equilibrium must lie in sector I (Figure 4-1), where, from the point of view of the situation before the tariff change, A's and C's balances are in surplus and B's is in deficit. The characteristics of sector I therefore outline the changes in relative prices that must take place as a result of the tariff reduction; in this sector B's price has risen relative to the prices of A and C. This establishes the most important proposition about discriminatory tariff reductions: A tariff reduction in a member country unambiguously improves the terms of trade of the partner country.
Notice that it cannot be determined, a priori, whether the terms of trade of the tariff-reducing country (A) rise or fall relative to the foreign country; an equilibrium in sector I is consistent with either result. But given the elasticities of demand in A for the goods of B and C (these elasticities determine the change in the balances at constant international prices), there exists a line that determines the new equilibria for successively larger tariff reductions in A. Thus, if the point a represents the new equilibrium as a result of a small tariff reduction in A, then the point a' would indicate that for a slightly larger tariff reduction. The line Qaa' we shall call A's "tariff-reduction line." Its slope as drawn is negative, but in fact all that can be definitely established is that it must lie between the slopes of QC and QA'.
Now let us consider the effect of reduction in B's tariff on A's goods and the combined effect of both A's and B's tariff reductions. B's tariff reduction creates a surplus in A's balance and deficits in the balances of B and C, necessitating an improvement in A's terms of trade relative to both other countries. In the diagram the new equilibrium, as a result of B's tariff reduction alone, must be in sector III, following the same line of reasoning as in the analysis of A's tariff reduction. B's tariff-reduction line is described by Qbb', with any slope between that of QB' and QC'.
The final effect of any given set of mutual discriminatory tariff reductions can be determined by adding the results. If A's tariff reduction results in a new equilibrium at, say, a, and B's tariff reduction results in a new equilibrium at, say, b, the combined effect is determined by completing the parallelogram formed by the two tariff-reduction lines Qa and Qb, establishing the point T1 as the new equilibrium. Similarly, the points T2, T3, and T4 are the new equilibria for the respective sets of points on the tariff-reduction lines, (a', b'), (a, b'), and (a', b).
All the attainable points lie northeast of CC', but they might lie in any of the three sectors, I, II, and III. The characteristics of these zones indicate the general conclusions that follow from discriminatory tariff reductions: in sector I, B's terms of trade have unambiguously improved; in sector III, A's terms of trade have unambiguously improved; and in sector II, C's terms of trade have unambiguously worsened (the indicated change in the terms of trade is unambiguous in the sense that the improvement or deterioration is with respect to both the other countries). In all three sectors the terms of trade of the rest of the world worsen with respect to at least one and perhaps both of the member countries.
The entire area northeast of CC, however, is not attainable by given tariff reductions; given the elasticities of demand in the two member countries, only the area east of A's and north of B's tariff-reduction line encloses the point of final equilibrium, and this area is necessarily smaller than the area northeast of CC. But the attainable area must nevertheless enclose all of zone II, yielding another important conclusion: Some sets of tariff reductions necessarily improve the terms of trade of both member countries with respect to the rest of the world (this might not include the specific tariff reductions implied by a free-trade area, however). A special case is that in which the members lower tariffs in a ratio that preserves the original intra-union terms of trade, resulting in a new equilibrium along OQ-extended; in this case it is obvious that the terms of trade of the outside world unambiguously fall, because the balance of payments of each individual country in the union improves while that of the outside world worsens, as a result of the tariff reductions at constant world prices. But this special case is only one of many instances in which the terms of trade of the outside world fall with respect to both members; indeed, there is a general presumption that this is the normal case. as the balance of payments of the union as a whole necessarily improves (at constant prices) while that of each country in the rest of the world worsens.
Finally, one can consider the possibility of independence or complementarity in national (but not in world) consumptions. The smaller the cross elasticities of demand in member countries between the exports of the partner country and the exports of third countries are, the greater is the likelihood that the terms of trade of one of the member countries will deteriorate with respect to foreign countries. At the limit-where A's tariff reduction does not reduce imports into A from foreign countries, and where B's tariff reduction does not reduce imports into B from foreign countries-the terms of trade of one of the member countries is likely to improve, while that of the other member country is likely to fall, because the tariff reductions cause a deficit in one member and a surplus in the other member, whereas the balance of the rest of the world is unaltered (there is an exception if the tariffs are reduced in a way that preserves the intra-union balance; in that case world prices remain unchanged). As we pass the limit-as some complementarity appears in the consumptions of member countries-there arises the possibility that the terms of trade of the rest of the world improve with respect to both member countries. Thus, if B's and C's goods were complementary and, similarly, if A's and C's goods were complementary in B's consumption, B's tariff reduction alone would prompt a fall in B's terms of trade. Then the combined tariff reductions would stimulate, at constant world prices, a surplus in foreign countries and a deficit in the union as a whole, occasioning an improvement in the terms of trade of the outside world relative to the union.
The following generalizations now emerge from this study of tariff preferences:
1. A discriminatory tariff reduction by a member country improves the terms of trade of the partner country with respect to both the tariff reducing country and the rest of the world, but the terms of trade of the tariff-reducing country might rise or fall with respect to third countries.
2. The degree of improvement in the terms of trade of the partner country is likely to be larger the greater is the member's tariff reduction; this establishes the presumption that a member's gain from a free-trade area will be larger the higher are the initial tariffs of partner countries.
3. It cannot be established, a priori, that arbitrary sets of discriminatory tariff reductions by member countries must improve the terms of trade of both member countries; it is possible that the terms of trade of one of the members deteriorate relative to third countries.
4. Nevertheless, there exists a presumption that the terms of trade of both member countries improve relative to the outside world. This presumption is established by the fact that the balance of trade of the preference area as a whole must improve, while that of each country in the rest of the world must deteriorate. It follows immediately that the terms of trade of one of the members improve relative to third countries; if, for example, the balance of trade of a member country deteriorates as a result of the tariff reduction (at constant world prices), the terms of trade of the partner country must improve.
5. Moreover, there are numerous sets of tariff reductions that must improve the terms of trade of both member countries. A special case is that in which tariffs are reduced so as to leave the intra-union terms of trade unaltered.
6. The above propositions hold where all goods are substitutes in national consumptions. If complementarity is present between the goods of partner countries and the outside world, there arises the possibility that the terms of trade of the latter improve relative to both member countries.
It remains now to indicate briefly the significance of the three assumptions made at the beginning, and to contrast the results with those that derive from traditional tariff theory. The assumption that initial tariffs are low ensures that the tariff reductions reduce the value of tariff proceeds and create deficits in the government budgets; our conclusions would not hold if, for example, initial tariffs were prohibitive. The assumption that the tariff changes are small is necessary for similar reasons, because large tariff changes would be likely to change the composition of imports and exports; and because the proposition relating to the equality of the budgetary effect (when income taxes are raised) and the income effect implicit within the price change would not be exact. The assumption of substitution in world markets, however, is one that requires more intensive examination.
If complementarity is present in the world economy the conclusions reached in this paper might be fundamentally changed; in general terms (even if the requirement that the system is dynamically stable be imposed), almost any result can occur. Analysis of complementarity would therefore deteriorate into a difficult exercise in taxonomy, and one which is probably unrewarding unless actual statistics can be introduced. The assumption of substitution seems to be necessary to get definite results and to establish a useful " normal " case with which more complicated examples can be compared.
It must not be thought, however, that the restrictive assumption of universal substitution is any less necessary in analysis of the traditional theory of tariffs or, indeed, in any of the other branches of international trade theory. The unambiguous results that appear to derive from traditional theory are equally based on the assumption of substitution, but the assumption is hidden by the usual two-country model employed in that branch of analysis, whereas an analysis of discriminatory tariffs logically requires at least a three-country model of the world economy and thus explicit recognition of the problem of complementarity. Only if complementarity is assumed to be slight or absent does the proposition of traditional tariff theory-that an (undiscriminatory) tariff reduction worsens the terms of trade of the tariff-reducing country -- hold, just as this assumption is necessary to establish that an undiscriminatory tariff reduction improves the terms of trade of the partner country.
The propositions now established for three countries hold also for an arbitrary number of countries. Suppose that there are n + 1 countries, numbered 0, 1, 2, . . ., n, and that the exports of country 0 are numeraire. Let Bi be the balance of trade (or payments) of the ith country, expressed in terms of the numéraire, and let pj denote the price of the exports of the jth country, with pj initially equal to unity (by appropriate choice of units). The system can be written
where t is a parameter representing the combined tariff reductions. By differentiation we obtain
The solution for dpi/dt is
where Delta is the Jacobian delta(B1, . . . , Beta) / delta ( pl , ..., Peta) and Deltaji is the cofactor of its jth row and ith column. The assumption of gross substitution in world markets implies that Deltaji and Delta are of opposite sign, so that the ratio of the two is negative.8
Suppose that the countries 0 and 1 are the member countries. Then it follows immediately that a tariff reduction in one of the member countries, say country 1,9 improves the terms of trade of the partner country, since, in that case, delta Bj / delta t < 0 for every j = 1, 2, . . ., n; the expression on the right of (3) is negative.
Taking the tariff changes in both countries into account, it is not definite that a member country's terms of trade rise. This can be seen by separating the first term in (3) from the other to get
The first term might be positive or negative depending on the elasticities of demand in the two member countries and on the size of the relative tariff reductions. But, if a member's balance worsens as a result of the tariff reductions, it follows that partner's terms of trade must improve; the uncertainty as to sign appears to apply only if the balances of both members improve.
It is readily shown, however, that the terms of trade of both members cannot deteriorate. To see this, consider the intra-union terms of trade, and note that this might change in any direction. But if the intra-union terms of trade of one of the members improve, then the terms of trade of that member must improve relative to third countries. Suppose, for instance, that the intra-union terms of trade of country 0 improve so that
It follows, from (5), that
where zeta is a positive number. Substituting (6) in (4) we get
Now the first term is obviously negative. The second term will be negative provided the numerator and the denominator of the term containing determinants are of the same sign; this is readily shown to be the case, making use of Mosak's theorem and another theorem about determinants.10 This is sufficient to prove that one of the member country's terms of trade must improve.
There are a number of special cases in which the terms of trade of both members improve, relative to outside countries. The case considered in this chapter is that where the intra-union terms of trade are unchanged; the proof in the general case follows readily by setting the expression in (5) equal to zero, and substituting in (4) to get the same results as in (7) without the first term.
1 Adapted from: Manchester School Econ. Soc. Stud., 32, 1-13 (Jan. 1964).
2 The three main works on the theory of customs unions are those of Viner , Meade , and Scitovsky , but mention should also be made of the articles of Makower and Morton , Johnson , and Lipsey [45 and 46].
3 The significance of the assumption that exports are gross substitutes, in relating the results of multicountry models to two-country models, is brought out in Chapter 3. It is further explored in Chapters 7 and 21.
4 Some goods might be complements in a nation's consumption without interfering with the assumption that all goods are gross substitutes in world markets. We assume here that all goods are net and gross substitutes in A's consumption, but the implications of relaxing this assumption will be discussed later.
5 Let A, B, and C be the balances of the three countries and dt the change in A's tariff. With units chosen to make each price initially unity, the change in B's balance at constant terms of trade, as a proportion of the tariff change, is
where Iba is the level of imports from B to A and etaba.b is the negative (own) elasticity of demand for B's goods in A due to a change in the price of B's goods; and the change in C 's balance can be written
where etaca.b is the positive (cross) elasticity of demand for C 's goods in A due to the change in price of B's goods. Now by Cournot's law we have
On the other hand, from Walras' law we have
where etaaa.b is the positive (cross) elasticity of A's demand for home goods due to a change in B's price, and Iaa is home consumption. It follows that
6 The price effects treated in footnote 5 can be split into pure substitution elasticities and income propensities as follows:
where mba and mca are the marginal propensities to spend in A on imports from B and C, and the primes denote that the elasticities have no income effects.
The increased income taxes reduce disposable income in A by Iba dt, so that the budgetary effects alter B's and C's balances as a proportion of the tariff change, according to the equations
The combined impact of the price and budgetary effects, before world prices change is, therefore,
7 The three schedules are drawn as straight lines to emphasize that the analysis is exact for small changes only.
8 By Mosak's theorem -that if the off-diagonal elements of Delta are positive (implied by the assumption of gross substitution) and if the matrix of Delta is Hicksian, then all the elements of Delta-1 are negative --and by the stability theorems of Arrow and Hurwicz, Hahn, Negishi, and Uzawa -- that if all the off-diagonal elements of A are positive and the row or column sums are negative, the matrix of Delta is Hicksian.
9 The proof that if a country 0 lowers its tariff, the terms of trade of country 1 improve is slightly more difficult, and requires the introduction of a theorem developed by Metzler  for the Keynesian case, which I have applied to the classical case. But because the choice of numéraire cannot affect relative prices, the reader's intuition should persuade him that the analysis in this chapter is sufficient.
10 By Jacobi's ratio theorem
DeltaDelta11,ji = Delta11Deltaji - DeltajiDelta1i ;
but from Mosak's theorem, and the stability theorems, it follows that the two terms on the left have the same sign, so that the difference in the right is positive. This means that the ratio of the determinants in the second equation is negative.
See Metzler (, p. 26) for a previous application to the generalized Keynesian system.
 H . G. JOHNSON, " Discriminatory Tariff Reduction: A Marshallian Analysis," Indian Jour. Econ., 38 (July 1957).
 R. G. LIPSEY, "The Theory of Customs Unions: Trade Diversion and Welfare," Economica, 24, No. 93, 40-46 (Feb. 1957).
 R. G. LIPSEY, "The Theory of Customs Union: A General Survey," Econ. Jour., 70, 496-513 (Sept. 1960).
 H. MAKOWER and G. MORTON, "A Contribution Towards a Theory of Customs Unions," Econ. Jour., 63, 33-49 (March 1953).
 J. E. MEADE, The Theory of Customs Unions. Amsterdam: North Holland, 1956.
 L. A. METZLER, "A Multiple-Country Theory of Income Transfers," Jour. Pol. Econ., 59, 14 29 (Feb. 1951).
 T. SCITOVSKY, Economic Theory and Western European Integration. Stanford: Stanford University Press. 1958.
 J. VINER, The Customs Union Issue. New York: Carnegie Endowment for International Peace. 1950.