Tariff equilibrium with customs union *.
1. THE MODEL
The basic framework of our analysis is the neo-classical two-sector, two-factor and 3 country model of international trade. Each country (potentially) produces two homogeneous products, [Q.sub.1] and [Q.sub.2], with the aid of two factors of production, capital K and labour L. Each sector has the constant elasticity of substitution (CES) production function
[Q.sup.j.sub.i] = [[a.sub.i][K.sup.[beta]i].sub.ij] + [b.sub.i] [L.sup.[beta]i].sub.ij].sup.1/[beta]i] (i = 1, 2; j = 1, ..., 3) ... ... ... ... ... (1)
where [Q.sup.j.sub.i] denotes quantity of commodity i supplied by country j, [K.sub.ij] capital employed in sector i of country j, [L.sub.ij] the labour employed in sector i of country j, and [[rho].sub.i] = 1/(1 - [[beta].sub.i]) is the elasticity of substitution. We assume that factors of production move costlessly between industries within a country, but are completely immobile between countries. Commodities move internationally at zero cost of transport. Individuals in each country maximise the CES utility function
[u.sub.j] = [[[[alpha].sub.1] [X.sup.[gamma].sub.1j] + [[alpha].sub.2] [X.sup.[gamma].sub.2j].sup.1/[gamma] (j = 1,... 3)
where [X.sub.ij] denotes the amount of commodity i (i = 1,2) consumed in country j (j = 1,..,3). The factor endowments in each country are given by
[V.sup.j] = [[[bar.L].sup.j]/[[bar.K].sup.j]] (j = 1, ..3)
where [L.sup.j] denotes labour and [K.sup.j]capital available in country j. Both commodity and factor markets are assumed to clear competitively in the sense that all agents act as if they could buy or sell unlimited quantities at the prevailing market prices. The tariff rate imposed by country j on the imports of commodity i is represented by [t.sup.j.sub.i] (i = 1, 2; j = 1,..., 3).
Let [p.sup.*] be the relative price of commodity 2 in terms of commodity 1 in the world economy, [p.sup.j] the relative price of commodity 2 in terms of commodity 1 in country j, [Q.sup.j] = [Q.sup.j.sub.1] + [p.sup.j][Q.sup.j.sub.2] the value of total output in country j, and [X.sup.j] = [X.sup.j.sub.1] + [p.sup.j][X.sup.j.sub.2] the value of expenditure in country j both measured in terms of the rest commodity. Under profit maximisation the marginal rate of substitution of capital for labour in sector 1 will be equated in each country to the marginal rate of substitution of capital for labour in sector 2. Furthermore the value of marginal product of capital in sector 1 will be equated to the value of marginal product in sector 2.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2a)
[partial derivative][Q.sup.j.sub.1]/[partial derivative][K.sub.1j] = [p.sup.i]([partial derivative][Q.sup.j.sub.2]/[partial derivative][K.sub.2j] (j = 1,..,3) ... ... ... (2b)
The full employment conditions in factor markets are
[L.sub.1j] + [L.sub.2j] = [[bar.L].sup.j] [K.sub.1j] + [K.sub.2j] = [[bar.K].sup.j] (j = 1, ..., 3) ... ... ... ... ... (2c)
Given the world price ratio [p.sup.*] and the tariff rates [t.sup.j.sub.1] = 0 and [t.sup.j.sub.2] = [t.sup.j] we note that the domestic relative price is given by
[p.sup.j] = [p.sup.*] (1 + [t.sup.j]) (j = 1,..,3) ... ... ... ... ... ... (3a)
Suppose that country j exports commodity 1 and imports commodity 2. Let [E.sup.j.sub.1] be the exports of commodity 1, and [M.sup.j.sub.2] be the imports of commodity 2. Then under balanced trade the relation that expenditures equal total output plus tariff revenue can be shown symbolically as:
[X.sup.j] = [Q.sup.j]+ [t.sup.j] [p.sup.*]([X.sup.j.sub.2] - [Q.sup.j.sub.2]) ... ... ... ... ... ... ... (3b)
Utility maximisation subject to the budget constraint leads to the demand functions
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3c)
Inserting the second demand equation into the relation between output, expenditures and tariff revenue we get the equation
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3d)
To obtain the solution for the world economy we start from an arbitrary value of the world price ratio. Given [p.sup.*] we obtain the domestic price ratio from (3a), the associated production allocation ([L.sub.1j], [L.sub.2j], [K.sub.1j], [K.sub.2j], [Q.sub.j.sub.1], [Q.sub.j.sub.2]) from the equilibrium relations 2 and 1, the total output measured in terms of the first commodity from
[Q.sup.j] = [Q.sup.j.sub.1] + [p.sup.j] [Q.sup.j.sub.2],
the total expenditure from (3d), the demand for the two commodities from (3c), and excess supply of commodity 2 in country j as
[ES.sup.j.sub.2] = [Q.sup.j.sub.2] - [X.sup.j.sub.2]).
The world equilibrium is determined as that value of world price ratio for which the world excess supply of commodity 2 equals zero, i.e.
[ES.sup.w.sub.2] = [ES.sup.1.sub.2] + [ES.sup.2.sub.2] + [ES.sup.3.sub.2] = 0
When considering the issue of the customs union we first assume that countries 2 and 3 form the union. Thereafter we consider the union to consist of countries 1 and 2, and lastly of countries 1 and 3. In each case we determine the endowment vector of the union as the sum of the endowment vectors of the union members. Since the tariff and subsidy rates are set equal to zero for trade between the union countries we consider the determination of equilibrium in the world economy with the union in two steps. First, we take the union as one country with the new endowment vector and the rest of the world as the second country. The tariff rate of the union is determined as the average of the tariff rates on imports of the two union countries. The tariff rates of the third country do not change. To determine the world equilibrium with customs union we start with an arbitrarily given value of the world price ratio. For that price ratio we determine in the non-union country the resource allocation as in the previous case. But for the union we note that total expenditure of the union does not equal the value determined by Equation (3d). Suppose that the union imports the first commodity, and that the tariff rate of the union equals [t.sup.u]. Then total expenditure of the union is given by the relation
[X.sup.u] = [Q.sup.u] + [[t.sup.u]/(1+[t.sup.u])][M.sup.u.sub.1]
where [M.sup.u.sub.1] denotes imports of the union from the non-union (third) country. Since in equilibrium imports of the union from the third country equals the excess supply of the first commodity in non-union country, [M.sup.u.sub.1] = [ES.sup.nu.sub.1] we determine it as the value of the excess supply of commodity 1 in the non-union country. The world equilibrium is determined as that value of the world price ratio for which the world excess supply of commodity 2 in this simplified two country model equals zero.
Once the equilibrium domestic price ratio in the union is determined we obtain the resource allocation within the union as the corresponding allocation. Here the only problem is faced when confronted with the problem of allocating the tariff revenue between the two union countries. In this case we follow the convention of dividing the tariff revenue in proportion to the country's GDP in total GDP of the union.
2. SOME ILLUSTRATIVE EXAMPLES
Customs unions are usually analysed by comparing a particular customs union equilibrium with some arbitrarily given tariff equilibrium. We consider the parameter values: [a.sub.1] = 0.25; [b.sub.1] = 0.75; [[beta].sub.1] = 0.5; [a.sub.2] = 0.75; [b.sub.2] = 0.25; [[beta].sub.2] = -0.5; [[alpha].sub.1] = 0.3; [[alpha].sub.2] = 0.7; and) [gamma] = 0.6. Hence the value elasticity of substitution in sector 1 equals 2, and that in sector 2 equals 2/3, and the value of the elasticity of substitution in consumption equals 2.5.
The endowment vectors in the three countries are given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
We note that countries 2 and 3 are relatively capital abundant and that country 1 is relatively labour abundant as
[[bar.k].sub.1] = 0.5 < [[bar.k].sub.w], = 1; [[bar.k].sub.2] = 1.4 > [[bar.k].sub.w] = 1; [[bar.k].sub.3] = 1.1 [[bar.k].sub.w] = 1
where [[bar.k].sub.j] is the capital-labour ratio in country j (j = 1,..,3) and [[bar.k].sub.w] is the capital-labour ratio in the world economy.
Free Trade Equilibrium
According to Heckscher-Ohlin theorem we expect countries 2 and 3 to export the relatively capital intensive commodity, and country 1 to export the relatively labour intensive commodity. Table 1 shows the results of calculations, where w denotes the wage rate, r the rental rate of capital both measured in terms of commodity 1, and [ES.sup.j.sub.i] (i = 1,2; j = 1,..,3) the excess supply of commodity i in country j. Since the endowment vectors are within the factor price equalisation set the three countries have the same sectoral capital-labour ratios. As a result they all have the same wage and rental rates. Country 1 exports the relatively labour intensive commodity, namely commodity 1 whereas the countries 2 and 3 export the relatively capital intensive commodity, namely commodity 2.
We assume that country 1 imposes 20 percent tariffs on the imports. The tariff rate in country 2 is 10 percent and the tariff rate in country 3 is 2 percent. Under tariffs we note that world price of commodity 2 in terms of commodity 1 is the same for the three countries. But the equilibrium values of domestic prices differ between the countries because of the different tariff rates. As a result the equilibrium values of sectoral capital-labour ratios and of wage rate and of rental rate of capital deviate from each other in the three countries. The solution reported in Table 1 indicates that as a result of tariffs the domestic price ratio goes up in country 1 and decreases in countries 2 and 3. As the domestic price ratio increases (decreases) the equilibrium capital-labour ratio in the two sectors decrease (increase) and as a result the wage rate decreases (increases) and the rental rate of capital increases (decreases). Furthermore imports of commodity 2 in country 1, and imports of commodity 1 in countries 2 and 3 decrease substantially. The imposition of tariffs leads to welfare losses in the three countries. The welfare loss of country 1 amounts to 1.2011 percent of the free trade equilibrium utility level. The loss in the case of country 2 is 0.3004 percent, and the loss in the case of country 3 is 0.0104 percent. Hence the welfare loss is larger, the larger the difference across countries in factor composition.
In the case of the customs union we consider three cases. First countries 2 and 3 form a union. Then the union is formed by countries 1 and 2, and finally by countries 1 and 3. The external tariff and subsidy rates as well as the results of calculations are reported in Table 2.
When countries 2 and 3 form the customs union the endowment vactors of the non-union and union become
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The union applies the tariff rate of 6 percent and the non-union country the 20 percent tariff rate. We note that in equilibrium the non-union country (country 1) exports commodity 1 and imports commodity 2. On the other hand the union as a whole imports commodity 1 and exports commodity 2. But this does not mean that each of the union countries imports commodity 1 and exports commodity 2. The union member country 2 imports commodity 1 and exports commodity 2 whereas the other union member country 3 exports commodity 1 and imports commodity 2. Hence trade diversion effect of Viner (1950) is important. As a result of the customs union the non-union country when compared relative to the tariff equilibrium will be better off. Similarly country 3 gains from customs union while country 2 looses.
When countries 1 and 2 form the customs union the endowment vectors of non-union and union become
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
In this case consider first the free trade solution between the union and non-union solution. We note that under free trade equilibrium will be reached when the world price ratio equals 1.437. In equilibrium the relatively capital abundant non-union country will export the capital intensive commodity, commodity 2, whereas the relatively labour abundant country, the union, will export the relatively labour intensive commodity, commodity 1. When the union imposes tariffs on the imports of commodity 2 the world demand for the commodity decreases leading to a decrease in the world price ratio. The imposition of tariffs by the non-union country on the imports of commodity 1 will further reduce the world price ratio. With the tariff rates of 2 percent in the non-union country and 15 percent in the union we note that the non-union country becomes an exporter of commodity 1 and an importer of commodity 2. The union in this ease is assumed to grant subsidies to the exports of commodity 2. The subsidy rate is 15 percent. Consideration of the solution in Table 2 reveals that in equilibrium the non-union country (country 3) exports commodity 1 and imports commodity 2. On the other hand the union as a whole imports commodity 1 and exports commodity 2. But within the union country 1 exports commodity 1 and country 2 commodity 2. There is substantial amount of intra union trade. As a result of the customs union the non-union country when compared relative to the tariff equilibrium is worse off. The union countries 1 and 2 are both better off relative to the tariff equilibria.
When countries 1 and 3 form the customs union the endowment vectors of the non-union and union become
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The union applies the 11 percent tariff rate and the non-union country (country 2) the 10 percent tariff rate. In this case the non-union country exports the commodity 2 and imports the commodity 1. On the other hand the union as a whole imports commodity 2 and exports commodity 1. But this does not mean that each of the union countries imports commodity 1 and exports commodity 2. The union member country 1 imports commodity 2 and exports commodity 1 whereas the other union member country 3 exports commodity 2 and imports commodity 1. Hence trade diversion effect is important. As a result of the customs union the non-union country when compared relative to the tariff equilibrium will be worse off. Similarly country 1 looses from the customs union while country 3 gains.
The effects of the customs union on the country's welfare level relative to its position under tariffs is shown in Table 3. From the table it follows that the non-union country gains in one and looses in two of the three cases. On the other hand both of the union countries gain in one case (union of 1 and 2) only. In the other two cases one of the countries gains from the customs union whereas the other looses. The gainer is always the country 3 which has the lowest tariff rate and which has a capital-labour ratio that is closer to that of the world economy than the other two economies.
When countries 2 and 3 form the union we note that these countries import at the start the same good (commodity 1). There is initially no trade among them. But after the formation of the union the initial trade pattern is changed. While country 2 still imports commodity 1 country 3 imports commodity 2. The non-union country experiences a marginal increase in exports of commmodity 2 and also experiences a terms of trade gain. As a result, the non-union country gains from the formation of the union. The welfare effect on the union becomes ambiguous. Country 2 increases its exports. But as a result of the terms of trade effect there is a welfare loss. On the other hand trade pattern changes in country 3. Because of the terms of trade effect the country ends up gaining from the formation of the union.
In the case of the union between countries 1 and 2 or 1 and 3 we note that these countries initially import different goods. Hence, there is trade between them. After the formation of the union trade increases in each of the union countries. But the non-union country experiences a decrease in trade. Furthermore the trade pattern in the non-union country changes in the case of the union between the countries 1 and 2, but remains the same in the case of the union 1 and 3. The non-union country looses in both cases. We note that trade creation by itself does not determine the welfare effect for the union countries. Both of the countries forming the union gain in the case of the union 1 and 2. In the case of the union 1 and 3 country 3 gains and country 1 looses from the formation of the union.
Optimal Tariffs and Customs Union
The analysis until now has been carried under the assumption that the tariff rates have been chosen arbitrarily as 20 percent in country 1, 10 percent in country 2 and 2 percent in country 3. There is nothing optimal about these tariff rates. When countries form a customs union they take the average tariff rate as the tariff rate of the union. We now turn to the question of optimal tariffs under customs union, and concentrate on the case when countries 2 and 3 form the union. The non-union country is country 1.
Given the endowment vectors of the non-union and union countries
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
we note that the optimal tariff rates of the non-union for given values of the tariff rates for the union and of the union for given values of the tariff rates for the non-union are as follows:
Reaction of the Non-union Union Tariff Rate Optimal Non-union Tariff Rate 0 11 20 6 Reaction of the Union Non-union Tariff Rate Optimal Union Rate 0 22 20 13
The intersection of the reaction functions of the non-union and of union yields the optimal values of the tariff rates. Hence the optimal value of the tariff rate for the non-union country is 6.2 percent and for the union 19.2 percent.
Table 4 shows the tariff equilibrium when country 1 imposes optimal tariff rate of 6.2 percent and the countries 2 and 3 set the tariff rates at their initial levels of 10 and 2 percent respectively. Next, we assume that country 1 holds the tariff rate at its optimal level of 6.2 percent, and that countries 2 and 3 form a customs union by setting the common external tariff rate at its optimal level of 19.2 percent. In this case we note that both of the union countries gain from the formation of the customs union. On the other hand the non-union country looses from the customs union.
Table 5 summarising the welfare effects of free trade, tariff equilibria and customs union reveals that free trade as world equilibrium may not be attainable. For some of the countries customs union with optimal tariffs may be superior as in the case of the customs union 2 and 3. The non-union country even though it imposes optimal tariffs looses from the formation of the customs union.
The analysis reveals the difficulties in obtaining general results in this area. As a step we have developed a model which illustrates by means of examples some pieces of the puzzle. The examples show the importance of country size, factor endowments and initial tariff rates of non-union and union countries as the determinants of the welfare effects of customs union. When countries forming the union import at the start the same good there is initially no trade among them. But after the formation of the union the initial trade pattern may change. The non-union country may gain whereas one of the union countries may experience a welfare loss. When countries forming the union initially import different goods, the non-union country may experience a welfare loss. In general one cannot assert that countries forming the union will gain from the customs union unless the union imposes the optimal tariffs. Finally, one can assert that the customs union can improve its members welfare over free trade by imposing optimal tariffs as long as the union is large enough. The example shows that it may be difficult to sustain free trade in the world economy.
Kemp, M. C., and H. Y. Wan Jr. (1976) An Elementary Proposition Concerning the Formation of Customs Union. Journal of International Economics 6: 95-98.
Viner, J. (1950) The Customs Union Issue. New York: Carnegie Endowment for International Peace.
* Owing to unavoidable circumstances, the discussant's comments on this paper have not been received.
Subidey Togan is Dean, Faculty of Economics, Administrative and Social Sciences, Bilkent University, Bilkent, Ankara, Turkey.
Table 1 Equilibrium Solutions under Free Trade and Tariffs Free Trade Country 1 Country 2 Country 3 p * 1.4370 1.4370 1.4370 Tariffs (%) 0 0 0 p 1.4370 1.4370 1.4370 k1 0.0519 0.0519 0.0519 k2 1.6136 1.6136 1.6136 w 0.6052 0.6052 0.6052 r 0.8858 0.8858 0.8858 ES1 284.4612 -227.5760 -56.8972 ES2 -197.9550 158.3691 39.5941 Welfare 456.3287 808.4249 687.7262 Tariffs Country 1 Country 2 Country 3 p * 1.4383 1.4383 1.4383 Tariffs (%) 20 10 2 p 1.7260 1.3075 1.4101 k1 0.0295 0.0703 0.0551 k2 1.3372 1.7856 1.6462 w 0.5947 0.6122 0.6065 r 1.1538 0.7697 0.8615 ES1 145.3230 -109.2380 -36.0951 ES2 -101.0380 75.9495 25.0957 Welfare 450.8477 801.0112 687.6546 Table 2 Alternative Equilibria under Custom Unions Customs Union 2 and 3 Non-union Country 2 Country 3 Country in the in the (Country 1) Union Union Union Capital/Labour 0.50 1.25 1.40 1.10 p * 1.4365 1.4365 1.4365 1.4365 Tariffs (%) 20 6 6 6 Subsidy (%) 0 0 0 0 p 1.7238 1.3552 1.3552 1.3552 k1 0.0296 0.0626 0.0626 0.0626 k2 1.3389 1.7176 1.7176 1.7176 w 0.5948 0.6094 0.6094 0.6094 r 1.1517 0.8122 0.8122 0.8122 FS1 146.2791 -146.3410 -152.4800 6.1389 PS2 -101.8300 101.8759 109.2318 -7.3558 Welfare 451.0019 800.5178 688.8359 Customs Union 1 and 2 Non-union Country 2 Country 3 Country in the in the (Country 1) Union Union Union Capital/Labour 1.10 0.95 0.50 1.40 p * 1.3020 1.3020 1.3020 1.3020 Tariffs (%) 2 0 0 0 Subsidy (%) 0 15 15 15 p 1.3230 1.4973 1.4973 1.4973 k1 0.0668 0.0456 0.0456 0.0456 k2 1.7556 1.5456 1.5456 1.5456 w 0.6110 0.6025 0.6025 0.6025 r 0.7879 0.9407 0.9407 0.9407 FS1 28.0292 -26.9653 256.4001 -283.4250 PS2 -20.6918 20.7082 -170.3140 191.0223 Welfare 686.9919 450.9596 806.8272 Customs Union 1 and 3 Non-union Country 2 Country 3 Country in the in the (Country 1) Union Union Union Capital/Labour 1.40 0.80 0.50 1.10 p * 1.4016 1.4016 1.4016 1.4016 Tariffs (%) 10 11 11 11 Subsidy (%) 0 0 0 0 p 1.2742 1.5558 1.5558 1.5558 k1 0.0765 0.0405 0.0405 0.0405 k2 1.8369 1.4855 1.4855 1.4855 w 0.6144 0.6002 0.6002 0.6002 r 0.7403 0.9945 0.9945 0.9945 FS1 -77.9073 77.8777 228.5249 -150.6470 PS2 55.5846 -55.5655 -149.0540 93.4880 Welfare 798.6080 1142.3540 449.0892 693.2647 Table 3 Welfare Levels of the Countries Country I Country II Country III Free Trade 456.3287 803.4249 687.7262 Tariff Equilibria 450.8477 801.0112 687.6546 Customs Union 2 and 3 451.0019 800.5178 688.8359 Customs Union 1 and 2 450.9596 806.8272 686.9919 Customs Union 1 and 3 449.0892 798.608 693.2647 Percentage Change in Welfare Level Customs Union 2 and 3 0.0342 -0.0616 0.1718 Customs Union 1 and 2 0.0248 0.7261 -0.0964 Customs Union 1 and 3 -0.3900 -0.3000 0.8158 Table 4 World Equilibrium under Optimal Tariffs and Customs Union Optimal Tariffs Country 1 Country 2 Country 3 p * 1.6182 1.6182 1.6182 Tariffs 6.2 10.0 2.0 p 1.5749 1.3482 1.4539 k1 0.0390 0.0636 0.0500 k2 1.4670 1.7272 1.5938 w 0.5995 0.6098 0.6044 r 1.0123 0.8059 0.9012 ES1 217.7704 -147.4170 -70.3083 ES2 -146.8450 99.4048 47.4095 Welfare 452.0511 804.2844 688.6425 Customs Union Non-Union Union Union Country 1 Union Country 2 Country 3 p * 1.6182 1.61817 1.6182 1.6182 Tariffs 6.2 19.2 19.2 19.0 p 1.7185 1.3575 1.3575 1.3575 k1 0.0299 0.0622 0.0622 0.0622 k2 1.3430 1.7144 1.7144 1.7144 w 0.5949 0.6093 0.6093 0.6093 r 1.1468 0.8143 0.8143 0.8143 ES1 152.9192 -152.9490 -156.0520 3.1032 ES2 -94.5013 94.5231 105.2001 -10.6771 Welfare 443.7561 804.6481 692.2811 Table 5 Welfare Levels of the Countries Country I Country II Country III Free Trade 456.3287 803.4249 687.7262 Tariff Equilibria with Arbitrary Tariff Rates 450.8477 801.0112 687.6546 Tariff Equilibria with Optimal Tariff Rates 452.0511 804.2844 688.6425 Customs Union 2 and 3 Starting with Arbitrary Tariff Schedules 451.0019 800.5178 688.8359 Customs Union 2 and 3 Starting with Optimal Tariff Schedules 443.7561 804.6481 692.2811
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|Title Annotation:||INTERNATIONAL ECONOMICS|
|Publication:||Pakistan Development Review|
|Date:||Dec 22, 1994|
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