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Tariff and quota reform with international capital mobility.

1. Introduction

When international trade is conducted, the form it takes is far from free trade. Typically, trading countries employ both price constraints in many forms, including import tariffs on some imports and quantity controls that often take the form of import quotas on some other imports. In recent decades, international trade theorists have devoted a great deal of energy to examining the welfare effects of trade policy reforms, particularly tariffs, just as their use has declined.(1) Indeed, Neary (1995) notes the stylized fact that

ironically, over the same period tariffs have lost the importance they once had as barriers to international trade. Under the auspices of the General Agreement on Tariffs and Trade and of regional free trade groupings such as the European Community, tariffs have been progressively reduced to extremely low levels, at least on trade between developed countries. This has not meant that protectionist instincts have been totally abandoned, of course. On the contrary, the reduction in average tariff levels has been accompanied by an explosion in the use of nontariff barriers, especially quantitative restrictions. (p. 531)

This calls for an analysis of trade liberalization in the presence of irremovable tariffs on one subset of imports and irremovable quotas on another, which is exactly what Neary (1995) accomplishes in the absence of international capital mobility.(2) There has been a rapid increase in international capital mobility via the integration of world capital markets, especially during the 1980s and 1990s.(3) However, the implications of international capital mobility for piecemeal trade liberalization with preexisting tariffs on one subset of imports and preexisting quotas on the remainder of imports are, to date, not known in the literature. The results reported here fill this gap.

The principal result of this paper is that international capital mobility raises the cost of tariff protection on one subset of imports, even if there are irremovable quotas on the remainder of imports. The results of the investigation reported here can also be seen as extending a second strand of the literature on the theory of trade policy in the presence of international capital mobility (Neary 1988; Neary and Ruane 1988), to the case of an economy where both tariffs and quotas are in existence.

The analysis I conduct is for a very general Arrow-Debreu, but small open, economy admitting of an arbitrary number of goods and factors, intermediate-goods and joint production, a convex production set for the economy, constant returns to scale in every activity, and perfect competition. I investigate the welfare consequences of piecemeal trade policy reforms with and without international capital mobility. Specifically, I examine trade reforms with and without international capital mobility, such as tariff reductions in the presence of irremovable quotas, and relaxations of quota constraints in the presence of irremovable tariffs. New rules for piecemeal trade policy reforms are revealed by my investigation and compared to existing reform rules such as those presented in Neary (1988, 1995).

Neary and Ruane (1988) examine the welfare losses from tariff protection in a small, open economy when some factors are internationally mobile. In this instance, international capital mobility raises the cost of tariff protection regardless of the relative factor intensity of import-competing production. They also point out that, although international capital mobility does not change the nature of the costs of protection, it does permit a greater output supply response and hence a larger production loss from protection.(4) In a companion article, Neary (1988) finds that "international capital mobility has no first-order effect on the cost of quota protection, raises the cost of tariff protection and lowers the welfare cost of a voluntary export restraint (VER)." In the case of quantitative restrictions, the price rise required to reduce imports to the constrained level is less when capital is mobile, because of the enhanced output supply response, than when it is not.

Neary (1995) examines the welfare effects for a large country of trade liberalization when trade is restricted by both irremovable tariffs and quotas. Two important results relevant to the present work are the rules for tariff reform and rules for quota reform in the absence of international capital mobility. First, in the presence of fixed quotas, Neary (1995) finds that a radial reduction of all tariffs toward zero must raise welfare. Second, Neary (1988) states that "relaxing the quota on a good whose implicit tariff is higher than the highest explicit tariff in a small open economy must raise welfare, provided the good in question is a net substitute for all tariff-constrained goods" (p. 544). These important results pertain to the case of tariff reform in the presence of quotas and to quota reform given tariffs and in the absence of international capital mobility.

One would like to know the answer to the following question: In the presence of international capital mobility, given irremovable tariffs, what are the consequences for the real GNP or welfare of the country in question if import quota restraints are relaxed? Similarly, given that irremovable quantitative restrictions are in place, what would be the implications of tariff reduction for the national welfare or real income of the country? I demonstrate that, given irremovable quotas on one category of imports, free trade is the optimal policy toward imports of the other category of imports. This conclusion is true with or without international capital mobility and regardless of factor-intensity rankings. Furthermore, in the scalar case, international capital mobility reduces the optimal implicit excess tariff on the quota-constrained import if an irremovable tariff is in place on the other import.

The plan of the paper is as follows. First, I introduce a very simple model that will be used to address the questions raised above. Next, section 3 presents the fundamental expressions (6) and (7) that relate changes in welfare to changes in tariff and quota policy with and without international capital mobility. Details of the derivation are contained in the appendix. Section 4 examines trade liberalization policies with and without international capital mobility leading to the results stated above. The final section summarizes the major results.

2. The Model

In the following, I present a fairly standard model of a competitive, small, open economy admitting of intermediate goods and joint production with an arbitrary number of goods and factors, and a convex production set for the economy with a linearly homogenous technology in every activity.(5) Existence of equilibrium is ensured because the economy considered is an Arrow-Debreu economy. The country is considered small in the sense that it is too small a player to influence world prices of the commodities or factors that it trades. By competitive, I mean that all agents in the economy act as price takers and that there are no distortions other than those introduced by trade policy. The model assumes that a representative agent maximizes revenue in production and minimizes expenditure in consumption. Since the production set is convex, the matrix of price derivatives of the general equilibrium supply curves is positive semidefinite.(6)

Assume that this country imports two categories of goods, category 1, subject to tariff restrictions, and category 2, subject to binding quotas. In addition, category 1 goods contain an untaxed numeraire good. Domestic and world price vectors of the importable goods are represented by p[prime] = ([p[prime].sub.1] [p[prime].sub.2]), [Mathematical Expression Omitted], respectively. Let t[prime] = ([t[prime].sub.1] [t[prime].sub.2]), and [Mathematical Expression Omitted], so that [t.sub.i] is the difference between domestic and world prices, and [Mathematical Expression Omitted] is the import-demand vector, where i = category 1, 2 and [t.sub.1] is the vector of tariffs on type 1 goods.(7)

Whereas the quantity of tariff-restricted goods imported, [m.sub.1], is endogenously determined, the amount of quota-constrained goods, [Mathematical Expression Omitted], is exogenously fixed by government policy. Since these quantity constraints are binding for category 2 goods, the domestic relative prices are strictly greater than the corresponding world prices, so that [Mathematical Expression Omitted] is determined endogenously in the economy. The tariff-revenue and quota-rents are [t[prime].sub.1] [m.sub.1] and [Mathematical Expression Omitted], respectively. The tariff revenue accrues to the home government and is assumed to be rebated as a lump sum to the household sector. Similarly, the quota rents accrue to domestic importers or to the home government in the case of quota-license auctioning and are entirely retained within the country. For the small, open, home country, I examine both the case with and without international capital mobility. In the next section, I present a very basic four-equation model that I use as a vehicle for addressing the questions raised.

Structure

The national expenditure function, denoted e(p, u), is defined over domestic prices and the utility of the home-country representative agent,s The GDP function summarizes the production or the supply side of the economy, and is described by g(p, k), where k is the total amount of capital employed in the home country.(9) When capital is immobile, I make the simplifying assumption that total capital in use is equal to domestically owned capital, so that GDP and GNP are equal, and I assume that net factor payments to foreigners are zero.(10) The gross domestic product depends on domestic relative prices, factor endowments, and technology, the latter assumed to be convex and characterized by constant returns to scale. Since I place no other restrictions on the economy's technology, my results continue to hold with intermediate- and joint-goods production. From standard properties of the expenditure and GDP functions, we know that the Hicksian demand functions for importable goods are [e.sub.p](p, u) and that the vector of import-competing outputs is x = [g.sub.p](p, k).(11)

The Hicksian import demand functions are the difference between domestic demand and output, given by [m.sub.1] in the case of imports subject to tariffs, and [Mathematical Expression Omitted] for imports subject to quantity restrictions such as quotas. These are, respectively,

[m.sub.1] = [e.sub.1](p, u) - [g.sub.1](p, k) (1)

and

[Mathematical Expression Omitted] (2)

With k denoting total capital employed in the home economy and [Mathematical Expression Omitted] representing the quantity of domestically owned capital, the foreign-owned capital employed in the home country is [Mathematical Expression Omitted]. Let r represent the domestic rental rate of capital and [r.sup.*] the fixed-world rate.(12) Then, net factor payments to foreigners are [Mathematical Expression Omitted].

The budget constraint in the presence of tariffs and quotas is

[Mathematical Expression Omitted] (3)

In Equation (3), national expenditure must equal GDP plus any revenue generated from trade restrictions less net factor payments to foreigners. Further, the domestic rental rate of capital is given by

r = [g.sub.k](p, k). (4)

The Equations (1), (2), (3), and (4) constitute the complete model. From the budget constraint (3), I obtain general welfare effects in the presence of tariffs and quotas, (5), with and without international capital mobility. By utilizing this relationship and Equations (1), (2), and (4), I derive the key Expressions (6) and (7) below for the general equilibrium effects on welfare of changes in transfers, tariffs, and quantity restraints both with and without international capital mobility.

3. General Welfare Effects

In this section, I provide a sketch of the derivation of Equation (5), which is the fundamental expression required for determining the implications of trade liberalization policies. This expression is relevant when capital is both mobile and immobile.(13) Totally differentiating budget constraint (3), and noting that the change in welfare measured in numeraire good units is dy = [e.sub.u]du, I obtain (14)

[Mathematical Expression Omitted], (5)

where dy is the change in real income. Equation (5) continues to hold with or without international capital mobility when tariffs and quotas are in force.

Expression (5) is used throughout the subsequent analysis to determine the effects of trade liberalization policies with and without international capital mobility. However, individual policy analyses require the elimination of the endogenous change in tariff-constrained imports, [dm.sub.1], and the endogenous changes in unit-quota rents, [dp.sub.2], from the right-hand side of Equation (5) by relating [dp.sub.2] and [dm.sub.1] to exogenous variables both in the presence and absence of international capital mobility. Expressions for [dp.sub.2] and [dm.sub.1] with and without international capital mobility are contained in the appendix.

Welfare Changes with Tariff and Quota Constraints

In the appendix, I derived Expressions (A4), (A5), (A6), and (A7) for [dp.sub.2] and [dm.sub.1] with and without international capital mobility. By substituting these expressions into Equation (5), I determine the implications of trade liberalization with and without international capital mobility. In this subsection, I first derive general equilibrium welfare expressions in the presence of tariffs and quotas, creating Equation (6). International capital mobility is then introduced, and the corresponding Expression (7) is obtained.

This first case is presented to illustrate the implications of pursuing quota policies and provides a basis for a comparison of the effects of international capital mobility when these policies are pursued. A similar formulation of the tariff and quota case with immobile capital is presented by Neary (1995, p. 538, equation 2.16).

Assume that in the small, open economy under investigation, both tariffs and quotas coexist. When capital is internationally immobile, domestic rental rates of capital are endogenously determined, dr [not equal to] 0, and total capital in use is fixed; that is, dk = 0. In this case, I make the simplifying assumption that [Mathematical Expression Omitted], so that [Mathematical Expression Omitted] is zero despite dr [not equal to] 0. In Equation (5), setting [Mathematical Expression Omitted] equal to zero and from equation (A6) substituting the expression for [dm.sub.], I obtain the welfare effects of trade reform when capital is immobile in the presence of tariffs and quotas:

[Mathematical Expression Omitted]. (6)

Here, [Mathematical Expression Omitted] represents the total price responsiveness, including indirect effects attributable to the binding quota. The inverse of the coefficient of dy, [Mathematical Expression Omitted], is the shadow price of foreign exchange under a tariff and a quota, since it gives the marginal welfare effect of an extra unit of the numeraire. When tariffs are the only trade restriction in use, [Mu] = [[1 - [t[prime].sub.1] [x.sub.11].sup.-1], where [Mathematical Expression Omitted] is usually called the "tariff multiplier," following Jones (1969), since any exogenous shock increasing income results in a higher demand for all goods, including importable goods subject to tariffs.(15) The increase in imports results in higher tariff revenue, which is assumed to be rebated as a lump sum to the household sector and therefore a further rise in demand for all goods beyond the initial increase in income. Both [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are described in detail in the appendix. The coefficients of [dt.sub.1] and [dm.sub.2] represent the marginal cost of tariff increases and the marginal benefit of relaxing quotas, respectively. Thus, Equation (6) relates exogenous trade policy shocks to changes in welfare in the presence of tariffs and quotas.

The introduction of international capital mobility requires a different substitution than performed above to account for the additional output-supply effects from endogenous capital flows. The relevant expression for a change in the import demand for tariff-constrained goods, [dm.sub.1], taking account of endogenous changes in domestic prices of quota-constrained imports, is expressed as Equation (A7), which includes the additional output-supply effects present with international capital mobility. When capital is internationally mobile, the domestic rental, r, equals the fixed world rental, [r.sup.*], so that dr = [dr.sup.*] = 0 and dk [not equal to] 0. With coexisting tariffs and quotas, in the presence of international capital mobility, substituting the expression for [dm.sub.1] from Equation (A7) into Equation (5) and rearranging, I obtain

[Mathematical Expression Omitted]. (7)

Equation (7) describes the welfare implications of an exogenous change in tariff rates, [t.sub.1], or quota levels, [Mathematical Expression Omitted], in the presence of tariffs, quotas, and international capital mobility. Here, [Mathematical Expression Omitted] represents the total price responsiveness, including indirect effects due to the binding quota and any output-supply effects from endogenous capital flows. The inverse of the coefficient of dy, [Mathematical Expression Omitted], represents the shadow price of foreign exchange under tariffs and quotas with international capital mobility and is assumed positive. The term [Mathematical Expression Omitted] represents the direct and indirect income responsiveness for category 1 goods, including any additional output-supply effects from endogenous capital flows. Both terms, [Mathematical Expression Omitted] and [Mathematical Expression Omitted], are described in detail in the appendix. Equation (7) relates exogenous trade policy shocks to changes in welfare in the presence of tariffs, quotas, and international capital mobility, and thereby extends Neary (1995, p. 538, equation 2.16).

In this section, I developed a very basic model with multiple trade restrictions on price as well as quantity, both with and without international capital mobility. These models are very general in specification. The key Equations (6) and (7) describe how exogenous shocks to trade policy from abroad affect the welfare of a small, open economy. In the following, I focus on these two equations and on how welfare responds to changes in the exogenous variables.

4. International Capital Mobility and Trade Reform in the Presence of Tariffs and Quotas

There exists a rich literature on the importance of international capital mobility for trade policy.(16) This section examines trade reforms with coexisting tariffs and quotas under international capital mobility, to my knowledge a case heretofore unexplored. These results are compared to trade reforms with immobile capital. The cases are described by Equations (6) and (7) above. The coefficients of [dt.sub.1] and [dm.sub.2] represent the marginal cost of tariff increases and the marginal benefit of relaxing quotas, respectively.

Consider the case of tariff reform where quotas are irremovable. Therefore, [Mathematical Expression Omitted], and from Equation (7), I obtain

[Mathematical Expression Omitted], (8)

where [Mathematical Expression Omitted] is the relevant shadow price of foreign exchange and [Mathematical Expression Omitted] represents the compensated price responsiveness for category 1 goods, given the induced changes in domestic prices of category 2 imports, including any additional output supply effects due to endogenous capital flows. But in the expression for [Mathematical Expression Omitted], the matrices pre- and post-multiplying the final term are transpositions of each other. Hence, that term is a matrix quadratic form and is unambiguously negative definite. Thus, in the presence of fixed quotas, international capital mobility raises the cost of tariff protection on other imports with no qualifications.(17)

The cost of tariff protection in the presence of fixed quotas and international capital mobility is given by the coefficient of [dt.sub.1], which, as noted above, equals [t.sub.1]d[Alpha], with [Alpha] being a scalar in Equation (8). As discussed in the appendix, the compensated price response is greater in an economy with existing quantitative restrictions such as quotas. International capital mobility reinforces the effect because of the additional output-supply response in the economy from endogenous capital flows, so that [Mathematical Expression Omitted] is smaller algebraically than [Mathematical Expression Omitted]. The analogous expression to Equation (8) with immobile capital is given by Neary (1995, p. 541, equation 4.1), where [Mathematical Expression Omitted] in that case equals [Mathematical Expression Omitted], since there are no additional output-supply effects. Comparison of Equation (8) with Neary's equation (4.1) reveals the following:

PROPOSITION 4.1. In the presence of fixed quotas, international capital mobility raises the cost of tariff protection on other imports.

The imposition of tariffs directly lowers welfare because of higher domestic prices for tariff-restricted imports and indirectly lowers welfare because of binding import quotas. The indirect effect stems from induced changes in demand for category 2 goods because of higher relative prices for tariff-restricted goods. Binding quotas prevent the rise in imports of type 2 goods and therefore domestic prices adjust, leading to a change in the demand for type 1 goods and an additional welfare loss. International capital mobility permits a larger output-supply response due to endogenous capital flows and therefore an even greater welfare loss.

Since the matrix [Mathematical Expression Omitted] remains negative definite with the introduction of international capital mobility, a second result is immediately evident from Equation (8):

PROPOSITION 4.2. Given irremovable quotas on one category of imports, the optimal policy toward imports of the other category of imports is free trade. This is true with or without international capital mobility and regardless of the factor intensity rankings of the two categories of imports. Since quota rents and tariff revenues are both retained by the home country, the distortion created by fixed quotas cannot be reduced by adjusting tariffs away from free trade. Proposition 2 extends Neary's (1995) result to the case of international capital mobility.

We now turn to the effects of quota reforms in the presence of irremovable tariffs and international capital mobility so that [dt.sub.1] = 0. From Equation (7), I have

[Mathematical Expression Omitted]. (9)

The optimal quota policy is derived by setting the coefficient of [Mathematical Expression Omitted] equal to zero and rear-ranging terms to yield

[Mathematical Expression Omitted], (10)

which gives the welfare-maximizing implicit excess tariff, [Mathematical Expression Omitted], on quota-constrained goods, given irremovable tariffs, [t.sub.1], and international capital mobility. It is helpful to rewrite Equation (10) in a slightly modified notation:

[Mathematical Expression Omitted], (10[prime])

where [Mathematical Expression Omitted] and [Mathematical Expression Omitted]. Comparing this with equation (5.2) in Neary (1995), which he obtains for the case when capital is not internationally mobile; that is, comparing with [Mathematical Expression Omitted], we get

[Mathematical Expression Omitted]. (11)

In general, Equation (11) cannot be signed. However, we do get an unambiguous sign for [Mathematical Expression Omitted] if both k and [m.sub.2] are scalars (i.e., there is only one quota-constrained good and only one type of mobile capital). Rewriting Equation (11) as

[Mathematical Expression Omitted], (11[prime])

we know that in all cases, [E.sub.22], [Mathematical Expression Omitted], and [g.sub.kk] are negative. In addition, it is assumed that [E.sub.12] is positive and that [g.sub.1k] and [g.sub.2k] (which equals [g.sub.k2]) have the same sign. Now the whole right-hand side is negative, so that we have the following proposition.

PROPOSITION 4.3. In the case of a single quota-constrained importable good and only one internationally mobile capital good, given an irremovable tariff on one import, international capital mobility reduces the optimal implicit excess tariff on the quota-constrained import.

Suppose that a quota is imposed on the type 2 good that generates the same implicit tariff whether capital is internationally mobile or not. With international capital mobility, the required quota is more binding and has a higher direct welfare cost (by restricting imports of good 2), which is not offset by its presumptively higher indirect welfare benefit (by encouraging imports of good 1).(18)

5. Conclusions

For a very general open economy, admitting of an arbitrary number of goods and factors, intermediate- and joint-goods production, a convex production set for the economy, constant returns to scale in every activity, and perfect competition, international capital mobility raises the cost of tariff protection in the presence of fixed quotas. This extends Neary's (1988) result to the case of coexisting trade policies. Given irremovable quotas on one category of imports, the optimal policy toward imports of the other category of imports continues to be free trade in the presence of international capital mobility. This is true with or without international capital mobility and is true regardless of factor intensity. Furthermore, if there is only one quota-constrained good and only one type of capital, given an irremovable tariff on one import, international capital mobility reduces the optimal implicit excess tariff on the quota-constrained import.

We live in a world with significant protectionist tendencies and hence many forms of trade restrictions. The presence or absence of internationally mobile capital is crucial to any welfare analysis of trade liberalization policies. Although international capital mobility does not change the nature of the effect of trade reform, it does change the degree of reform recommended when some policies are fixed. In addition, in some instances, factor intensities matter. Finally, protectionist policies, such as coexisting tariffs and quotas, are even more punitive without qualification when capital is internationally mobile.

Appendix

In this appendix, I use Equations (1), (2), and (4) above to obtain expressions in terms of exogenous variables for changes in tariff-constrained imports and changes in unit-quota rents, both with and without international capital mobility. I will first address the general equilibrium import-demand function for tariff-constrained imports, [dm.sub.1].

First, I differentiate the vector of import-demand functions, as expressed by Equation (1). This results in

[Mathematical Expression Omitted], (A1)

where Mathematical Expression Omitted], for i = 1, 2 is the vector of income effects on the demand for importable goods. The coefficient on dk, [g.sub.pk], is a matrix of generalized Rybczynski derivatives that give the output effects of increases in factor supplies. Each term in the matrix may be positive or negative, depending on whether the goods subject to trade restrictions use the factor intensively or not, in a general equilibrium sense.(19) The terms [e.sub.ij] and [g.sub.ij] represent how the demand and output, respectively, of importables of good i respond to changes in the domestic price of good j. In the absence of international capital mobility, dk = 0. When capital is internationally mobile the domestic rental, r, equals the fixed world rental, [r.sup.*], so that dr = [dr.sup.*] = 0. Then, from Equation (4) I obtain

[Mathematical Expression Omitted], (A2)

as the change in capital used in the home country.(20) Substituting this into Equation (A1) and rearranging yields, I obtain

[Mathematical Expression Omitted]. (A3)

Equations (A1) and (A3) are used extensively in the derivations. In [Mathematical Expression Omitted]. The first term [g.sub.ij] represents how the output of importables of good i responds to changes in the domestic price of good j. The other term in the matrix represents an additional supply response in the economy due to an endogenous capital flow. This term is a bilinear form in a negative-definite matrix for i [not equal to] j and a quadratic form in a negative-definite matrix for i = j. Consider i [not equal to] j when category i goods are capital intensive and category j goods are not capital intensive. Then the generalized Rybczynski derivatives, [g.sub.ik], and the Stopler-Samuelson derivatives, [g.sub.kj], are of different signs and [Mathematical Expression Omitted] algebraically, since [Mathematical Expression Omitted] is unambiguously positive.(21) In summary, international capital mobility induces an enhanced output-supply response that increases the total output-supply response of category i goods to a change in the price of category j goods if category i = j, or if i [not equal to] j and i, j are both not capital intensive or both capital intensive.

The next step is to eliminate endogenous changes in unit quota rents, [dp.sub.2], from Equations (A1) and (A3). Totally differentiate Equation (2) for i = 2, noting that [dt.sub.1] = [dp.sub.1], and invert the import-demand function for [Mathematical Expression Omitted]. This results in

[Mathematical Expression Omitted] (A4)

when capital is internationally immobile and

[Mathematical Expression Omitted] (A5)

in the presence of international capital mobility.

The full expression in the absence of international capital mobility for changes in the general equilibrium demand for tariff-constrained imports, [dm.sub.1], taking account of endogenous changes in domestic prices of quota-constrained imports, is found by substituting Equation (A4) into (A1), noting that [dt.sub.1] = [dp.sub.1], and rearranging to obtain

[Mathematical Expression Omitted]. (A6)

The expression [Mathematical Expression Omitted] represents the compensated price responsiveness for category I goods given the induced changes in domestic prices of category 2 imports. The term ([e.sub.12] - [g.sub.12])[([e.sub.22] - [g.sub.22]).sup.-1]([e.sub.21] - [g.sub.21]) is a matrix quadratic form in a negative definite matrix, and the price responsiveness of demand is unambiguously algebraically greater when quotas are present. Since the quota is assumed binding, domestic prices of the quota-constrained goods must adjust to any changes in the domestic prices of tariff-constrained goods. This leads to a change in the demand for type 1 goods. The coefficient of [dt.sub.1], therefore, reflects the Le Chatelier principle where the restriction is a binding quota. Neary (1995, p. 536, equation 2.10) derives this expression for the tariff and quota case without international capital mobility.

The coefficient of dy represents the direct and indirect response of category 1 goods to a change in income, where [Mathematical Expression Omitted]. The interpretation of [Mathematical Expression Omitted] is similar to that of [Mathematical Expression Omitted] above. An increase in income raises the demand directly for category 1 goods, and there is an indirect effect from the induced change in domestic prices of category 2 goods. Binding quotas prevent the rise in imports of category 2 goods. Therefore, domestic prices adjust for the quota-constrained goods. The change in domestic prices leads to a change in demand for type 1 goods. The result is identified in Neary (1995, p. 536, equation 2.11) for the tariff and quota case.

The matrix ([e.sub.12] - [g.sub.12])[([e.sub.22] - [g.sub.22]).sup.-1] shows how relaxing the quota on category 2 goods changes the demand (in a general equilibrium sense) for category 1 imports. We know from Hatta (1977) that all the terms in this matrix are negative if all category 2 goods are net substitutes for each other and for all category 1 goods. That is, relaxing the quota leads to a fall in the domestic price of the quota-constrained goods, which tends to lower the import demand for the tariff-restricted category of goods, provided the aforementioned Hatta condition holds.

The analogous expression to Equation (A6) in the presence of international capital mobility is found by substituting Equation (A5) into (A3), noting that [dt.sub.1] = [dp.sub.1], and rearranging to give the tariff-constrained import-demand function for [m.sub.1], given binding quantitative restrictions, so that

[Mathematical Expression Omitted]. (A7)

Here, [Mathematical Expression Omitted] represents the compensated price responsiveness for category 1 goods, given the induced changes in domestic prices of category 2 imports, including any additional output supply effects attributable to endogenous capital flows. In the expression for [Mathematical Expression Omitted], the matrices pre- and postmultiplying the final term are transpositions of each other. Hence, that term is a matrix quadratic form and is unambiguously negative definite.

I finally turn to the determination of the sign of [Mathematical Expression Omitted], where [Mathematical Expression Omitted]. If category 1 goods and category 2 goods are substitutes in import demand and are both capital intensive or both are not capital intensive, then [Mathematical Expression Omitted] is smaller than ([e.sub.12] - [g.sub.12])[([e.sub.22] - [g.sub.22]).sup.-1] in absolute value and the elements of the vector of are smaller than the corresponding elements of [Mathematical Expression Omitted].

I would like to thank Nadeem Naqvi and Beth Franck for guidance and encouragement while working on this project and two referees for their helpful comments.

1 See Hufbauer and Elliot (1994) for an up-to-date assessment of U.S. trade policies in 21 sectors.

2 Aside from considering the optimal implicit excess tariff, neither Neary (1995) nor I explore issues associated with tariff equivalents of quotas or any other distortions. The interested reader is referred to Anderson (1998), Anderson, Bannister, and Neary (1995), and Anderson and Neary (1994), who all deal with the modern theory of effective protection, including obtaining the tariff equivalent of quotas, VERs, and other foreign trade and domestic distortions.

3 See, for instance, Corden (1994, p. 3).

4 See also Jones (1984).

5 Examples of variations in the standard small open economy model are found in Chandra and Naqvi (1997), Hatzipanayotou and Michael (1995), Neary (1995), and Naqvi and Wiener (1991).

6 The convexity of the production set ensures the uniqueness of an equilibrium that will be stable. For example, in a two-input production possibilities frontier, a convex production possibilities frontier will ensure first that there will be only one point of tangency between the relative price line and the production possibilities frontier. Therefore, a unique equilibrium for the economy exists. Second, as the relative price of a commodity rises, the general equilibrium output-supply response of the commodity will be positive. The same argument holds true for a larger number of commodities.

7 All vectors are column vectors, and a prime ([prime]) indicates a transposition. In referring to commodities, I refer to category and type interchangeably.

8 The expenditure function derives from

e(p, u) = min [p[prime]c: U(c) [greater than or equal to] u; p [greater than] 0].

Neary and Roberts (1980) provide a detailed description of the properties of the constrained and the unconstrained expenditure functions.

9 The GDP function represents an envelope function describing

g(p, k) = max [p[prime]x: F(x, k) [less than or equal to] 0],

the dependence of the maximum value of net output on commodity prices and factor endowments, given the production set F(x, k) [less than or equal to] 0 is convex. Other factors in fixed supply are also arguments of the GDP function but are not made explicit.

Other factors of production that are not traded on world markets are inelastically supplied, and their endowments are denoted by L; their domestically, endogenously determined factorprices are w, and I do not make either L or w explicit, since I never consider a change in the endowment of the nontraded factors of production.

10 My focus is on endogenous capital flows due to changes in tariffs, transfers, and quantitative restrictions. Neary and Ruane (1988) and Neary (1995) also examine the implications of exogenous factor flows in the presence of individual trade restrictions and coexisting tariffs and quotas, respectively.

11 See Neary (1985). The derivatives of the expenditure function with respect to prices are Hicksian (compensated) demand functions, [e.sub.p](p, u), and the second derivative, [e.sub.pp](p, u) is negative definite. The derivative of the Hicksian demand functions with respect to utility is the income effect vector, [e.sub.pu](p, u).

The price derivatives of the GDP function are the output-supply vectors, [g.sub.p](p, k) = x(p, k). The prices of the mobile factors are [g.sub.k](p, k) = [r.sub.k](p, k). The effect of factor price changes on factor demand is given by [g.sub.kk](p, k) = [r.sub.k](p,k). Also, dx = [x.sub.1][dp.sub.1] + [x.sub.2][dp.sub.2] + [x.sub.k]dk, where [x.sub.1] = [g.sub.p1]; [x.sub.2] = [g.sub.p2]; [[x.sub.k] = [g.sub.pk].

12 Neary and Roberts (1980) show the standard properties of an expenditure function continue to hold for the restricted expenditure function. Neary (1985) extends these results to the GDP function. These results can be reinterpreted for quantity restrictions such as quotas.

13 It is worth emphasizing that whenever I consider a change in tariffs or quotas, these are radial changes, so that [dt.sub.1] = [t.sub.1]d[Alpha] and [dm.sub.2] = [m.sub.2]d[Beta], where [Alpha] and [Beta] are scalars.

14 From equation (3), we have

[Mathematical Expression Omitted].

Noting that [dp.sub.1] = [dt.sub.1], since [Mathematical Expression Omitted] is constant for a small country, using Equations (1) and (2) and [g.sub.k]dk = rdk, I obtain Equation (5).

15 It has been known under a variety of other names, such as the tariff multiplier (Jones 1969), the aggregate marginal propensity to consume evaluated at world prices (Lloyd 1974), the aggregate income terms evaluated world prices (Fukushima 1981), and the Hatta normality condition (Turunen-Red and Woodland 1991), among others.

Following standard practice, it is assumed henceforth that all shadow prices of foreign exchange are positive, or else many paradoxical results ensue. See Smith (1987), Neary (1995, p. 539-40), or Dixit (1975) for a further discussion.

16 See Neary (1988), Neary and Ruane (1988), and Chandra and Naqvi (1997), to name a few.

17 I am grateful to a referee for pointing out this feature and hence significantly strengthening proposition 1 below.

18 I am grateful to a referee for pointing me to the unambiguous outcome in the scalar case.

19 Recall that the Rybczynski theorem states that at given prices, an increase in supply of a factor raises the output of the good that uses the expanding factor intensively and reduces the output of the other good that uses the expanding factor unintensively.

20 When differentiating the domestic rental rate of capital, I partition the domestic price vector into category 1 and category 2 domestic price vectors to focus attention on the individual Rybczynski matrices, which may be different across the two categories.

21 Recall that the Stopler Samuelson Theorem states that an increase in the relative price of a good raises the real reward to the factor used intensively in the production of that good and reduces the reward to the other factor used unintensively in the production of that good.

References

Anderson, James E. 1998. Effective protection redux. Journal of International Economics 44:21-44.

Anderson, James E., Geoffrey J. Bannister, and J. Peter Neary. 1995. Domestic distortions and international trade. International Economic Review 36:139-57.

Anderson, James E., and J. Peter Neary. 1994. Measuring the restrictiveness of trade policy. World Bank Economic Review 8:151-69.

Chandra, Vandana, and Nadeem Naqvi. 1997. Protection and the shadow price of foreign exchange with increasing returns and international capital mobility. Canadian Journal of Economics 30:959-67.

Corden, W. Max. 1994. Economic Policy Exchange Rates and the International System. Chicago: University of Chicago Press.

Dixit, Avinash K. 1975. Welfare effects of tax and price changes. Journal of Public Economics 4:103-23.

Fukushima, Takashi. 1981. A dynamic quantity adjustment process in a small open economy, and welfare effects of tariff changes. Journal of International Economics 14:513-29.

Hatta, Tatsuo. 1977. A recommendation for a better tariff structure. Econometrica 45:1859-69.

Hatzipanayotou, Panos, and Michael S. Michael. 1995. Tariffs, quotas, and voluntary export restraints with endogenous labor supply. Journal of Economics 62:185-201.

Hufbauer, Gary C., and Kimberly A. Elliot. 1994. Measuring the Costs of Protection in the United States. Washington, DC: Institute for International Economics.

Jones, Ronald W. 1969. Tariffs and trade in general equilibrium: Comment. American Economic Review 59:418-24.

Jones, Ronald W. 1984. Protection and the harmful effects of endogenous capital flows. Economics Letters 15:325-30.

Lloyd, Peter. 1974. A more general theory of price distortions in open economies. Journal of International Economics 9:469-79.

Naqvi, Nadeem, and Klaus Wiener. 1991. External increasing returns and the shadow price of foreign exchange. Journal of International Economics 30:177-84.

Neary, Peter. 1985. International factor mobility, minimum wage rates, and factor-price equalization: A synthesis. Quarterly Journal of Economics 100:551-70.

Neary, Peter. 1988. Tariffs, quotas, and voluntary export restraints with and without internationally mobile capital. Canadian Journal of Economics 21:714-35.

Neary, Peter. 1995. Trade liberalization and shadow prices in the presence of tariffs and quotas. International Economic Review 36:531-54.

Neary, Peter, and K. W. S. Roberts. 1980. The theory of household behavior under rationing. European Economic Review 13:25-42.

Neary, Peter, and Frances Ruane. 1988. International capital mobility, shadow prices, and the cost of protection. International Economic Review 29:571-85.

Smith, Alasdair. 1987. Factor shadow prices in distorted open economies. In Protection and Competition in International Trade: Essays in Honor of W. M. Corden, edited by H. Kierzkowski. Oxford: Basil Blackwell.

Turunen-Red, Arja H., and Alan D. Woodland. 1991. Strict pareto-improving multilateral reforms of tariffs. Econometrica 59:1127-52.
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