Athens Laboratory of Economic Policy Studies Department of Economics Athens University of Economics and Business

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1 DISCUSSION PAPER No. 1 TERMS OF TRADE SHOCKS AND DOMESTIC PRICES UNDER TARIFFS AND QUOTAS: A NOTE Konstantine Gatsios November 2000 Athens Laboratory of Economic Policy Studies Deartment of Economics Athens University of Economics and Business

2 Terms of Trade Shocks and Domestic Prices under Tariffs and Quotas: A Note Konstantine Gatsios Athens University of Economics and Business, IMOP and CEPR November 2000 Abstract The aer develos a two-good, small-country, general equilibrium trade model with endogenous labour suly, where trade is restricted by a tariff or an imort quota. Within this framework, it is shown that, contrary to Anam (1989), under an imort quota domestic and world rices may vary in the same direction. This is due to the ossibly ositive emloyment effects of terms of trade shocks. In such a case, comared to fixed labour suly, variable labour suly is likely to make the domestic rices less sensitive to foreign rice volatility. JEL Classification: F10: International Trade Theory F13: Commercial Policy Key words: imort restrictions, variable labour suly, terms of trade Corresondence: Konstantine Gatsios Athens University of Economics and Business PO Box Athens Greece Tel: Fax: gatsios@aueb.gr

3 1. Introduction Until fairly recently, the traditional view regarding the effects of changes in the terms of trade on domestic rices has been that quotas are suerior to tariffs in terms of insulating domestic rices against foreign terms of trade shocks (see, for instance, Dasguta and Stiglitz 1977, Krueger 1984, Markusen and Melvin 1984). The basic argument was that while a tariff ermits domestic rices to vary directly with world rices, a quota comletely insulates internal rices against terms of trade shocks. Anam (1989) challenged this traditional result on the grounds that it was derived from the study of artial equilibrium models. He demonstrated that in a general equilibrium context, where the income effects of changes in the terms of traded are accounted for, the orthodox intuition did not hold. In articular, he showed that domestic rices can be more vulnerable under a quota than under a tariff, and under a quota, unlike the case of a tariff, domestic rices vary inversely with foreign rices. This aer modifies and qualifies Anam s (1989) results. In articular, it shows that they are sensitive to the assumtion of fixed factor sulies that he adots. In the resence of variable factor sulies due to endogenous domestic suly resonses (i.e., labour), I argue that under an imort quota domestic and foreign rices may vary in the same direction. This is because, alongside the negative income effects, there may now be ositive emloyment effects as well. The latter may overtake the former. Moreover, it is shown that comared to fixed labour suly, variable labour suly is likely to exert a damening effect on the imact of foreign rices on domestic rices. I develo, for my uroses, a simle general equilibrium trade model of a small oen economy where labour suly is variable due to endogenous suly resonses, and trade is restricted either through a tariff or a quota. Anam s aer, then, becomes a secial case of this model. As exected, changes in labour suly due to changes in the terms of trade will now affect directly not only roduction, but also utility which increases with leisure. It turns out that Anam s result, namely that domestic rices vary to the oosite direction than world rices, holds only if the imorted good is labour intensive and a comlement to leisure in consumtion. If, on the other hand, the imorted good is non-labour intensive and a substitute to leisure in consumtion, then domestic and world rices may vary in the same direction. 1

4 2. The model and the results Consider a small oen economy roducing one exorted and one imorted good using two or more factors of roduction in fixed suly 1. The country is also endowed with a constant number of identical individuals whose work hours are variable. Let L denote the variable domestic labour suly 2. Let the exorted good be the numeraire with normalised rice equal to one. Denote by the world rice of the imorted good, and by its domestic relative rice. The difference between the domestic and the world rice is denoted by t( = ) and is due to a tariff or an imort quota. Individual utility deends on the consumtion of the two goods and leisure, all of them assumed to be normal goods. The aggregate exenditure function E (,L,u ) catures the minimum exenditure to achieve a utility level u at relative rice and emloyment L. The exenditure function is increasing in and L, strictly concave in (i.e., E < 0 ) and strictly convex in L (i.e., ELL > 0 ). Its derivative with resect to (i.e., E ) gives the comensated demand function for the imorted good, and with resect to L (i.e., EL ) gives the reservation wage, w ~ (see, for instance, Dixit and Norman 1980). The cross derivative, E L, catures the way the imorted good and leisure are related in consumtion; if E L is ositive (resectively, negative), then they are substitutes (resectively, comlements) in consumtion. Finally, since all goods and leisure are normal goods, then E > 0 and E > 0. Lu Let R (,L) denote the country s gross national roduct (GDP) function that shows the maximum revenue from roduction of all goods given the rice, the labour suly L, and the stock of factors in fixed suly. Throughout the aer, the fixed factors are omitted from the GDP function since they do not affect the analysis and the results. The GDP function is strictly convex in (i.e., R > 0 ) and strictly concave in L (i.e., RLL < 0 ). Its derivative with resect to (i.e., R ) gives the suly function of the imorted good, and with resect u 1 The two-good assumtion is a facilitating one. The analysis would go through if we assumed many traded goods. 2 The literature on variable labour suly in international trade models is not very large (see, for instance, Kem and Jones 1962, Frenkel and Razin 1975, Martin 1976, Neary 1978, Martin and Neary 1980, Dixit and Norman 1980, Woodland 1982, and Mayer 1991). In modelling endogenous labour suly two aroaches have been develoed. The traditional one, which I follow here, assumes that the number of workers is fixed, but work hours are flexible. In the second aroach, work hours are fixed, but labour force articiation is endogenous. 2

5 to (i.e., R ) gives the marginal revenue roduct of labour. Following Dixit and Norman L L (1980), the cross derivative of the GDP function, R L, may be interreted as a general equilibrium measure of factor intensity. R L is ositive if the domestic outut of the imorted good increases following an increase in labour suly; in this case, we call the imorted good labour intensive, while in the oosite case ( i.e., RL < 0 ) we call it non-labour intensive 3. Since our interest is in net imorts, the model is secified in terms of the trade exenditure function that equals the excess of domestic exenditure over the country s GDP. That is, (,u,l) = E(,L,u ) R(,L) (1) The roerties of the trade exenditure function are related to those of the exenditure and the GDP functions. Thus, the function is strictly concave in (i.e., < 0 ) and strictly convex in L (i.e., LL > 0 ) 4. Furthermore, its derivative with resect to (i.e., ) gives the imort demand function. That is, (,L,u ) = E (,L,u ) R (,L) (2) In equilibrium, the country s exenditure equals revenue from roduction lus revenue from the revailing trade restriction. Tariff revenue or quota rents are lum-sum distributed to the country s households. Thus, using equations (1) and (2) the country s income-exenditure identity, either in the case of a tariff or an imort quota, is given by (,L,u ) = t (,L,u ) (3) where under a quota t( = ) is endogenously determined through the endogenous determination of. 3 With many goods and factors R ij would be a matrix, where i denotes outut rices and j denotes endowments or, more generally, inut sulies. Observe that all elements of any row can be ositive, meaning that if any sector uses a articular factor intensively in the way defined in the text, it does not necessarily follow that it would use any other factor unintensively. An examle of this is the secific-factors model. 4 In the two-good, two-factor model with constant returns to scale technology, the wage is not affected by emloyment. Hence R LL = 0, so that LL = ELL. 3

6 Equilibrium in the labour market requires that the reservation wage ( w ~ ) equals the net wage which, in turn, equals the marginal revenue roduct of labour ( i.e.,rl ). Thus, EL (,L,u ) = RL (,L) or L (,L,u )= 0 (4) In the case of a tariff, it is clear that, for a given tariff level, d = d, so that domestic and world rices move together in the same direction. The interesting case is that of an imort quota to which I now turn. Equations (2), (3) and (4) can be solved for the three endogenous variables u, L, and as functions of the exogenous terms of trade. Differentiating equations (2), (3) and (4) gives 1 Lu u 0 LL L 0 L du dl d = 0 d 0 (5) The determinant of the coefficient matrix is q = LL ~ < 0, where ~ = L 1 LL L < 0. This ensures Walrasian stability (see, for instance, Takayama 1985, ). 5 The system of equations (5) give the effect of an increase in world rices on domestic rices in the case of a quota as ( ) d 1 1 u L LL d = ~ (6) Lu If labour suly were fixed, then the equation above would take the form d d 1 = u (6 ) 5 With a fixed labour suly equation (4) in the text will now be R L (,L) = w, where w denotes the wage rate. The rest of the equations describing the model, i.e., (1)-(3), remain intact excet that now L will no longer be an element of the exenditure function. The system of equations (5) in the text will be given now by du 0 1 RL dw = 0 d. d u 0 0 4

7 Equation (6 ) is Anam s result (1989, equation 6). That is, in a general equilibrium context with fixed labour suly, domestic rices vary inversely with foreign rices in the case of an imort quota, i.e., d d < 0 6. An increase in world rices (i.e., d > 0 ) reduces income from quota rents. Lower income reduces the demand for imorts, which, in turn, reduces the domestic rice of the imorted good. But when labour suly is variable, then besides a corresonding to the above negative direct income effect ~ 1 i.e., ), there is also an indirect effect that works through ( u changes in emloyment, namely deending on the sign of ~ 1 1 L LL Lu. This effect is ambiguous, its sign L; that is, it deends on the factor intensity of the imorted good and on its relationshi to leisure in consumtion. For instance, if the imorted good is labour intensive ( i.e., RL > 0 ) and a comlement to leisure in consumtion ( i.e., EL < 0 ), then L < 0. Similarly, if the imorted good is non-labour intensive and a substitute to leisure in consumtion, than > 0. L Consider, first, the case where the imorted good is non-labour intensive in roduction and a substitute for leisure in consumtion ( i.e., L > 0 ). Then, an increase in world rices may increase or decrease domestic rices. This is because, with variable labour suly, the reduction in income from quota rents reduces both the reservation wage and leisure, thus increasing labour suly and reducing the roduction of the non-labour intensive imorted good. Moreover, since the imorted good and leisure are substitutes in consumtion, demand for the imorted good increases. The lower roduction and the higher demand for the imorted good increases its excess demand and, consequently, it raises its domestic rice. Hence, if this indirect effect outweighs the direct effect, then world and domestic rices fluctuate in the same direction. Moreover, comared to the case of a fixed labour suly, it is 6 Following Anam (1989), equation (9 ) in the text can be written as 1 d = z ε d, where 1 z = u is the marginal roensity to imort, 0 < z < 1 by normality, and ε = < 0 reresents the (comensated) rice elasticity of imort demand. Equation (9 ) can further be written in roortional terms as 1 [ ( + t) ] = z ε. This exression is similar to equation (8) in Anam s aer, the difference being that he assumes an ad valorem tariff. This, however, has no bearing on the analysis. So, unlike the case of a tariff, z > ε 1+ t, then where = ( ), domestic rices vary inversely with a quota. Furthermore, when ( ) > so that a given trade shock causes the domestic rices to vary more than foreign rices under a quota than under a tariff. 1 5

8 now less likely for domestic rices to fluctuate more than world rices. 7 If, on the other hand, the direct effect on domestic rices outweighs the indirect effect, then domestic rices vary in the oosite direction to world rices, but, now, variable labour suly definitely decreases the effect of foreign rice volatility on that of domestic rices. When the imorted good is labour intensive and a comlement to leisure in consumtion ( i.e., L < 0 ), then domestic rices vary inversely with world rices. The indirect emloyment effect is negative and it reinforces the direct income effect. It is unclear, however, whether variable labour suly increases or decreases the resonse of domestic rices to change in world rices, since both the numerator and the denominator of equation (6) increase in absolute value. I summarise the discussion above in the following Proosition Proosition: Assume that the imorted good is non-labour intensive and a substitute to leisure in consumtion. Then, under an imort quota, domestic and world rices may vary in the same direction. In any case, variable labour suly exerts a damening effect on the imact of world rices on domestic rices. If, on the other hand, the imorted good is labour intensive and a comlement to leisure in consumtion, then world and domestic rices vary in the oosite direction. 7 This is because comared to equation (6 ) the denominator of equation (6) increases in absolute value, whereas 1 the numerator is likely to decrease in absolute value, unless the emloyment effect LLLLu is too big comared to the income effect u. It should be ointed out that in this, as well as in following comarisons of the same kind, matrices are evaluated at the same vector of factor endowments. 6

9 3. Conclusions Anam (1989) demonstrated that in a general equilibrium model where income effects are accounted for, domestic rices (i) can be more vulnerable under a quota than under a tariff, and (ii) under a quota, unlike the case of a tariff, domestic rices vary inversely with foreign rices. This aer investigates the imlications of variable labour suly for these results 8. If the suly of labour is variable due to endogenous suly resonses, then, in the case of an imort quota, changes in the terms of trade give rise to emloyment effects that may reinforce or counter the negative income effects. In articular, if the imorted good is non-labour intensive and a substitute to leisure in consumtion then the emloyment effects are ositive and may outweigh the negative income effects, resulting to domestic rices fluctuating in the same direction with foreign rices. Moreover, comared to fixed labour suly, variable labour suly under a quota is likely to exert a damening effect on the imact of world rices on domestic rices. It is imortant to note that for these results to occur it is needed not only the resence of variable factor sulies but, in addition, that such a resence is due to endogenous suly resonses (i.e., labour) and not to international mobility (i.e., caital). In the latter case it is easy to confirm that in the case of an imort quota changes in the terms of trade generate only negative direct income effects. As a result, the world and domestic rices vary in the oosite direction. 8 Mayer (1991) uses a two-good, two-factor model with variable labour suly to examine, among other things, the emloyment effects of changes in the terms of trade, as well as in imort tariffs. It is easy for one to check that the model used here can be used to reroduce several of his results. Namely, a deterioration in the terms of trade definitely raises the country s labour suly if the imorted good is labour intensive in roduction and a comlement to leisure in consumtion. The same emloyment effects confers an increase in the imort tariff. 7

10 References Anam, M. (1989) Terms of trade shocks and domestic rices under tariffs and quotas, Euroean Economic Review 33: Dasguta, P. and J. Stiglitz (1977) Tariffs versus quotas as revenue raising devices, American Economic Review 67: Dixit, A.K. and V. Norman (1980) The theory of international trade: a dual general equilibrium aroach (Cambridge: Cambridge University Press). Frenkel, J.A. and A. Razin (1975) Variable factor sulies and the roduction ossibility frontier, Southern Economic Journal 41: Kem, M.C. and R.W. Jones (1962) Variable labor suly and the theory of international trade, Journal of Political Economy 70: Krueger, A.O. (1984) Trade olicies in develoing countries in R. Jones and P. Kenen (eds): Handbook of international economics (Amsterdam: North-Holland). Markusen, J.R. and J.R. Melvin (1984) The theory of international trade and its Canadian imlications (Toronto: Butterworth). Martin, J.P. (1976) Variable factor sulies and the Heckscher-Ohlin-Samuelson model, Economic Journal 86: Martin, J.P. and J.P. Neary (1980) Variable labour suly and the ure theory of international trade, Journal of International Economics 10: Mayer, W. (1991) Endogenous labor suly in international trade theory: two alternative models, Journal of International Economics 30: Michael, M.S. (1992) International factor mobility, non-traded goods, tariffs, and the terms of trade, Canadian Journal of Economics 25: Neary, J.P. (1978) Caital subsidies and emloyment in an oen economy, Oxford Economic Paers 30: Takayama, A. (1985) Mathematical economics (Cambridge: Cambridge University Press). Woodland, A.D. (1982) International trade and resource allocation (Amsterdam: North- Holland). 8