The effects of import quotas on national welfare: does money matter?
I. Introduction
Recent evidence shows that there is an increasing use of nontariff barriers to trade (NTBs), and especially of quantitative restrictions, such as import quotas, in the world economy to protect importcompeting industries (see Table I).(1) International trade theory, however, has traditionally focused on the welfare effects of tariffs as well as on the equivalence between tariffs and quotas, with little attention paid to the welfare implications of quotas. The latter have basically been restricted within the traditional HeckscherOhlin trade model, where, for the case of a small open economy, import quotas always reduce welfare. A few recent studies have attempted to fill in this gap in the literature. For instance, Young [19] compares optimal tariffs and quotas for a large country in a stochastic environment. Neary [14], on the other hand, investigates the welfare implications of tariffs, quotas and voluntary export restraints under different assumptions on capital mobility. Finally, Chao, Hwang and Yu [3; 4] examine the welfare effects of import quotas under variable returns to scale. Although the existing literature has generated important policy implications, most of the analysis has been conducted within a barterexchange framework. It is well known, however, that the introduction of money can alter results obtained within a nonmonetary environment.(2) Accordingly, this paper attempts to reexamine the welfare effects of import quotas for a small monetary economy. We develop a twosector trade model in which money enters the economy [TABULAR DATA FOR TABLE I OMITTED] through a generalized cashinadvance constraint. Building on previous work, we allow for nonuniform monetization across sectors. Put differently, the share of purchases which must be made using cash varies across goods (markets). Interestingly, we find that if the consumption of the exportable commodity requires larger cash balances than the consumption of the importable, then contrary to standard results, an import quota may promote national welfare. Moreover, we characterize the optimal level of import quotas by deriving a formula for the computation of the optimal domesticprice ratio. We then extend our basic framework to allow for economic growth, induced by technical progress, to explore the possibility of immiserizing growth in the presence of import quotas. Johnson [10] has shown that growth can be welfarereducing in a small open economy with a tariff distortion. Bhagwati [2] generalizes this theory of immiserizing growth to the case of alternative types of distortions. Nevertheless, as shown in Alam [1], an important exception to this generalization is the case of a quota, where growth is always welfareenhancing. Chao and Yu [5] elaborate further on this important exception, by examining the welfare implications of growth for a quotadistorted small economy under variable returns to scale. This paper continues this line of research by studying the issue of immiserizing growth in the context of a small monetary economy with quota distortions. We find that growth always improves welfare if the growing industry displays a higher degree of monetization than the static one. If the converse is true then, contrary to Alam's results (obtained for a barter economy), growth can be immiserizing. The organization of the paper is as follows. The next section develops the analytical framework and section III examines the welfare implications of quotas. Section IV characterizes the optimal quota level and section V investigates the issue of immiserizing growth. Section VI concludes the paper. II. The Analytical Framework Consider a standard twosector trade model of a small open economy. The representative agent's preferences are described by a strictly quasiconcave utility function U = U([D.sub.1], [D.sub.2]) (1) where [D.sub.1] and [D.sub.2] denote, respectively, the consumption of the exportable and importable commodities. In trying to maximize this utility function, the agent faces a standard private budget constraint [Mathematical Expression Omitted], (2) where [p.sub.j] and [X.sub.j] denote, respectively, the domestic nominal price and the production level of good j, [Mathematical Expression Omitted] is the nominal money holdings (money supply), and S represents the quota revenue in nominal terms, which is assumed to be redistributed to households (private agents) in a lumpsum fashion. Table IIa. Developing Countries' Outstanding Trade Credits as a Percentage of 1987 Exports Traditional exports 16.7 Nontraditional exports, of which: 155.1 * capital goods 403.2 * consumer durables 17.7 * other manufactures 44.0 Total 81.9 Table IIb. Average Maturity of Trade Credits (Months) in Selected Developing Countries Traditional exports 1.9 Nontraditional exports, of which: * capital goods 48.4 * consumer durables 2.1 * other manufactures 5.2 Notes: Nontraditional goods refer mainly to manufactured goods excluding steel, fertilizers, pulp and paper, which have been traditionally traded on the same basis as primary commodities. They include consumer durables, capital goods and other manufactures. Source: [21]. Money serves as a medium of exchange. Hence, building on Stockman [17] and Lucas and Stokey [12], we introduce a generalized cashinadvance (CIA) or liquidity constraint which captures the transactions role of money, that is, [[Phi].sub.1][p.sub.1][D.sub.1] + [[Phi].sub.2][p.sub.2][D.sub.2] [less than or equal to] M, (3) where [[Phi].sub.j] [element of] [0, 1], j = 1, 2, denotes a constant share of purchases of good j. This constraint requires the individual to hold sufficient money balances to finance at least a certain part of consumption purchases. In general, consumption of one good requires larger cash balances, per unit of value, than consumption of the other good and hence [[Phi].sub.1] [not equal to] [[Phi].sub.2].(3) This may be justified in a number of different ways. First, it can be considered as the outcome of existing (a) regulations regarding the terms of payments of imports and the obtaining and use of credit (foreign and domestic) to finance imports [11]; and (b) export credits (as Tables IIa and IIb indicate even export credits alone differ across sectors). Second, one can actually view [D.sub.1] and [D.sub.2] as being composite goods, consisting of different proportions of both nondurable goods and flow services of durables. Since nondurable goods are subject to a different degree of credit rationing than durables, one can expect [[Phi].sub.1] [not equal to] [[Phi].sub.2].(4) Third, empirical evidence found in Cramer and Reekers [6] indicates different money demands and liquidity/sales ratios across sectors, which provides additional support for the assumption [[Phi].sub.1] [not equal to] [[Phi].sub.2]. Finally, notice that if [[Phi].sub.1] = [[Phi].sub.2] = [Phi] then the velocity of circulation, defined as [Mathematical Expression Omitted], is constant (= [Phi]) and, in particular, independent of income and of monetary expansions. This, however, contradicts empirical evidence found in a series of papers [13; 15]. The optimal allocation of income between [D.sub.1] and [D.sub.2] is described by: [U.sub.2]/[U.sub.1] = (1 + [Gamma])p, (4) where [U.sub.j] [equivalent to] [Delta]U/[Delta][D.sub.j], j = 1, 2, denotes the marginal utility of good j, [Gamma] [equivalent to] ([[Phi].sub.2]  [[Phi].sub.1])/(1 + [[Phi].sub.1]), with [absolute value of [Gamma]] [less than] 1, and p is the domestic price of good 2 in terms of good 1. At the optimum, the marginal domestic rate of substitution (MDRS) between the two goods must be equal to the market tradeoff. Notice that [Gamma] gives the proportional increase or decrease in the market price, depending on whether [[Phi].sub.2] is greater or smaller than [[Phi].sub.1], due to the monetary distortion (the CIA constraint). If [[Phi].sub.1] = [[Phi].sub.2] = 0, as it is the case in any barter economy, then [Gamma] = 0, resulting in the familiar condition MDRS = p. The same result also holds in the more general case where [[Phi].sub.1] = [[Phi].sub.2] [greater than] 0.(5) For simplicity, we assume that there are no barriers to export while a quota (Q) is imposed on imports, i.e., Q [equivalent to] [D.sub.2](p, Y)  [X.sub.2](p) [greater than] 0, (5) where Y denotes the real national income of the economy. Let [p.sup.*] be the world relative price of good 2 in terms of good 1, taken as constant by this small open economy. Then the real quota revenue is given by (p  [p.sup.*])Q. Furthermore, in equilibrium, [Mathematical Expression Omitted] and so the private budget constraint, equation (2), becomes [D.sub.1] + p[D.sub.2] = [X.sub.1] + p[X.sub.2] + (p  [p.sup.*])Q. (2[prime]) To close the model, we next provide a brief description of the supply side of the economy. The two goods are produced with constantreturnstoscale technologies which use two factors of production, capital (K) and labor (L). Furthermore, both of these factors are assumed to be inelastically supplied and intersectorally mobile. Profit maximization then on behalf of the firms and competitive factor markets yield the standard condition for equilibrium in the production side of the economy; namely, that the marginal domestic rate of transformation (MDRT) equals the domesticprice ratio (p), that is, MDRT = d[X.sub.1]/d[X.sub.2] = p, (6) where [X.sub.1] and [X.sub.2] denote the production levels of the two goods. III. The Welfare Analysis In this section, we study the welfare implications of an import quota. This is accomplished in three steps. First, totally differentiating (1) and applying (4), we have dU/[U.sub.1] = d[D.sub.1] + (1+ [Gamma])pd[D.sub.2]. (7) Second, differentiating (2[prime]), in conjunction with (6), yields d[D.sub.1] = (p  [p.sup.*])dQ  pd[D.sub.2]. (8) Finally, substituting (8) into (7), we obtain (1/[U.sub.1])(dU/dQ) = (p  [p.sup.*]) + [Gamma]p(d[D.sub.2]/dQ). (9) According to (9), the welfare effect of an import quota has two components. The first term on the righthand side of (9) gives the standard direct welfare impact of a change in the quota level. The second term, on the other hand, represents the indirect effect of the quota on welfare and is due to the existence of a CIA constraint. In the special case of a barter economy, [[Phi].sub.1] = [[Phi].sub.2] = [Gamma] = 0 and this indirect effect vanishes; hence, a tightening of the import quota (dQ [less than] 0) always lowers social welfare [notice from (9) that if [Gamma] = 0 then dU/dQ = (p[p.sup.*])[U.sub.1] [greater than] 0, where p [greater than] [p.sup.*] since the quota generates a wedge between the domestic and worldprice ratio]. This is a wellknown result in the trade literature with barter exchange, which also holds when [[Phi].sub.1] = [[Phi].sub.2] [greater than] 0. Nevertheless, under a generalized CIA constraint this conclusion is in need of revision due to the presence of the indirect effect mentioned above. Notice that a tightening of the quota (a decrease in Q) reduces the consumption of the importables (i.e., d[D.sub.2]/dQ [greater than] 0; see the next section for further elaboration). According to (9), if [[Phi].sub.1] [less than] [[Phi].sub.2], ([Gamma] [element of] (0, 1]), then the two effects work in the same direction and hence the traditional negative effect of an import quota on welfare is strengthened. If, on the other hand, [[Phi].sub.1] [greater than] [[Phi].sub.2] and hence [Gamma] [element of] [ 1, 0), then the two effects mentioned above work in opposite directions. The economic intuition is as follows. In the case where [[Phi].sub.1] [less than] [[Phi].sub.2] (or [Gamma] [element of] (0, 1]), the MDRS = (1 + [Gamma])p is greater than the worldprice ratio [p.sup.*] (= the marginal foreign rate of transformation, MFRT). Thus, eliminating the import quota will bring MDRS as close to the worldprice ratio [p.sup.*] as possible, which is welfareenhancing. If, on the other hand, [[Phi].sub.1] [greater than] [[Phi].sub.2], and hence [Gamma] [element of] [1, 0), then a freetrade policy will result in MDRS = (1 + [Gamma])[p.sup.*] [greater than] [p.sup.*] = MFRT, which is a suboptimal situation. Since the MDRS is a decreasing function of [D.sub.2], tightening the quota level (decreasing Q) lowers the consumption of importables, raises the domestic price, and reduces the gap between the MDRS and [p.sup.*] (= MFRT).(6) This raises in turn the level of welfare, working thus against the adverse direct welfare effect of import quotas. IV. The Optimal Quota Level To determine the optimal level of the import quota we set dU = 0 in equation (9). Hence, we obtain [1 + [Gamma](d[D.sub.2]/dQ)][p.sup.Q] = [p.sup.*], (10) where [p.sup.Q] stands for the optimal domesticprice ratio. Next, notice that differentiation of [D.sub.2] = [D.sub.2](p, Y) implies pd[D.sub.2] = [Epsilon]Qdp + [Mu]d Y, (11) where [Epsilon] [equivalent to] (p/Q)(d[D.sub.2]/dp) [greater than] 0 denotes the demand elasticity of good 2 and measures the substitution in consumption in response to a change in p, given a utility level. [Mu] [equivalent to] p([Delta][D.sub.2]/[Delta]Y) [[Mu] [element of] (0, 1)], on the other hand, is the marginal propensity to consume good 2. Also, total differentiation of (5) yields dQ = d[D.sub.2]  [Sigma]Qdp/p, (12) where [Sigma] [equivalent to] (p/Q)(d[X.sub.2]/dp) [greater than] 0 denotes the output elasticity of good 2 and measures the substitution in production in response to a change in p. Substituting (11) into (12) yields pdQ = ([Epsilon] + [Sigma])Qdp + [Mu]dY. (13) Moreover, equation (9), in conjunction with (11), (13) and the definition dY [equivalent to] dU/[U.sub.1], yields the following expression for the effect of quotas on domesticprice ratio: dp/dQ = [Beta]/Q, (14) where [Beta] [equivalent to] {[1  [Mu](1 + [Gamma])]p+ [Mu][p.sup.*]}/([Epsilon]+[Sigma][Alpha]) and [Alpha] [equivalent to] 1  [Mu][Gamma] [greater than] 0. The stability of the equilibrium requires dp/dQ [less than] 0.(7) We, therefore, assume that [Beta] [greater than] 0 so that a tightening of import quotas (dQ [less than] 0) always raises the domesticprice ratio. Finally, combining (10), (12) and (14), we obtain the following expression for the optimal domesticprice ratio under an import quota: ([p.sup.Q]  [p.sup.*])/[p.sup.*] =  [Gamma][Epsilon][p.sup.*]/[(1 + [Gamma])[Epsilon] + [Sigma]]. (15) Notice that if [Gamma] = 0, which is the case if [[Phi].sub.1] = [[Phi].sub.2] [greater than or equal to] 0, then the standard result [p.sup.Q] = [p.sup.*] emerges; namely that free trade is the optimal policy.(8) If the degree of monetization in the exportable sector is lower than in the importable sector, i.e., [[Phi].sub.1] [less than] [[Phi].sub.2], then [Gamma] [equivalent to] ([[Phi].sub.2]  [[Phi].sub.1])/(1 + [[Phi].sub.1]) [element of] (0, 1] and [p.sup.Q] [less than] [p.sup.*]. This implies that if the initial situation is free trade, then a zero quota remains the optimal policy since lowering the quota level beyond the freetrade level cannot decrease p further. However, if an effective import quota already exists, then loosening the quota restriction (increasing Q) is desirable because it will result in a lower domesticprice ratio. This in turn reduces the wedge between the MDRS and the worldprice ratio, which is welfareimproving. If, on the other hand, [[Phi].sub.1] [greater than] [[Phi].sub.2], then we have [Gamma] [element of] [ 1, 0) and [p.sup.Q] [greater than] [p.sup.*]. Thus, an optimal (positive) quota level exists and is given by [Q.sup.*] ([p.sup.Q]) = [D.sub.2] ([p.sup.Q], Y([p.sup.Q]))[X.sub.2]([p.sup.Q]). As mentioned in the previous section, this occurs because raising the quota level increases the domesticprice ratio and hence the MDRS. This again narrows the gap between the MDRS and [p.sup.*], offsetting thus the direct adverse welfare effect at a positive level of the import quota ([Q.sup.*] [greater than] 0). V. Technical Progress and the Possibility of Immiserizing Growth To examine the possibility of immiserizing growth, we next extend our framework to allow for technical progress. Accordingly, the production process of good j is described by the following constantreturnstoscale production function: [X.sub.j] = [F.sub.j]([K.sub.j], [L.sub.j], [[Tau].sub.j]), j = 1,2, (16) where [[Tau].sub.j] denotes a Hicksneutral technological parameter of industry j. Totally differentiating (16), we have d[X.sub.j] = [F.sub.Kj]d[K.sub.j] + [F.sub.Lj]d[L.sub.j] + [F.sub.[Tau]j]d[[Tau].sub.j], j = 1, 2, (17) where [F.sub.ij], denotes the partial derivative of [F.sub.j] (marginal product) with respect to i, i = K, L and [Tau]. Under the assumption of competitive factor markets, each of the two factors is paid the value of its marginal product, i.e., w = [p.sub.j][F.sub.Lj] and r = [p.sub.j][F.sub.Kj], j = 1,2, (18) where w and r stand for the wage rate and the rental rate of capital, respectively. Moreover, full employment of factors of production implies [L.sub.1]+[L.sub.2] = L and [K.sub.1]+[K.sub.2] =K. (19) Without loss of generality, we assume that technical progress takes place in industry 2 only, so that d[[Tau].sub.1] = 0 [less than] d[[Tau].sub.2] [equivalent to] d[Tau]. Totally differentiating (19) and using (17) and (18), we derive the new condition for equilibrium in the production of the two goods: MDRT = d[X.sub.2]/d[X.sub.1] = p/(1 + g), (20) where g [equivalent to] [p.sub.2][F.sub.[Tau]2]d[Tau]/(rd[K.sub.2] + wd[L.sub.2]) [greater than] 0 denotes the shift factor due to technical progress. Given Q, total differentiation of (2[prime]) together with (20) yield d[D.sub.1] + pd[D.sub.2] = gd[X.sub.1]. (21) Substituting (21) into (7), we then have dU/[U.sub.1] = [Gamma]pd[D.sub.2]  gd[X.sub.1]. (22) Next, since [D.sub.2] = [D.sub.2] (p, Y) and [X.sub.2] = [X.sub.2] (p, [Tau]), totally differentiating (5), for a given level of import quota, implies [Mu]dY = ([Epsilon] + [Sigma])Qdp + ([Delta][X.sub.2]/[Delta][Tau])pd[Tau]. (23) Substituting (20) and dY = dU/[U.sub.1] into (23), we obtain [Mu]dU/[U.sub.1] = ([Epsilon] + [Sigma])Qdp  (1 + g)([Delta][X.sub.1]/[Delta][Tau])d[Tau]. (23[prime]) Also, (5) and (20) together imply pd[D.sub.2] = [Sigma]Qdp  (1 + g) ([Delta][X.sub.1]/[Delta][Tau])d[Tau]. Substituting this expression into (22) and noting that gd[X.sub.1] = g([Delta][X.sub.1]/[Delta][Tau])d[Tau], we obtain dU/[U.sub.1] = [Gamma][Sigma]Qdp  ([Delta][X.sub.1]/[Delta][Tau])[(1 + g)[Gamma] + g]d[Tau]. (22[prime]) Using (22[prime]) and (23[prime]), straightforward application of Cramer's rule yields the welfare effect of technical progress: dU/[U.sub.1] = [U.sub.1]([Delta][X.sub.1]/[Delta][Tau])[[Epsilon][Gamma](1 + g) + g([Epsilon] + [Sigma])]/([Epsilon] + [Sigma][Alpha]). (24) Recall next that technical progress takes place in the second industry and hence, given factor prices, it raises the production level of the second good at the expense of the first, i.e., [Delta][X.sub.1]/[Delta][Tau] [less than] 0.(9) Thus, from (24), we conclude that dU/d[Tau] [greater than] 0 if [[Phi].sub.2] [greater than or equal to] [[Phi].sub.1] and dU/d[Tau] [greater than or less than] 0 if [[Phi].sub.2] [less than] [[Phi].sub.1]. (25) The following proposition summarizes the main results of this section. PROPOSITION. For a small monetary economy with import quotas, growth induced by Hicksneutral technical progress is welfareenhancing if the degree of monetization in the growing sector is higher than the one in the static sector, i.e., if the consumption of the goods produced in the growing sector requires larger cash balances. If the static sector displays a higher degree of monetization, then growth can be immiserizing. Consider first the special case of a barter economy where [[Phi].sub.1] = [[Phi].sub.2] = 0, as in Alam [1]. Equation (24) then simplifies to dU/d[Tau] = g[U.sub.1]([Delta][X.sub.1]/[Delta][Tau]) [greater than] 0. This confirms Alam's finding; namely, in the presence of an import quota, growth is always welfareenhancing, which is an important exception to Bhagwati's [2] result on the possibility of immiserizing growth. In the case of a monetary economy, however, this exception is disputable and the possibility of immiserizing growth emerges once again. Specifically, as it can be seen from (24), if the growing sector is more monetized (i.e., more liquiditywise constrained) then [[Phi].sub.1] [less than] [[Phi].sub.2] and growth once again always improves social welfare. The economic explanation of this result is similar to the one given before; namely, if [[Phi].sub.1] [less than] [[Phi].sub.2], (4) implies that the MDRS is greater than the worldprice ratio [p.sup.*].(10) Since technical progress in industry 2 raises the production level of good 2 at the expense of good 1, the domesticprice ratio p falls, [D.sub.2] rises, and hence MDRS decreases. This then reduces the wedge between MDRS and MFRT, and hence it works together with the direct effect of growth in enhancing welfare. Nevertheless, if [[Phi].sub.1] [greater than] [[Phi].sub.2] so that the MDRS is initially below the MFRT, technical progress in industry 2 drives MDRS further away from MFRT. Thus, if this adverse monetary distortion effect dominates the direct welfareenhancing effect of technical progress, then growth will be immiserizing. VI. Concluding Remarks We have studied the effects of import quotas in a generalized cashinadvance economy and have shown that, depending on the degree of creditrationing in each sector, the standard conclusion that a tightening of an import quota reduces social welfare may not hold. In particular, if the exportable sector is more liquidity constrained, then an optimum import quota exists. If, on the other hand, the importable sector is more liquidity constrained, then an export quota is in order. Finally, in a small monetary economy with quota distortions, growth can be immiserizing, contrary to findings by Alam [1] in the context of a barter economy. Although our results indicate that quotas may be desirable to enhance social welfare, they are only secondbest policies. The firstbest policy in the presence of a liquidity (CIA) constraint is a consumption tax, which can restore the optimal situation where MDRS = MDRT = MFRT.(11) Intuitively, the cashinadvance constraint introduces a demandside distortion which makes the consumption tax unavoidable. A quota restriction, however, affects the consumption as well as the production side of the economy, creating thus an unnecessary divergence between the given worldprice ratio and the domestic marginal rate of transformation. We would like to thank an anonymous referee of this journal for helpful comments and suggestions. 1. In 1981 (1986) about 19.6 (23.1) per cent of all industrialcountry imports were subject to NTBs, with quantitative restrictions covering 12.2 (14.4) per cent. Also, in a study involving 50 developing countries, Erzan et al. [8] show that NTBs are sometimes responsible for at least half of the protection impact, with quantitative restrictions being the most frequently used nontariff measures. On average, 24 per cent of all tariff lines were affected by quantitative restrictions. 2. For instance, Drabicki and Takayama [7] show that the theory of comparative advantage breaks down in a monetary world under fixed exchange rates when the balance of payments is not in equilibrium. Similarly, in a real trade model with a transactionsbased demand for money, Stockman [18] shows that changes in inflation can cause changes in the pattern of trade even in the absence of real changes in comparative advantage. 3. This formulation of the CIA constraint is slightly more general than the one considered in Stockman [17], where [[Phi].sub.j] = 1, j = 1, 2, as well as the one adopted in Lucas and Stokey [12] where there are two types of goods, pure cash goods with [Phi] = 1 and pure credit goods with [Phi] = 0. 4. A similar argument can be made with regard to necessary and luxury goods. 5. It should be noted that in a dynamic model, [Gamma] will also depend on the nominal interest rate. This point is further developed in Palivos and Yip [16]. 6. Following the standard practice in the literature, we assume that both consumption goods are normal which implies that the MDRS is a decreasing function of [D.sub.2]. 7. To see this, consider the priceadjustment rule dp/dt = [Xi](p), where t denotes time, [Xi](Q(p)) is a smooth, signpreserving function of excess demand Q(p) [equivalent to] [D.sub.2](p, Y(p))  [X.sub.2](p), and [Xi][prime] [greater than] 0. The stability of the equilibrium requires that (dp/dt)/dp [less than] 0 or, equivalently, [Xi][prime]dQ/dp [less than] 0. 8. Recall that [[Phi].sub.1] = [[Phi].sub.2] = 0 represents the case of a barter economy. 9. This can readily be obtained from (20). 10. 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