Import quotas, foreign capital and income distribution: a comment.

Gilbert, John ; Tower, Edward

I. Introduction

In a recent paper in this journal, Yeh (1998) provides an analysis which appears to add new intellectual rigor to what is a now a very old argument for protection. The notion that import restrictions are desirable because they may encourage foreign direct investment, which attempts to 'jump' the barriers imposed, has long been a popular argument for protectionism. The fallacy of the argument in the case of import tariffs was dealt with over twenty years ago by Brecher and Diaz-Alejandro (1977), henceforth BD, who showed that tariff jumping foreign investment was immiserizing. Yeh presents an interesting extension where an import quota is used rather than a tariff. His analysis shows that capital inflow in response to an import quota will raise social welfare. He further asserts that the post capital inflow level of welfare may in fact be higher than the free trade welfare level while the quota remains binding, thus ostensibly providing a new justification for import restrictions for the small economy. The purpose of this comment is to show that this conclusion is incorrect: the Yeh analysis provides no justification for intervention. We also modify and supplement the geometric approach of BD to present an integrated algebraic and geometric derivation of the results, to provide a more compact, and intuitively compelling description of the arguments in both BD and Yeh than was available previously. In the process we also correct a minor mistake in the geometry BD use to clarify their logic.

II. Framework

The budget constraint of a small open economy producing two final goods (1 and 2) with two factors of production (K and L) using constant returns to scale technology. and facing home prices [p.sub.i] can be expressed using the GNP(1) and expenditure(2) functions as:

G([p.sub.1], [p.sub.2], K, L) = E([p.sub.1], [p.sub.2], u) (1)

This equation merely states that the total value of production must be equal to the total value of expenditure Let good 1 be the (capital intensive) importable. Suppose this economy imposes a tariff or a quota which causes the home import price to lie above the world price of the import by t. The constraint becomes:

G([p.sub.1], [p.sub.2], K, L) + t[M.sub.1] = E([p.sub.1], [p.sub.2], u) (2)

where

t = [p.sub.1] - [[p.sub.1].sup.*] (3)

[M.sub.1] being the volume of imports and [[p.sub.1].sup.*] being the world price of good 1. Both world prices are fixed. By Hotelling's Lemma the derivatives of the GNP function with respect to prices yield the profit maximizing levels of output, and with respect to factors yield factor prices in a competitive equilibrium. Similarly, the derivatives of the expenditure function with respect to prices are Hicksian demands. By totally differentiating expression (2) holding the world price of both tradeables and factor endowments constant we thus obtain:

dW = td[M.sub.1] (4)

where we have simplified by making use of the definition of imports and the fact that by (3) [dp.sub.1] = [[dp.sub.1].sup.*]. The change in welfare is defined as dW ?? [E.sub.u]du. This expression is the familiar deadweight loss of the tariff. With a subsequent inflow of foreign capital, assuming that the owners of the foreign capital repatriate all of their earnings, the budget constraint becomes:

G([p.sub.1], [p.sub.2], K + K[prime],L) + t[M.sub.1] - rK[prime] = E([p.sub.1], [p.sub.2], u) (5)

where K[prime] is FDI. Totally differentiating (5) holding the price of the exportable and the recipient country factor endowments constant yields:

dW = rdK[prime] + td[M.sub.1] - [rdK[prime] + K[prime]dr]. (6)

How can we interpret expression (6)? The first term is the expansion of output as a result of augmenting the capital stock (the value of the marginal product of capital multiplied by the incremental change in the foreign capital stock). The second term is the cost of the trade distortion. It is the value of a unit of the importable to the home economy ([p.sub.1]) minus the foreign exchange cost of acquiring it ([[p.sub.1].sup.*]) multiplied by incremental imports. The term in brackets is the change in payments to foreign owned capital, consisting of the earnings of newly placed foreign capital plus the change in earnings of the initial stock of foreign capital. We rewrite (6) to yield:

dW = td[M.sub.1] - K[prime]dr (7)

so the incremental change in welfare is the movement of imports across the trade distortion minus the reduction in payments to the initial stock of foreign capital. Let us call the first term the Harberger (1971) effect, after Harberger's insight that the change in economic welfare is the movement of a good across a distortion, multiplied by the size of the distortion. Let us call the second term the investment terms-of-trade effect.

III. The Tariff

Figure 1 uses the logic of equation (7) to show the effects of tariffs and quotas with capital inflows. Figure 1a replicates with modification the corresponding figure of BD. Figures 1b and 1c we add for clarity. First we analyze the imposition of a tariff. For the time being ignore the dotted lines. Imposing an import tariff with no capital inflow moves the economy from F to T, shrinking home utility, u, and raising both r and [p.sub.1]. The economy continues to be non-specialized and the tariff is binding.

As capital flows in, the Rybczynski Theorem tells more of good 1 will be produced, shrinking imports. Since the tariff is still binding, [P.sub.1] is fixed. and this fixes r. Thus according to (7) utility steadily declines.(3) The range TA in Figure 1 a could be called the Brecher-Diaz-Alejandro slide, for this is the focus of their discussion. Point A is the point at which the excess demand for good 1 at the tariff distorted price falls to zero.

Further capital inflows shrink the excess demand still further. At point A the tariff becomes non-binding (there is water in the tariff) and [p.sub.1] falls towards [[p.sub.1].sup.*], reaching it at point M. Stolper-Samuelson implies a monotonic fall in r. In this range [M.sub.1] ?? 0. Thus the analysis is just as it would be for a zero import quota. Consequently from (7) utility rises monotonically.(4) AM could be called the Yeh ascent since it is the range emphasized in Yeh (1998).

Further capital inflows in the range from M to M[prime] cause the excess demand for good 1 to become increasingly negative at free trade prices, so our economy exports increasing quantities of good 1. [p.sub.1] is constant in this range and so is r. Since the implicit tariff in this range is zero, utility is constant. MM[prime] is the Mundell plateau after Mundell (1957).

At M[prime] the economy specializes in good 1. Further inflows of capital shrink r and raise wages, leaving [p.sub.1] unchanged. Equation (7)'s investment terms-of-trade effect monotonically raises utility. We refer to the range M[prime]D as the MacDougall (1960), Berry-Soligo (1969) ascent. as it follows from the logic in their pieces.

IV. The Quota

Now let us analyze Yeh's quota. Suppose an import quota on 1 is levied, which in the absence of foreign investment creates a price wedge that is equivalent to the tariff already analyzed. We go from F to T in all three parts of Figure 1.

Foreign investment reduces the excess demand for good 1 pushing [p.sub.1] down and r along with it. dM = 0, so from the investment terms-of-trade effect in (7) this cheapening of the foreign capital already in the country raises utility. Thus we move along the dotted lines in Figure 1. At E the quota becomes non-binding. Further capital inflows move us along EM and then onto the common tariff quota path MM[prime]D.

V. Conclusion

If the capital inflow is high enough (in the range M[prime]D) home utility rises above the free trade level under both a tariff and a quota. Is this an argument for an import tariff or a quota? No, because in that range r lies below the free trade level, so the distortion has created no incentive for foreign investors to shower the home economy with additional capital (a point BD make for tariffs). Bhagwati (1971, proposition 5) says it best: 'Reductions in the "degree" of an only distortion are successively welfare increasing until the distortion is fully eliminated.'

Notes

1. See Dixit and Norman (1980) for details on the dual approach to trade theory. The GNP function is defined as: G([p.sub.1],[p.sub.2],K,L) ?? max{[p.sub.1][q.sub.1] + [p.sub.2][q.sub.2]: ([q.sub.1],[q.sub.2]) [element of] Y}, where: Y = {([q.sub.1],[q.sub.2]) : [q.sub.1] = [f.sup.1] ([K.sub.1],[L.sub.1]), [q.sub.2] = [f.sup.2]([K.sub.2] [L.sub.2]), [K.sub.1] + [K.sub.2] = K, [L.sub.1] + [L.sub.2] = L} is the set of outputs which can be produced given the endowment vector (i.e., the production possibilities set). The GNP function can be shown to be positive for all positive prices and factor endowments, continuous, linearly homogeneous and convex in prices for all factor endowments, and non-decreasing and concave in factor endowments for all prices.

2. Minimizing the expenditure necessary to attain a target level of utility (u) at given prices allows us to define the aggregate expenditure function: E([p.sub.1][p.sub.2], u) [equivalent to] min {[p.sub.1][z.sub.1] + [p.sub.2][z.sub.2], : [Mu] ([z.sub.0], [z.sub.2]) [greater than or equal to] u}. We assume that the underlying direct social utility function, [Mu], is non-negative, continuous, quasi-concave, and increasing in consumption of all goods, The expenditure function is non-decreasing, homogeneous of degree one, and concave in prices.

3. If utility is homogeneous of degree one in consumption of the two goods, both [M.sub.1] and u decline at a constant rate as shown until point A is reached.

4. Note that utility is kinked at A, whereas BD draw it as a smooth curve.

References

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Bhagwati, J. N. (1971). The Generalized Theory of Distortions and Welfare, Ch. 12 of Jagdish N. Bhagwati, Ronald W. Jones, Robert A. Mundell, and Jaroslav Vanek, (eds.), Trade, Balance of Payments, and Growth: Papers in International Economics in Honor of Charles P. Kindleberger, North Holland Publishing Company, 1971.

Brecher, R. A. and Diaz-Alejandro, C. F. (1977). "Tariffs, Foreign Capital and Immiserizing Growth," Journal of International Economics, 7(4):317-322.

Dixit, A. and Norman, V. (1980). Theory of International Trade: A Dual General Equilibrium Approach Cambridge University Press, London.

Harberger. A. C. (1971). "Three Basic Postulates for Applied Welfare Economics: An Interpretive Essay" Journal of Economic Literature, 9(3):785-97.

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Rybczynski, T. M. (1955) "Factor Endowments and Relative Commodity Prices" Economica, 336-41.

Stolper, W. F. and Samuelson, P. A. (1941) "Protection and Real Wages" Review of Economic Studies, 9:58-73.

Yeh, Y-H. (1998) "Import Quotas, Foreign Capital, and Income Distribution" The American Economist, 42(1):95-100.