Relationship between trade and factor mobility

relationship between trade and factor mobility

This paper addresses the relation between goods trade and international factor mobility in general terms. The basic theorems of international trade, suitably. ditions in the real world: there may be perfect factor mobility but no trade, or world and that country A is so small in relation to B that its production conditions and Let us begin with a situation where factors are immobile between A and B but. This paper develops a two-country model of trade and factor mobility, in whi on the relationship between goods and factor trade, reconciling the conflicting.

Mobility may involve the movement of factors across industries within a country, as when a worker leaves employment at a textile firm and begins work at a automobile factory. Finally mobility may involve the movement of factors between countries either within industries or across industries, as when a farm worker migrates to another country or when a factory is moved abroad.

Trade: Chapter Factor Mobility and Trade - Overview

The standard assumptions in the literature are that factors of production are freely i. The rationale for the first assumption, that factors are freely mobile within an industry, is perhaps closest to reality. The skills acquired by workers and the productivity of capital are likely to be very similar across firms producing identical or closely substitutable products. Although there would likely be some transition costs incurred, such as search, transportation and transaction costs, it remains reasonable to assume for simplicity that the transfer is costless.

As a result this assumption is rarely relaxed.

Factor Mobility and Trade - Overview

The assumption that factors are easily movable across industries within a country is probably unrealistic, especially in the short-run. Indeed this assumption has been a standard source of criticism for traditional trade models.

In the Ricardian and Heckscher-Ohlin models, factors are assumed to be homogeneous and freely and costlessly mobile between industries.

When changes occur in the economy requiring the expansion of one industry and a contraction of another, it just happens. There are no search, transportation or transaction costs. There is no unemployment of resources. Also, since the factors are assumed to be homogeneous, once transferred to a completely different industry, they immediately become just as productive as the factors that had originally been employed in that industry.

Clearly, these conditions cannot be expected to hold in very many realistic situations. Such a line, which I shall call the R line, is drawn in Figure Capital will flow in until its marginal product is equalized in A and B, which will be at the point where A can produce enough steel and cotton for consumption equilibrium at S without trade, and at the same time make the required interest payment abroad.

This point is clearly reached at P' directly above S. At any point along the R line to the northwest of P', country A would have to import steel in order to consume at S that is, demand conditions in A cannot be satisfied to the northwest of P'. At P' demand conditions in A are satisfied and the interest payment can be made abroad at the same price ratio as before the tariff was levied.

Thus the capital movement need not continue past this point, although any point to the southeast of P' would be consistent with equilibrium. Production takes place in A and P', consumption is at S, and the transfer of interest payments is the excess of production over consumption in A, SP' of cotton.

We initially assumed a prohibitive tariff; in fact, even the smallest tariff is prohibitive in this model! A small tariff would not prohibit trade immediately: Because of the price change some capital would move in and some trade would take place. But as long as trade continues, there must be a difference in prices in A and B equal to the ad valorem rate of tariff -- hence a difference in marginal products -- so capital imports must continue.

International Factor Mobility - 1

Marginal products and prices can only be equalized in A and B when A's imports cease. The tariff is now no longer necessary! Because marginal products and prices are again equalized, the tariff can be removed without reversing the capital movement. The tariff has eliminated trade, but after the capital movement there is no longer any need for trade. This is not really such a surprising result when we refer back to the assumptions. Before the tariff was imposed we assumed both unimpeded trade and perfect capital mobility.

We have then two assumptions each of which is sufficient for the equalization of commodity and factor prices. The effect of the tariff is simply to eliminate one of these assumptions -- unimpeded trade; the other is still operative. However, one qualification must be made. If impediments to trade exist in both countries tariffs in both countries or transport costs on both goods and it is assumed that capital owners do not move with their capital, the interest payments on foreign-owned capital will be subject to these impediments; this will prevent complete equalization of factor and commodity prices.

This question could have been avoided had we allowed the capitalist to consume his returns in the country where his capital was invested.

relationship between trade and factor mobility

The proposition that capital mobility is a perfect substitute for trade still stands however, if one is willing to accept the qualification as an imperfection to capital mobility. Effect of Relative Size The previous section assumed that country A was very small in relation to country B. It turns out, however, that the relative sizes of the two countries make no difference in the model provided complete specialization does not result.

Suppose as before that country A is exporting cotton in exchange for steel. There are no impediments to trade and capital is mobile. But we no longer assume that A is small relative to B. Now A imposes a tariff on steel raising the internal price of steel in relation to cotton, shifting resources out of cotton into steel, raising the marginal product of capital, and lowering the marginal product of labor.

A's demand for imports and her supply of exports fall. This decline in demand for B's steel exports and supply of B's cotton imports raises the price of cotton relative to steel in B; labor and capital in B shift out of steel into cotton raising the marginal product of labor and lowering the marginal product of capital in B. Relative factor returns in A and B move in opposite directions, so the price changes in A which stimulate a capital movement are reinforced by the price changes in B.

The marginal product of capital rises in A falls in B; capital moves from B to A, contracting B's and expanding A's production block.

relationship between trade and factor mobility

The assumption that capital is perfectly mobile means that factor and commodity prices must be equalized after the tariff. It is necessary now to show that they also will be unchanged. The price of cotton relative to steel is determined by world demand and supply curves. To prove that prices remain unchanged it is sufficient to show that these demand and supply curves are unchanged -- or that at the pretariff price ratio demand equals supply after the capital movement has taken place.

But we know that at the old price ratio marginal products, hence incomes, are unchanged -- thus demand is un changed. All that remains then is to show that at constant prices production changes in one country cancel out production changes in the other country. This proposition can be proved in the following way: If commodity and factor prices are to be unchanged after the capital movement has taken place, then factor proportions in each industry must be the same as before; then the increment to the capital stock used in A will, at constant prices, increase the output of steel and decrease the output of cotton in A, and the decrement to the capital stock in B will decrease the output of steel and increase the output of cotton in B.

But the increase in A's capital is equal to the decrease in B's capital, and since production expands at constant prices and with the same factor proportions in each country, the increase in resources used in producing steel in A must be exactly equal to the decrease in resources devoted to the production of steel in B. Similarly, the decrease in resources used in producing cotton in A is the same as the increase in resources devoted to cotton production in B.

Then, since production functions are linear and homogeneous, the equal changes in resources applied to each industry in opposite directions imply equal changes in output. Therefore, the increase in steel output in A is equal to the decrease in steel output in B, and the decrease in cotton output in A is equal to the increase in cotton output in B that is, world production is not changed, at constant prices, by a movement of capital from one country to another.

International Trade and Factor Mobility

In the world we are considering it makes no difference in which country a commodity is produced if commodity prices are equalized. This proposition can perhaps be made clearer by a geometric proof. In Figure a, TaTa is A's transformation curve before the tariff, and T'aT'a is the transformation curve after the tariff has been imposed and the capital movement has taken place.

At constant prices equilibrium moves along A's R line from Pa to P'a, increasing the output of steel by RP'a and decreasing the output of cotton by RPa. Similarly, in Figure b, TbTb is country B's transformation curve before the capital movement and T'bT'b is the transformation curve after capital has left B. The proof is given in Figure OOa and OOb are the efficiency loci of A and B with production taking place along these loci at Pa and Pb, corresponding to the same letters in Figures a and b.

At constant prices labor-capital ratios in each industry must be the same as before, so equilibrium must move to P'b, corresponding to P'b in Figure b[probably b]. Because the capital outflow from B must equal the capital inflow to A, A's cotton origin must move to the right by just the same amount as B's cotton origin moves to the left that is, from Oa to O'a; and A's production equilibrium at constant prices must move from Pa to P'a The proof that world supply is unchanged at constant prices is now obvious, since JPaP'a and KPbP'b are identical triangles.

It means that world supply functions are independent of the distribution of factor endowments. More simply it means that it makes no difference to world supply where goods are produced if commodity and factor prices are equalized.

Because world supply and demand functions are not changed by the capital movements, so that the new equilibrium must be established at the same prices as before, our earlier assumption that A is very small in relation to B is an unnecessary one. Which factor moves depends, of course, on which factor is more mobile. The assumption used here, that capital is perfectly mobile and that labor is completely immobile, is an extreme one which would have to be relaxed before the argument could be made useful.

But a great deal can be learned qualitatively from extreme cases and the rest of the paper will retain this assumption. When only capital is mobile, a labor-abundant country can attract capital by tariffs and a capital-abundant country can encourage foreign investment by tariffs.

The same is true for an export tax, because in this model the effect of an export tax is the same as that of a tariff.

relationship between trade and factor mobility

The analysis is not restricted to tariffs; it applies as well to changes in transport costs. An increase of transport costs of commodities will raise the real return of and thus attract the scarce factor, and lower the real return and thus encourage the export of the abundant factor.

The effect of any trade impediment is to increase the scarcity of the scarce factor and hence make more profitable an international redistribution of factors. Later we shall consider, under somewhat more realistic assumptions than those used above, the applicability of this proposition as an argument for protection.

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Factor Mobility Impediments and Trade To show that an increase in impediments to factor movements stimulates trade, we shall assume that some capital is foreign-owned and illustrate the effects on trade of taxing this capital.

Strictly speaking, this is not an impediment to a capital movement; but if it were assumed that a steady capital flow was taking place, the tax on foreign-owned capital would operate as an impediment.

relationship between trade and factor mobility

We shall use Figures and Begin with equilibrium initially at P' in Figure No impediments to trade exist, but because factor and commodity prices are already equalized no trade takes place. We assume that O'O" of capital in Figure is foreign-owned, so a transfer equal in value to YY' in Figure is made.

Consumption equilibrium in A is at S. If a tax is now levied on all foreign capital its net return will be decreased, and since factor prices must be equalized in A and B, all of it O'O" must leave A.

As capital leaves A, her production block contracts. At constant prices more cotton and less steel are produced. The price of steel relative to cotton tends to rise but, because there are no impediments to trade, it is prevented from doing so by steel imports and cotton exports.

As all foreign capital leaves A, the final size of A's transformation function is TT, that consistent with domestically owned capital. Production equilibrium moves from P' to P, but consumption equilibrium remains at S because interest payments are no longer made abroad. PR is now exported in exchange for steel imports of RS. The effect of the tax has been to repatriate foreign capital and increase trade.

By similar reasoning it could be shown that a subsidy will attract capital and decrease trade, although in the latter case the capital movement will only stop when factor prices change that is, specialization takes place.

To achieve efficiency in world production it is unnecessary that both commodities and factors move freely. As long as the production conditions are satisfied, it is sufficient that either commodities or factors move freely.

But if some restrictions, however small, exist to both commodity and factor movements, factor- and commodity-price equalization cannot take place except in the trivial case where trade is unnecessary because prices are already equal. This principle applies only to those restrictions that are operative -- obviously it does not apply to import tariffs on goods which are exported, transport costs for factors that are immobile anyway, or quotas larger than those required for equalization to take place.

If it were not for the problem of transporting interest payments, referred to earlier, one mobile factor would be sufficient to ensure price equalization. When the labor-abundant country imposes the tariff, equalization will take place as long as the other country continues a free-trade policy and there are no transport costs involved.

But if the capital-abundant country imposes a tariff, inducing the export of capital, prices cannot be equalized even if the labor-abundant country maintains free trade unless the transfer of goods constituting interest payments is also tariff-free. The proposition that an increase in trade impediments stimulates factor movements and an increase in impediments to factor movements stimulates trade has implications as an argument for protection.

To examine these implications we shall relax some of the assumptions previously made -- first, by introducing trade impediments, then by decreasing the degree of factor mobility, and finally by relaxing the assumption that constant returns to scale apply by taking account of external economies.

We shall begin with a model similar to that used earlier except that we shall assume country A to be considerably smaller than country B. Suppose that, overnight, transport costs come into existence; this raises the price of importables relative to exportables, shifts resources into importables, raises the marginal product of the scarce factor, and lowers that of the abundant factor in each country. Incomes of A-capitalists and B-workers increase while incomes of A-workers and B-capitalists decrease.

These changes in factor returns create the incentive for a capital movement from B to A, a labor movement from A to B, or a combination of both movements. Where the final equilibrium will be depends on the degree of factor mobility. I shall assume that labor is immobile between countries but that capital is at least partially mobile. If we assume that capital is perfectly mobile, but that capitalists do not move with their capital, the latter will move from B to A until the return from capital invested in A is the same as from that invested in B; but this implies that marginal physical products cannot be equalized, since transport costs must be paid on the goods constituting interest payments.

But we shall not assume that capital is perfectly mobile. Instead suppose that B-capitalists insist on receiving a higher return on any capital they invest in A than on that which they invest in B, perhaps because of political instability, patriotism, risk, or economic uncertainty.

relationship between trade and factor mobility

Let us assume that B-capitalists require a 10 per cent higher return on capital invested in A than on that invested in B, but that if this interest differential rises above 10 per cent, capital is perfectly mobile.

Suppose further that the return to capital in both countries before introducing transport costs was 12 per cent, and that the effect of introducing transport costs is to lower the marginal product of capital in B to 11 per cent and to raise it in A to 17 per cent.

Since the interest differential is less than 10 per cent, no capital movement will take place. It is at this point that we shall consider the argument for a tariff in A.