Question

Give four reasons why the factor prices may not be equalized across countries. For each one, give a brief explanation and/or illustration of why it may prevent the Factor Price Equalization Theorem from holding. Note that these reasons should be within the context and the bounds of the model that we have studied, in terms its assumptions and implications, for example.

Answer 1

Commodity movements and factor movements are substitutes. The absence of trade impediments implies commodity-priceequalization and, even when factors are Immobile, a tendency toward factor-price equalization. It is equally true that perfect factor mobility results in factor-price equalization and, even when commodity movements cannot take place, in commodity-price equalization.

There are two extreme cases between which are to be found the conditions in the real world: There may be perfect factor mobility but no trade, or factor immobility with unrestricted trade. The classical economists generally chose the special case where factors of production were internationally immobile.

This paper will describe some of the effects of relaxing the latter assumption, allowing not only commodity movements but also some degree of factor mobility. Specifically it will show that an increase in trade impediments stimulates factor movements and that an increase in restrictions to factor movements stimulates trade.³ It will also make more specific an old argument for protection.

Trade Impediments and Factor Movements

Under certain rigorous assumptions the substitution of commodity for factor movements will be complete. In a two-country two-commodity two-factor model, commodity-price equalization is sufficient to ensure factor-price equalization and factor-price equalization is sufficient to ensure commodity-price equalization if (1) production functions are homogeneous of the first degree (that is, if marginal productivities, relatively and absolutely, depend only on the proportions in which factors are combined) and are identical in both countries; (2) one commodity requires a greater proportion of one factor than the other commodity at any factor prices at all points on any production function; and (3) factor endowments are such as to exclude specialization.⁴

These assumptions permit us to isolate some important influences deter mining the pattern of international trade and factor flows and for present purposes will be adhered to. Our first task is to show that an increase in trade impediments encourages factor movements.

Assume two countries, A and B, producing two final commodities, cotton and steel, by means of two factors, labor and capital.⁵ Country A is well endowed with labor but poorly endowed with capital relative to country B; cotton is labor-intensive relative to steel. For expositional convenience we shall use community indifference curves.

For the moment we shall assume that country B represents the "rest of the world " and that country A is so small in relation to B that its production conditions and factor endowments can have no effect on prices in B.⁶

Let us begin with a situation where factors are immobile between A and B but where impediments to trade are absent. This results in commodity- and factor-price equalization. Country A exports its labor-intensive product, cotton, in exchange for steel. Equilibrium is represented in Figure 6-1: TT is A's transformation function (production-possibility curve), production is at P, and consumption is at S. Country A is exporting PR of cotton and importing RS of steel. Her income in terms of steel or cotton is O Y.

Figure 6-1.

Suppose now that some exogenous factor removes all impediments to the movement of capital. Clearly, since the marginal product of capital is the same in both A and B, no capital movement will take place and equilibrium will remain where it is. But now assume that Aimposes a tariff on steel and for simplicity make it prohibitive.⁷ Initially the price of steel will rise relative to the price of cotton in A and both production and consumption will move to Q, the autarky (economic self-sufficiency) point. Factors will move out of the cotton into the steel industry, but since cotton is labor-intensive and steel is capital-intensive, at constant factor prices the production shift creates an excess supply of labor and an excess demand for capital. Consequently the marginal product of labor must fall and the marginal product of capital must rise. This is the familiar Stolper-Samuelson tariff argument.⁸

But since capital is mobile, its higher marginal product in A induces a capital movement into Afrom B, changing factor endowments so as to make A more capital-abundant. With more capital, A's transformation curve expands until a new equilibrium is reached.

Some help in determining where this new equilibrium will be is provided by Figure 6-2. Country A initially has OC of capital and OL of labor; OO' is the efficiency locus along which marginal products of labor and capital are equalized in steel and cotton. Equilibrium is initially at P, which corresponds to P on the production block in Figure 6-1. Factor proportions in steel and cotton are given by the slopes of OP and O'P, respectively.

Figure 6-2.

After the tariff is imposed, production moves along the efficiency locus to Q, corresponding to the autarky point Q in Figure 6-1. The slopes of OQ and O'Q indicate that the ratios of labor to capital in both cotton and steel have risen (that is, the marginal product of capital has risen and the marginal product of labor has fallen). Capital flows in and the cotton origin O' shifts to the right.

With perfect mobility of capital the marginal products of both labor and capital must be equalized in A and B. This follows from the assumption that the production functions are linear, homogeneous, and identical in both countries. Because marginal products in the rest of the world are assumed to be constant, the returns to factors in A will not change. Factor proportions in both steel and cotton in A then must be the same as before the tariff was imposed -- so equilibrium must lie along OP-extended at the point where it is cut by a line O"P'parallel to O'P, where O" is the new cotton origin. But this is not yet sufficient to tell us exactly where along OP-extended the point P' will be.

Because marginal products in the new equilibrium are the same as before the tariff, commodity prices in A will not have changed; but if both incomes earned by domestic factors and commodity prices are unchanged, consumption will remain at S (in Figure 6-1). Production, however, must be greater than S, because interest payments must be made to country B equal in value to the marginal product of the capital inflow. In Figure 6-1, then, production equilibrium must be at some point above or to the northeast of S.

To find the exact point we must show the effects of a change in capital endowments on production block. Because steel is capital-intensive we should expect the production block after the capital movement has taken place to be biased in favor of steel at any given price ratio; that this is so has been recently proved by Rybczynski [87].⁹

Because the same price ratio as at P will prevail, the locus of all tangents to larger and larger production blocks based on larger and larger endowments of capital must have a negative slope. Such a line, which I shall call the R line, is drawn in Figure 6-1.

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.¹⁰ The value of A's production has increased from O Y to O Y' in terms of steel, butYY' (which equals in value SP' of cotton) must be transferred abroad, so income is unchanged.

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. 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.) 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 Awhich 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.

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). 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 6-3a, T_aT_a is A's transformation curve before the tariff, and T'_aT'_ais 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 P_a to P'_a, increasing the output of steel by RP'_a and decreasing the output of cotton by RP_a. Similarly, in Figure 6-3b, T_bT_b is country B's transformation curve before the capital movement and T'_bT'_b is the transformation curve after capital has left B. At constant prices production in B moves along B's R line to P'_b, steel production decreasing by SP_b and cotton production increasing by SP'_b.

To demonstrate the proposition that world supply curves are unchanged, it is necessary to prove that RP'_a equals SP_b and that RP_a equals SP'_b. The proof is given in Figure 6-4. OL_a and OC_a are, respectively, A's initial endowments of labor and capital; OL_b and OC_b are the endowments of B.OO_a and OO_b are the efficiency loci of A and Bwith production taking place along these loci atP_a and P_b, corresponding to the same letters in Figures 6-3a and 6-3b.

Figure 6-4.

Now when A imposes a tariff on steel, suppose that C_bC'_bof capital leaves B, shifting B's cotton origin from O_b to O'_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 3-3b[probably 6-3b]. 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 O_a to O'_a; and A's production equilibrium at constant prices must move from P_a to P'_a) The proof that world supply is unchanged at constant prices is now obvious, since JP_aP'_a and KP_bP'_b are identical triangles. P_aP'_a, representing the increase in steel output in A, equals P_bP'_b, the decrease in steel output in B, and the decrease in cotton output in A, JP_a, equals the increase in cotton output in B, KP'_b.¹¹

This relationship holds at all combinations of commodity and factor prices provided some of each good is produced in both countries. 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.¹²

The general conclusion of this and the preceding is that tariffs will stimulate factor movements. 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.

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