# Heckscher-Ohlin Theorem

 2. Assumptions Structure of the HO Model 1 - 8 same as those for FPE 9. Balance of Trade and No Leakages p*1z1 + p*2z2 = 0, (total value of imports must be equal to the total value of exports) zi + z*i = 0. (No leakages. Nothing is lost in transit) 10. Identical and homothetic preferences between countries. Homothetic preferences implies: As income increases consumption increases proportionately, i.e., the income elasticity of demand for each good = 1. Income consumption curve is a ray from the origin. Homothetic preferences

 3. The HO Theorem If assumptions (1) - (10) are satisfied, then each country exports the commodity which intensively uses its abundant factor. Implication: The price of the exportable is higher than that in autarky. (By SS Theorem, free trade raises the return to the abundant factor, which is intensively used in the export sector. In other words, free trade benefits the abundant factor and hurts the scarce factor. Example For example, if China is abundant in labor, it will export the labor-intensive product to the US. If the United States is capital abundant, it will export the capital-intensive product to China. Planning errors can cause exports of wrong commodities and starvation. In the Soviet famine of 1932-33, Stalin expected increases in output by collectivization and exported grains. As a result, 6-8 million people died of starvation. To prove the HO Theorem, we first need some definitions. Absolute (physical) Abundance Home Country is abundant in labor if L/K > L*/K* Figure 2. Abundance in labor. HC is abundant in capital if K/L > K*/L*. Proof of the HO Theorem Remark: (i) The relative supply curve, y1/y2(p1/p2) is positively sloped, because supply of y1 is positively related to p1/p2 whereas supply of y2 is negatively related to p1/p2. (ii) Similarly, the relative demand curve x1/x2(p1/p2) is negatively sloped as shown above because demand for x1 is negatively related to p1/p2 whereas demand for x2 is positively related to p1/p2. (iii) Since consumers in the two countries have identical preferences, relative demand are identical, i.e., x1/x2 = x*1/x*2 . However, while the relative supplies, y1/y2, is larger than y*1/y*2 because HC is labor-abundant. Relative demand and supply HO Theorem

 4. The Original version of the HO Theorem The original HO Theorem, however, was expressed in terms of relative abundance.  An economy's offer curve depends on both production and consumption conditions in that country. In the Ricardian trade model, it is easy to derive offer curves because each country specializes in the production of one commodity. This means that as the price of good changes production remains unchanged.           In the HO model, a change in the terms of trade, p* = p*1/p*2, necessarily results in a change in production mix. (Input allocations change, which alters output). Thus, it is a little tricky to derive an offer curve. First, note that an increase in the price of the capital intensive good reduces the wage-rent ratio, and decreases the capital intensities of both goods. This in turn causes a change in output mix. A trade indifference curve can be obtained from PPF and a community indifference curve. This can be shown in two steps, using a technique developed by James Meade, who received a Nobel prize in economics in 1977. Trade Indifference curve Definition: Trade Indifference curve is the locus of export-import combinations that yield the same level of utility. U(z1,z2) = U(x1 - y1,x2 - y2), where zi > 0 (import) (negative = export). Thus, to obtain a TI, we must subtract production from the indifference curve defined on consumption. Figure 5. Trade Indifference Curve The HO Theorem (Original) If assumptions (1) - (9) hold, and if the HC is relatively abundant in labor, i.e., (w/r)A < (w*/r*)A then HC exports the labor-intensive commodity. Assume that k2 > k1. By the Stolper-Samuelson Theorem, p1 and w are positively related, i.e., at the origin p1/p2 < p*1/p*2 in autarky iff w/r < w*/r*. ⇒ HC exports good 1. (2 offer curves): HC, abundant in labor (w/r < w*/r*), exports good 1, which uses its cheap factor (labor) intensively (and imports 2). Figure 6. An Alternative Proof of HO Theorem. Remarks No need for the assumption of identical and homothetic preferences. Absolute or physical abundance is empirically observable. One needs to gather data on factor supplies. However, relative abundance is difficult to observe. Trade data only reveals observed prices, not the hypothetical output or input prices that would be observed under the autarky scenario. This is a weakness. For this reason, empirical tests are all based on physical abundance.