world of economics

  • It was Paul Samuelson (1970 Nobel Prize in economics) who rigorously proved this factor–price equalization theorem. For this reason, it is sometimes referred to as the Heckscher–Ohlin–Samuelson theorem (H–O–S theorem).
  • The theorem says that when the prices of the output goods are equalized between countries as they move to free trade, then the prices of the factors (capital and labor) will also be equalized between countries. This implies that free trade will equalize the wages of workers and the rents earned on capital throughout the world.

The Factor–Price Equalization Theorem

  • Starting with the assumptions, we can state the factor–price equalization (H–O–S) theorem as follows: International trade will bring about equalization in the relative and absolute returns to homogeneous factors across nations.
  •  As such, international trade is a substitute for the international mobility of factors. What this means is that international trade will cause the wages of homogeneous labor (i.e., labor with the same level of training, skills, and productivity) to be the same in all trading nations. Similarly, international trade will cause the return to homogeneous capital (i.e., capital of the same productivity and risk) to be the same in all trading nations.
  • That is, international trade will make wage rate (w) the same in Nation 1 and Nation 2; similarly, it will cause interest rate (r) to be the same in both nations. Both relative and absolute factor prices will be equalized. We know that in the absence of trade the relative price of commodity X is lower in Nation 1 than in Nation 2 because the relative price of labor, or the wage rate, is lower in Nation 1. As Nation 1 specializes in the production of commodity X (the L-intensive commodity) and reduces its production of commodity Y (the K-intensive commodity), the relative demand for labor rises, causing wages (w) to rise, while the relative demand for capital falls, causing the interest rate (r) to fall. The exact opposite occurs in Nation 2.
  • That is, as Nation 2 specializes in the production of Y and reduces its production of X with trade, its demand for L falls, causing w to fall, while its demand for K rises, causing interest rate (r) to rise. To summarize, international trade causes w to rise in Nation 1 (the low-wage nation) and to fall in Nation 2 (the high-wage nation). Thus, international trade reduces the pre-trade difference in wage rate (w) between the two nations.
  • Similarly, international trade causes interest rate (r)to fall in Nation 1 (the K-expensive nation) and to rise in Nation 2 (the K-cheap nation), thus reducing the pre-trade difference in r between the two nations. This proves that international trade tends to reduce the pre-trade difference in wage rate (w) and interest rate (r) between the two nations.
  • We can go further and demonstrate that international trade not only tends to reduce the international difference in the returns to homogeneous factors, but would in fact bring about complete equalization in relative factor prices when all of the assumptions made hold.
  • This is so because as long as relative factor prices differ, relative commodity prices differ and trade continues to expand. But the expansion of trade reduces the difference in factor prices between nations. Thus, international trade keeps expanding until relative commodity prices are completely equalized, which means that relative factor prices have also become equal in the two nations.

Relative and Absolute Factor–Price Equalization

We can show graphically that relative factor prices are equalized by trade in the two nations. In Figure, the relative price of labor (w/r) is measured along the horizontal axis, and the relative price of commodity X (PX /PY) is measured along the vertical axis.

  • Since each nation operates under perfect competition and uses the same technology, there is a one-to-one relationship between w/r and PX /PY. That is, each w/r ratio is associated with a specific PX /PY ratio.
  • Before trade, Nation 1 is at point A, with w/r = (w/r)1 and PX /PY = PA, while Nation 2 is at point A’ with w/r = (w/r)2 and PX /PY = PA’. With w/r lower in Nation 1 than in Nation 2 in the absence of trade, PA is lower than PA’ so that Nation 1 has a comparative advantage in commodity X.
  • As Nation 1 (the relatively L-abundant nation) specializes in the production of commodity X (the L-intensive commodity) and reduces the production of commodity Y, the demand for labor increases relative to the demand for capital and w/r rises in Nation 1. This causes PX /PY to rise in Nation 1.
  • On the other hand, as Nation 2 (the K-abundant nation) specializes in the production of commodity Y (the K-intensive commodity), its relative demand for capital increases and r/w rises (i.e., w/r falls). This causes PY /PX to rise (i.e., PX /PY to fall) in Nation 2.
  • The process will continue until point B = B’ at which PB = PB’ and w/r = (w/r) in both nations .
  • Note that PB = PB’ only if w/r is identical in the two nations, since both nations operate under perfect competition and use the same technology (by assumption). Note also that PB = PB’ lies between PA and PA’, and (w/r) lies between (w/r)1 and (w/r)2.
  • To summarize, PX /PY will become equal as a result of trade, and this will occur only when w/r has also become equal in the two nations (as long as both nations continue to produce both commodities).

Equalization of Absolute Factor Prices

  • Equalization of absolute factor prices means that free international trade also equalizes the real wages for the same type of labor in the two nations and the real rate of interest for the same type of capital in the two nations. However, given that trade equalizes relative factor prices, that perfect competition exists in all commodity and factor markets, and that both nations use the same technology and face constant returns to scale in the production of both commodities, it follows that trade also equalizes the absolute returns to homogeneous factors.
  • Note that trade acts as a substitute for the international mobility of factors of production in its effect on factor prices. With perfect mobility (i.e., with complete information and no legal restrictions or transportation costs), labor would migrate from the low-wage nation to the high-wage nation until wages in the two nations became equal.
  • Similarly, capital would move from the low-interest to the high-interest nation until the rate of interest was equalized in the two nations. While trade operates on the demand for factors, factor mobility operates on the supply of factors. In either case, the result is complete equalization in the absolute returns of homogeneous factors. With some (rather than perfect) international mobility of factors, a smaller volume of trade would be required to bring about equality in factor returns between the two nations.


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