# Application of the Factor–Price equalization theorem (Samuelson) on trade?

I'm trying to understand the factor price equalization theorem by Samuelson. I came across this graph but I don't know how to interpret it. Could anyone give me a short resume on what the graph is saying?

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Are this and your other two recent questions from a take-home exam or homework? It is perfectly fine if they are, but we'll need to flag them as homework so that you get the appropriate answers. – Jason B Dec 13 '11 at 1:41
No, they aren't from a take-home exam or homework, but from old exams. I'm preparing for my finals. – chizwiz Dec 13 '11 at 2:19
OK, in that case, they do count as homework: please do use the [homework] tag for such questions – EnergyNumbers Dec 13 '11 at 6:04

Keep in mind three key facts about the Hescher-Ohlin model, each of which make sense intuitively:

1. The Hescher-Ohlin Theorem (simplified here): In a 2 good x 2 country x 2 factor world, countries tend to export the good that is relatively intensive in the factor with which they are relatively well-endowed.
2. The Stopler-Samuelson Theorem: If the relative price of a good increases, then the price (w or r) of the factor used intensively in the production of that good increases, while the price of the other factor decreases.
3. Countries export (import) goods when the world (in this case foreign) price is above (below) the autarky (pre-trade domestic) price.

In the image we see factor price ratios on the horizontal axis, and relative goods prices on the vertical for countries I and II. By (3), we know that Country I exports steel and that Country II exports cloth since $(\frac{P_C}{P_S})_I > (\frac{P_C}{P_S})_{int} > (\frac{P_C}{P_S})_{II}$. I assume it is clear to you why the goods prices converge (if not, think about the relative supply and demand curves in the individual goods markets).

We also see that trade induces changes in relative factor prices, namely: $(\frac{w}{r})_I\downarrow$ and $(\frac{w}{r})_{II}\uparrow$. By (1 and 2), we intuit that cloth must be the relatively labor-intensive good and therefore that steel is relatively capital intensive.

In introductory trade classes, it is usually sufficient to simply state the SS and HO theorems as a justification for factor price convergence. That is, convergence in goods prices will imply convergence in factor prices.

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