THE STOLPER-SAMUELSON THEOREM
topic 4.4
The factor that is used intensively in the product whose price has risen gains from this price rise, while the other factor loses.
Consider figure 4.4.
There are two isoquants that overlap when the level of output is set the same for both goods, at $1 for T and $1 for S.
We are looking at country B here, the country which is abundant in labor. We know that B exports,T, and so when trade is opened it must be the price of T that increases.
If the value of Pt should increase while we keep Ps the same, the new isoquant for T is closer to the axis since it requires a lower quantity of T to constitute $1 of value.
So the new isocost line is obtained by rotating an isocost line clockwise. The new isocost line is tangent to the original S isoquant and the new T isoquant.
Looking at the intercepts, W must have increased while R must have decreased.
Looking at the intercepts and then comparing to the change in prices:
For capital units, their 'reward' R has decreased while the price of T has increased and the price of S is the same. So capital is definitely worse off.
For labor it is less clear why labor gains. W has increased to be sure, but then the price of good T has increased. We need to know whether the percentage increase in W is enough to offset the price increase.
It is. We need to look at the geometry of the diagram. Comparing the proportional shift inward of the T isoquant (which gives us the percentage price increase) and the proportional movement along the W axis, we see that W must increase proportionally more than Pt increases. So it is true that labor gains.
This illustrates the theorem.
Why is it that 'in the context of the H-O model this theorem translates into the simple statement that the abundant factor gains from trade while the scarce factor loses'?
According to HO the labor abundant country will export the labor intensive good, which is the good which must experience a price rise when trade is opened up (otherwise there is no incentive to export). The SS theorem says that if opening up to trade increases the price of T, then it will increase W becasue L is the factor used intensively in producing it.
So opening to trade benefits the abundant factor. Notice that to make this statement we have to link up both the HO and SS theorems. So it is not really a 'simple statement' after all!
A footnote about country A and B. If we start out with one country producing the same value of both goods (like in the case above) it cannot be the case that the other country is doing the same thing. In our model one country (A) is always more capital abundant than the other. Using the price definition of abundance, this means that the isocost lines in the two countries do not have the same slope. The labor abundant country, for example, has flatter slopes for the isocost lines, by the definition of labor abundance. If you look at the diagram, if one country is starting out with overlapping isocost lines, forcing the other country's isocost lines to have a different slope means that they cannot be overlapping. The bottom line is that it is impossible for A and B to be both simultaneously starting at a point with overlapping isocost lines.
