topic 4.2
Assume:
- isoquants manifest constant returns to scale
- both countries have identical isoquants (same technology)
- both countries have identical consumption preferences
- A is capital abundant
- S is capital intensive
- both countries start on the two unit isoquants
- the price of the two goods is equal in A (this is arbitrary and only to make the demonstration easier)
- there is perfect competitionm and so prices exactly equal the cost of production
Industry S is capital intensive, both countries have the same set of isoquants that expand along the same rays and look the same in every way. So figure 4.2 works for both countries. But because factor endowments are different each country will choose to produce on a different specific pair of (unit) isoquants, the isocost curve will be different and (at least in autarky) the slope -W/R will be different.
If capital and labor are perfectly mobile with a country then in equilibrium the wage rate and rental will be the same in both industries (why would labor accept a lower wage in one industry when they can move to the other industry?)
To summarize figure 4.2. Both countries have the same set of isoquants. S is relatively capital intensive and so the S isoquants expand along a ray to the left of the ray for industry T. Now let's discuss choosing actual production levels.
First we have to make a change in our definition of relative factor abundence. We shall adopt the 'price definition' of relative factor abundance:
A country is relatively capital abundant if the wage/rental payment in its country is higher than the wage rental in the other country.
This definition uses the measure of the relative price of the factor inputs instaed of quantities. This definition may not always match what we would get with the 'quantity' definition.
Restating the H-O theorem using the price definition of factor abundance:
When the autarky wage/rental ratio is higher in A than B (A is capital intensive)the autarky relative price of S is lower in A than in B (A will export S).
If the autarky price of S is lower in A than B we know that when trade is opened up A will export S and import T. So what this defintion is saying is that the capital abundant country will export the capital intensive good.
PROOF
We will prove H-O by using figure 4.2.
However, we will do it differently from the text. The text starts with country A and then does a comparison with country B. We will do the opposite, going from B to A.
Suppose that the two isoquants shown are the isoquants for producing one unit of each good.
Then by comparing isocost lines which would apply to producing one unit of each good we know which good has the higher cost per unit.
Because these countries have perfectly competitive markets:
price (per unit) = marginal cost = average cost
So, knowing about relative costs of production tells us something about the relative prices of goods.
To begin, suppose we ask what is the relative cost of producing one unit of S and one unit of T in country B.
Suppose Wb/Rb are as shown in figure 4.2 and so production (of one unit each) will occur at X and Y. Since the isocost line for producing one unit of S goes through X, and the isocost line for producing one unit of T goes through Y, we can see that the cost of producing (one unit of)S is greater than the cost of producing (one unit of) T [the S isocost line is further out]. This means that Ps>Pt.
Now move over to country A. By the definition of factor abundance Wa/Ra > Wb/Rb. If we rotate the two isocosts lines to make Wa/Wb higher the distance between the two isocost curves decreases. In fact, there comes a point where the two isocost lines will merge into one (this is shown on figure 4.2). At this point Ps + Pt. So Ps has fallen below its value in B.
[There is nothing really special about the case where Ps = Pt. This happens to be the case where the dollar price of both goods is the same. It is only used because it makes the fall in the price of S as we increase W/R especially clear.]
Since autarky Ps/Pt is lower in the country which is more capital abundant we have proved the H-O theorem. Capital abundant S will export the capital intensive good.
