A Two-Factor World: The Heckscher-Ohlin-Samuelson Model

Initial Assumptions

The Ricardian model supposed a world of  2 countries, 2 goods, and 1 factor of production.  In the Heckscher-Ohlin-Samuelson (HOS) model we have a world with 2 countries, 2 goods, and 2 factors.  Each country has a free-market economy consisting of consumers and competitive firms.  The only point of contact between countries is trade in goods: factors can not move between countries.  We assume that technologies are identical, but that each good uses one of the factors more intensively.

In this diagram we have two countries, Angola and Botswana, two goods, shoes and potatoes, and two factors, land and labor.  Shoes are a relatively labor-intensive good, requiring only a little land to graze cattle for hides, but a lot of labor.  Potatoes need a lot of land and only some labor.  Note that in this diagram the two countries differ by theor relative endowments of factors: Angola has a lot of land and not much labor; Botswana has a lot of labor and not much land.  In this picture they do not trade.

Now these two countries, which had previously sealed their borders, begin trading.  Basically, each specializes.  The country with a lot of labor specializes in the labor-intensive good, and vice versa.  Here is how the diagram would change:

We can show the same process by using production possibility frontiers for the two countries.

The diagram shows how production and consumption change with trade.  Here is an annotated version of the Angola diagram in the picture above, which may make it clearer:

The numbers are just added to help the explanation.  Note that Angola's trade has to be the opposite of Botswana's.

Factor-Price Equalization

Letís go back to the pre-trade situation.  Without trade, labor is relatively scarce in Angola and we would expect it to command a high price.  But in Botswana, labor is plentiful while land is scarce.  We would expect the relative payments that these factors receive to reflect this.  So in Angola the annual wage might be twice the annual rent on an acre of land, while in Botswana the annual wage might be one-half the annual rent on an acre.

You can see this is in the shapes of the PPFs above.  Before trade, a pair of shoes might trade for ten bushels of potatoes in Angola, but for only two bushels in Botswana.  Since labor is more  intensively used in shoes,  labor's reward relative to land will be higher in Angola.

With trade, this changes.  Angola does not have to rely on its own scarce labor to make shoes.  It can use its plentiful land to make potatoes, and trade potatoes for  Botswanan shoes instead.  Angolan wages will fall (relative to Angolan rents).  The reverse happens in Botswana.

Further Implications

The HOS model has two basic implications, illustrated above:

     1. Under free trade, countries tend to export the good that uses their relatively-abundant factor
         relatively intensively.

     2. Under free trade, relative factor prices will be the same in all countries.

There are two further implications about how prices and trading patterns change.  One  is that  if a country's factor endowments change, its trade will change as well.  Suppose Angola's labor force grew while all other factor endowments remained unchanged.

Angola will now be somewhat less reliant on trade, having a less skewed factor endowment than before.  It will make more shoes, and slightly fewer potatoes, than it did before.

It seems reasonable to expect that this change would also affect the international price, expecially if our world consists of only two countries.  If previously the international price was 5 bushels of potatoes per pair of shoes, now it might go to only 4 bushels per pair.  Botswana will now make a few more potatoes and a few fewer shoes.  Here is the corresponding. block diagram.  Essentially the trading pattern is the same but volume of trade is less.

Finally, what happens to relative factor prices?  If the relative price of the two traded goods changes for any reason, then the factor that is used relatively more intensively in the good that is now more expensive will benefit.  The factor that is used relatively more intensively in the good that is now cheaper will lose.  Thus the fact that shoes are now relatively cheaper ends up hurting labor everywhere.  (This is a "long-run" result, once land and labor have had the time to move between industries.)  Thus the relative abundance of land and labor in Angola have an effect on the relative returns to land and labor in Botswana, even though the land and labor markets are not directly linked -- workers cannot move from one country to the other, for example.

©1998 Colin Danby.