The HOS theorem states that a country which is relatively abundant in labour will have
comparative advantage in the labour intensive good and the relatively capita1 abundant
country will have comparative advantage in the capital intensive good. Thus it is the factor
abundance rather than technology which determines the pattern of trade. To prove the
theorem we use the relationship between w/r and Px /P2 which we have just established.
Assuming the X is labour intensive Figure 2.3 shows this relationship. The figure shows that
the foreign country is capital abundant and the home country labour abundant by the factor
price definition of relative factor abundance, since (wlr), > (wlr),. As a result of this, a
comparison of autarky prices tells us: (Px /Py )h < (Px /Py ), , or the home country's relative
price of X is less than the foreign country's relative price of X in autarky. Therefore, the home
country (labour abundant) will export X (labour intensive) and the foreign country (capital
abundant) will export Y(capita1 intensive).
As trade takes place the two countries' autarky prices will converge to the equilibrium world
price, just as in the Ricardian model, provided that there are no impediments to trade. The
Figure shows this equilibrium world price as (Px / P )* which is the commodity terms of trade
at which trade will take place in equilibrium and (w/r)* as the factorial terms of trade in
equilibrium. In the neoclassical model free trade not only equalizes the relative commodity
price in the two country but also equalizes the relative wage rate
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