International Trade - Theory and Policy, 2010a

The second important distinction is that variable proportions change the shape of the economy’s PPF. The
labor constraint with full employment can be written as
aLC(w/r)QC+aLS(w/r)QS=L,
where aLC and aLW are functions of (w/r).
The capital constraint with full employment becomes
aKC(w/r)QC+aKS(w/r)QS=K,
where aKC and aKW are functions of (w/r).
Under variable proportions, the production possibility frontier takes the traditional bowed-out shape, as
shown in Figure 5.6 "The PPF in the Variable Proportions H-O Model". All points on the PPF will maintain full
employment of both labor and capital resources. The slope of a line tangent to the PPF (such as the line
through point A) represents the quantity of steel that must be given up to produce another unit of
clothing. As such, the slope of the PPF is the opportunity cost of producing clothing. Since the slope
becomes steeper as more and more clothing is produced (as when moving production from point A to B),
we say that there is increasing opportunity cost. This means that more steel must be given up to produce
one more unit of clothing at point B than at point A in the figure. In contrast, in the Ricardian model the
PPF was a straight line that indicated constant opportunity costs.
Figure 5.6 The PPF in the Variable Proportions H-O Model
The third important distinction of variable proportions is that the magnification effects, derived
previously under a fixed proportions assumption, continue to work under variable proportions. To show
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