The production possibility frontier can be derived in the variable proportions case by using the
same labor and capital constraints used in the fixed proportions case but with one important
adjustment. Under variable proportions the unitfactor requirements are functions of the wagerental ratio (w/r). This implies that the capitallabor ratios (which are the ratios of the unitfactor
requirements) in each industry are also functions of the wagerental ratio. If there is a change in
the equilibrium (for some reason) such that the wagerental rate rises, then labor will become
relatively more expensive compared to capital. Firms would respond to this change by reducing
their demand for labor and raising their demand for capital. In other words firms will substitute
capital for labor and the capitallabor ratio will rise in each industry. This adjustment will allow
the firm to maintain minimum production cost and thus the highest profit possible.
The labor constraint with full employment can be written as,
where a_{LC} and a_{LW} are functions of (w/r).
The capital constraint with full employment becomes,
where a_{KC} and a_{KW} are functions of (w/r).
Under variable proportions the production possibility
frontier takes the traditional bowedout shape as shown in
the adjoining Figure. 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 which indicated constant opportunity costs.
International Trade Theory and Policy Lecture Notes: ©19972004 Steven M. Suranovic
Last Updated on 6/8/98
