International Trade Theory and Policy
by Steven M. Suranovic
Trade 607

The Production Possibility Frontier (Variable Proportions Case)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  Chapter 607: Last Updated on 6/8/98 