On the Derivation of the Production Possibility Curve

The main purpose of this paper is to present, for a two-commodity world, a method of deriving the production possibility curve directly from the isoquant diagram. While two such derivations exist in the literature, those of Savosnick and Travis,2 their techniques are not useful for all purposes. In particular, neither allows the comparison of the shapes of the production possibility curves under alternative production conditions, such as is the case where factor intensity reversals occur. Our approach will be, first, to present a geometric method of deriving the production possibility curve from the representative isoquants of the two commodities, and then to use this derivation to illustrate how the relative shapes of the production possibility curves differ when factor intensity reversals prevail. We will then use these curves to illustrate the traditional factor-intensity-reversal results. Our analysis will also make clear the factors which determine the shape of the production possibility curve, and will indicate the importance for the Heckscher-Ohlin theorem of explicitly excluding the possibility of factor intensity reversal. Throughout our analysis we will make the usual Heckscher-Ohlin assumptions that two goods are produced in two countries using labour and capital, that the goods vary in their factor intensities and the countries vary in their factor endowments, that both countries possess the same linear homogeneous production functions for the two goods, that perfect competition prevails, and that tastes in the two countries are identical and can be represented by utility functions which are homothetic.3 In Figure 1, point E on the ray OZ represents the endowment of capital and labour for the country under consideration. X0 and Y0 are the two isoquants for commodities X and Y which pass through E. These levels of output therefore represent the maximum possible output for the two commodities. These maximum output quantities are

Capital (architecture) · Capital good · Commodity · Econometrics · Economics · Economy · Factors of production · Geometry · Goods and services · Homothetic transformation · Market economy · Mathematical economics · Microeconomics · Point (geometry) · Production (economics) · Economic theories and models · Economic Theory and Policy · Mathematics

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