The Geometric Construction of Production Functions that Are Consistent with an Arbitrary Production-Possibility Frontier.

The production-possibility frontier is strictly concave and negatively sloped if two commodities are produced according to linearly homogeneous, strictly quasi-concave production functions that use, with different intensities, two factors of production that are available in fixed supply. In this paper, it is shown that any arbitrary, concave, negatively sloped production-possibility frontier can be generated by a pair of linearly homogeneous, quasi-concave production functions given fixed total endowments of two factors. Thus, the construction of such arbitrary production-possibility frontiers places no other restrictions on the underlying production technology.