THE TRANSFORMATION FUNCTION REVISITED

Introduction The transformation function for two‐sector production models has been used extensively in the international trade and general equilibrium literature. It has been derived both graphically and mathematically from individual sector production functions that are assumed to be linearly homogeneous. The result has been a convex set possessing first derivatives that have frequently been used. However, there seems to be a lack of research on further properties attributable to the transformation function. The purpose of this paper is to analyze these additional properties. We begin by proving that the transformation function is linearly homogeneous in all of its arguments. We then derive the standard first derivatives of the transformation function providing their usual economic interpretation. Finally, we conclude by deriving and interpreting the second‐order derivatives of the transformation function.