A Note on the Nonexistence of Optimal Price Vectors in the General Balanced-Growth Model of Gale - Hulsmann, J.; Steinmetz, V. (Econometrica, 1972)
IN THE GROWTH model of Kemeny-Morgenstern-Thompson [2, pp. 115-135], the production space is a closed convex and polyhedral cone in R2, with some further properties. In the growth model of Gale [1, pp. 285-303], the production space has to fulfil the same assumptions except that the cone need not be polyhedral. Therefore the model of Gale can be regarded as a generalization of the KMT-model. In this paper it will be shown that in contradiction to a central theorem of Gale, the existence of an optimal price vector cannot be guaranteed in this generalized production space. To describe the difficulty in the growth model of Gale, we enumerate the properties of the production space and the basic definitions given by him. The technological possibilities of production are described by the production space