Extensions and reductions in the von neumann model of an expanding economy

This paper introduces an extension of the v. Neumann model of an expanding economy. In addition to the conventional nonnegative input and output matrices A₁, B₁ representing technology, two matrices A₂, B₂ represent socio-political evaluations and show that there exist solutions to the 4-matrix model. The proof is based on an extension of a constructive proof given by O. Morgenstern and G. L. Thompson. It is shown that this proof is valid only under an additional assumption. The transformation of v. Neumann models (taking consumption into account) into 1 or 2 games is shown and adds an additional condition to M. Morishima's model to guarantee a solution. The equivalence of the v. Neumann model to a maximization problem under a (efficiency) constraint is presented. It is shown that E. Malinvaud's maximality and efficiency criterion - if based on the same assumptions (model) - are equivalent and specify the assumptions which will make the MT-model efficient. The economic evaluation is considered to be of utmost importance.