Solutions to the Decomposable von Neumann Model
A method is shown for finding all solutions to the generalized von Neumann model formulated by Kemeny, Morgenstern, and Thompson. The method uses results from decomposing economic production systems to extend the algorithm of Hamburger, Thompson, and Weil. THIS ARTICLE shows how the results derived by Weil [5, 6] for decomposable production systems can be used to extend the results of Hamburger, Thompson, and Weil [1] for performing calculations on the generalized von Neumann model of an expanding economy formulated by Kemeny, Morgenstern, and Thompson [2]. A method is shown for finding all solutions to a generalized von Neumann model. The model represents an economy of m goods and n fixed-coefficient, constantreturns-to-scale processes for producing those goods. The set of processes form an m by n input matrix A and an m by n output matrix B. When the jth process is operated at unit intensity the amount ai of the ith good must be supplied at the beginning of the production period and the amount bij of the jth good is produced at the end of the period. The element xj, xj > 0, Ixj = 1, of the stochastic column vector x is the level at which the jth activity is operated. The element yi of the stochastic row vector y is the price of the ith good. Von Neumann required that