In this thesis some simplified assumptions present in the von Neumann expanding economy are examined and replaced by more appropriate ones. First we explain more clearly the von Neumann original model and the Kemeny Morgenstern and Thompson's extension. We clarify the meaning of the open constrained economy which Morgenstern and Thompson derive from the von Neumann economy as a linear programming problem. Then we examine the exact meaning and relevance, in the ambit of the von Neumann's model, of different definitions of closed economy, in connection with the treatment of labour. We study critically all the ways of introducing consumption into the model. After we deal with the models which explicitly introduced externalities and processes which produce both goods and bads. Some of the previous generalizations have not been completely free from criticism; however some shortcomings can be solved introducing externalities as different commodities, distinguished on the basis of their users. These public intermediate commodities influence directly the use and the intensity of one or more productive processes. They are also one of the premises and foundations of the public sector normative and positive theory of De Viti De Marco. In our models we follow his line of reasoning and confine ourselves to the original (or KMT) model. We show how the rate of growth of the von Neumann's economy, where the prices of public commodities (bads) are determined by the equilibrium solution and paid through taxation, is greater than the one which would be determined by the private market equilibrium where public commodities (bads) are free. It is also possible to have no private market equilibrium, even if it always exists a constrained one which is a mixed economy equilibrium
