Optimality Criteria of Economic Growth as Examples of Optimal Resource Allocation Over Time

This is my PhD dissertation defended in 1966 at the University of Minnesota and it was never published. It has been cited and used in other researchers work so I now make it available. The problem of optimal resource allocation over time is formulated as an optimal control problem. This is where the existence of optimal programs is investigated (and sufficient conditions are provided) for the first time in economics. When earlier authors spoke of existence, they spoke of convergence of the integral defining the optimality criterion. Optimal programs were characterized in terms of market equilibria at each point in time as well as imputed prices for stocks of capital.One of the propositions in the paper establishes the principle of centralization of planning and decentralization of implementation (this closely relates to polycenterism advocated by European socialist parties in the late 1950s. If one uses a measure space of traders instead of the basic time interval and assume pure exchange then the existence theorem of this paper can greatly simplify the proof of existence of equilibrium in a or a much more flexible model of exchange with continuum of traders