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The model described has the same general features of the PILOT dynamic macro-economic model of U.S. designed to assess the long term impact of foreign competition, innovation, modernization, and energy needs. We derive the aggregate demand function of final consumer from individual demand functions in order to state its mathematical properties; we then estimate its parameters by a fit to empirical data. The equilibrium conditions are those of the Arrow-Debreu model, the only unusual feature is that investors calculate their rate of return using discounted normalized prices of future periods. If investors choose to normalize intra-period prices in the usual way by requiring that they sum to unity (or equivalently their average value is unity), the inverse demand functions turn out to be non-integrable. Equally satisfactory from the investors' point of view, is for them to choose instead to normalize intra-period prices. It is shown that the inverse-demand functions are integrable and derive a utility function for the economy which if maximized subject to the physical-flow constraints implies the equilibrium conditions. Keywords: economic growth.