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Simple proof of existence of equilibrium in a one-sector growth model with bounded or unbounded returns from below. (English) Zbl 1082.91057

In the article, the one-sector growth model is analyzed. The assumptions differ from those in previous papers: the utility may be not bounded from below, and the common Inada conditions on the one-period utility function is dropped. Preferences are time additively separable. To prove the existence of an optimal path, the classical approach is followed. It is proved that the value function solves the Bellman equation, and necessary and sufficient conditions for an optimal path are derived. Existence of a competitive equilibrium is justified. The proposed technique is extended to the study of a one-good sector model with heterogeneous agents.

MSC:

91B50 General equilibrium theory
37N40 Dynamical systems in optimization and economics
49L20 Dynamic programming in optimal control and differential games
91B62 Economic growth models
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