This account of turnpike theorems concentrates on the discrete time model, descended from the early von Neumann growth model and the Dosso model. It portrays the current state of the theory under the following five headings: (i) a turnpike in the von Neumann model, (ii) a turnpike in the Ramsey model, (iii) Ramsey models with discounting, (iv) turnpike theorems for competitive equilibria, and (v) further generalizations. It emphasizes von Neumann facets and neighborhood convergence as the author's principal contribution to the theory. Under (v), it discusses models that allow for habit formation so that current preferences are affected by past consumption, and for non-convex technologies that have an initial phase of increasing returns followed by a terminal phase of decreasing returns. The theorems that have been reviewed are all concerned with the convergence of optimal paths to stationary optimal paths. However, the method of the proofs is to show that optimal paths converge to one another. The considerable literature on continuous time models related to the literature on the investment of the firm and to the engineering literature on optimal control, as well as applications of the asymptotic results of optimal growth theory to the theory of finance, have not been reviewed.
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- David Cass, 1964. "Optimum Economic Growth in an Aggregative Model of Capital Accumulation: A Turnpike Theorem," Cowles Foundation Discussion Papers 178, Cowles Foundation for Research in Economics, Yale University.
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