Determinacy of Equilibrium in Infinite Horizon Economics a Perspective

Cover Determinacy of Equilibrium in Infinite Horizon Economics a Perspective
Determinacy of Equilibrium in Infinite Horizon Economics a Perspective
Walter J Muller
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He establishes his global result by proving that optimal paths must visit the neighborhood of the steady state and then citing the local stability results for such neighborhoods.
A number of authors have sought to generalize the global result of Scheinkman. Cass and Shell (1976) provide an excellent survey of this work. The approach has been to develop conditions on the geometry of the Hamiltonian function that are sufficient to yield results even when the rate of discount is not close to zero.
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Muller and Woodford's analysis is local in nature, so one would expect their results to be linked to the local results in this literature, and indeed they are. Consider the special case of their model in which there is one inf ini t e- 1 ived agent and no finite-lived agents. This is their extreme case (i), so the equilibrium is perfectly determinate or not structurally g stable depending upon n, the number of eigenvalues that are 27 less than p in modulus. With a slight translation of terms, this is exactly Scheinkman' s result.


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