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- Title
INTERTEMPORAL EFFICIENCY OF CAPITAL ACCUMULATION AND THE VON NEUMANN RAY.
- Authors
Sau, Ranjit K.
- Abstract
This article offers relatively simple geometrical proof for the turnpike theorem and the uniqueness of the intertemporally efficient path of infinite order. A number of theorems on intertemporal efficiency of capital accumulation and the von Neumann ray have been derived through high-level mathematical analysis. An economy with two goods is considered in this study. It is a closed model of production; outputs of every period become inputs in the next period, and so on. The intertemporally efficient path originating from any arbitrary initial resource endowments, subject to the condition that both the commodities are of positive amounts in the initial stocks, and maximizing the terminal capital stocks in any arbitrary non-negative proportions, remains in the neighborhood of the von Neumann ray most of the time, if the time horizon is far enough, even if finite. This is a version of the turnpike theorem. If a von Neumann ray, a balanced growth path at a maximal rate, exists, and is known to be dynamically efficient of any order, finite or infinite, it is necessarily unique in this model. For the multiplicity of such von Neumann ray contradicts the uniqueness of the intertemporally efficient growth path of infinite order.
- Subjects
TURNPIKE theory (Economics); SAVINGS; ECONOMIC models; CAPITAL stock; MATHEMATICS
- Publication
Quarterly Journal of Economics, 1965, Vol 79, Issue 4, p642
- ISSN
0033-5533
- Publication type
Article
- DOI
10.2307/1880656