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Green manure and nitrogenous fertilizer—a two-sector optimal-growth model

Published online by Cambridge University Press:  17 February 2009

David Mustard
David Mustard
Affiliation:
School of Mathematics, University of New South Wales, P. O. Box 1, Kensington, N.S.W. 2033
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Abstract

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A continuous-time model of a two-sector trading economy with a finitely-saturating production function and constant population is constructed. To apply it to the farm-economy problem of optimal trading of cereal for chemical nitrogenous fertilizer and of optimal allocation of land for green manure the special assumptions are made of similar technologies in both sectors and of a nitrogen-capital loss proportional to the cereal production. Optimal-control theory is applied to get the pair of controls that maximizes an infinite-horizon integral of utility of consumption. The analysis of the model is shown to reduce to that of the Ramsey-Koopmans one-sector neoclassical model of optimal growth. Calculations of the feedback control and optimal time-paths for the standardized dimensionless model are tabulated for a range of 7 utility functions of constant elasticity of marginal utility of magnitude 1 to 4 and of production functions of degree 2 to 4. Two particular analytic solutions are given. The application of the results both to the farm-economy model and to the Ramsey-Koopmans model is illustrated.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 2 , October 1986 , pp. 181 - 201
Copyright
Copyright © Australian Mathematical Society 1986

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