Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T07:45:48.557Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

[1]Abraham, T. P. and Nair, Chandrika, “Planning for fertiliser use under constraint”, pre-print from Proc. 14th Econometric Conference Jan 1–4, 1975 (Indian Statistical Institute, New Delhi, 1975).Google Scholar
[2]Bardhan, P. K., Economic growth, development and foreign trade (Wiley-Interscience, New York, 1970).Google Scholar
[3]Chakravarty, S. K., Capital and development planning, (M.I.T. Press, Cambridge, Mass., 1969).Google Scholar
[4]Government of India Planning Comission, Draft fifth five year plan, 1974–79, Volume 2 (Government of India Press, New Dethi, 1974).Google Scholar
[5]Hadley, G. and Kemp, M. C., Variational methods in economics (North-Holland Publishing Co., Amsterdam, 1971).Google Scholar
[6]Indian Council of Agricultural Research, All-India co-ordinated agronornic experiment scheme-annual reports (1969–1970, 1970–1971, 1971–1972, 1972–1973).Google Scholar
[7]Indian Council of Agricultural Research, Handbook of agriculture (I.C.A.R., New Delhi, 1961).Google Scholar
[8]Intriligator, Michael D., Mathematical optimization and economic theory (Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971).Google Scholar
[9]Koopmans, T. C., “On the concept of optimal economic growth”, in Study week on the econometric approach to planning, Pontificiae Scientiarum Scripta Varia XXVIII (Rand McNally, Chicago, 1965).Google Scholar
[10]Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V. and Mishchenko, E. F., The mathematical theory of optimal processes (Interscience Publishers, John Wiley & Sons, Inc., New York, 1962).Google Scholar
[11]Samuelson, P. A., “A catenary turnpike theorem involving consumption and the golden rule”, American Economic Review Vol. 55 (06, 1965), 486–496.Google Scholar
[12]Tinbergen, J. and Bos, H. C., Mathematical models of economic growth (McGraw-Hill Book Co., New York, 1962).Google Scholar
[13]Wan, H. Y. Jr, Economic growth (Harcourt Brace Jovanovich, Inc., New York, 1971).Google Scholar