The Ramsey model with logistic population growth and benthamite felicity function revisited

WSEAS Transactions on Mathematics

Volumn 8, Issue 3, 2009, Pages 97-106

  Ferrara, Massimiliano ^a   Guerrini, Luca ^b  

^a UNIVERSITY MEDITERRANEA OF REGGIO CALABRIA   (Italy)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Benthamite; Exact solution; Logistic population; Ramsey; Saddle point

Indexed keywords

BENTHAMITE; EXACT SOLUTION; LOGISTIC POPULATION; RAMSEY; SADDLE POINT;

DYNAMICAL SYSTEMS; ELASTICITY;

MACHINE TOOLS;

EID: 67849085176     PISSN: 11092769     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. E. Accinelli and J. G. Brida, Re-formulation of the Ramsey model of optimal growth with the Richards population growth law, WSEAS Transactions on Mathematics, 5, 2006, pp. 473-478.
2. E. Accinelli and J. G. Brida, The Ramsey model with logistic population growth, Economics Bulletin, 3, 2007, pp. 1-8.
3. R. J. Barro and X. Sala-i-Martin, Economic Growth, McGraw-Hill, New York, 1995.
4. G. Birkhoff and G. Rota, Ordinary Differential Equations, 3rd Edition, John Wiley and Sons, New York, 1978.
5. D. Cass, Optimum growth in an aggregative model of capital accumulation, Review of Economic Studies, 32, 1965, pp. 233240.
6. J. C. Day, Population Projections of the United States by Age, Sex, Race, and Hispanic Origin: 1995 to 2050, U.S. Bureau of the Census, Current Population Reports, Series P25-1130, Government Printing Office, Washington, DC, 1996.
7. E. D. Domar, Capital expansion, rate of growth, and employment, Econometrica, 14, 1946, pp. 137-147.
8. M. Ferrara and L. Guerrini, Economic development and sustainability in a two-sector model with variable population growth rate, Journal of Mathematical Sciences: Advances and Applications, 1, 2008, pp. 323-339.
9. M. Ferrara and L. Guerrini, Economic development and sustainability in a Solow model with natural capital and logistic population change, International Journal of Pure and Applied Mathematics, 48, 2008, pp. 435-450.
10. M. Ferrara and L. Guerrini, The neoclassical model of Solow and Swan with logistic population growth, Proceedings of the 2nd International Conference of IMBIC on "Mathematical Sciences for Advancement of Science and Technology (MSAST), Kolkata, India, 2008, pp. 119-127.
11. M. Ferrara and L. Guerrini, The Green Solow model with logistic population change, Proceedings of the 10th WSEAS International Conference on Mathematics and Computers in Business and Economics, Prague, Czech Republic, March 23-25, 2009, pp. 17-20.
12. M. Ferrara and L. Guerrini, The Ramsey model with logistic population growth and Benthamite felicity function, Proceedings of the 10th WSEAS International Conference on Mathematics and Computers in Business and Economics, Prague, Czech Republic, March 23-25, 2009, pp. 231-234.
13. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, 1990.
14. L. Guerrini, The Solow-Swan model with a bounded population growth rate, Journal of Mathematical Economics, 42, 2006, pp. 14-21.
15. R. F. Harrod, An essay in dynamic theory, Economic Journal, 49, 1939, pp. 14-33.
16. T. C. Koopmans, On the Concept of Optimal Economic Growth, in The Econometric Approach to Development Planning, North-Holland, Amsterdam, 1965.
17. T. R. Malthus, An Essay on the Principle of Population, Cambridge University Press, Cambridge, 1992.
18. J. Maynard Smith, Models in Ecology, Cambridge University Press, Cambridge, 1974.
19. L. S. Pontryagin et al., The Mathematical Theory of Optimal Processes, Interscience Publishers, New York, 1962.
20. F. P. Ramsey, A mathematical theory of saving, Economic Journal, 38, 1928, pp. 543-559.
21. P. Rupsys, The relationships between the diameter growth and distribution laws, WSEAS Transactions on Biology and Biomedicine, 4, 2007, pp. 172-191.
22. P. Rupsys, Stationary densities and parameter estimation for delayed stochastic logistic growth laws with application in biomedical studies, WSEAS Transactions on Biology and Biomedicine, 5, 2008, pp. 117-132.
23. C. P. Simon and L. E. Blume, Mathematics for Economists, Norton, New York, 1994.
24. W. T. Smith, A closed form solution to the Ramsey model, Economics Bulletin, 6, 2006, pp. 1-27.
25. R. M. Solow, A contribution to the theory of economic growth, Quarterly Journal of Economics, 70, 1956, pp. 65-94.
26. R. M. Solow, Technical change and the aggregate production function, Review of Economics and Statistics, 39, 1957, pp. 312-320.
27. T. W. Swan, Economic growth and capital accumulation, Economic Record, 32, 1956, pp. 334-361.
28. P. F. Verhulst, Notice sur la loi que la population pursuit dans son accroissement, Correspondance Mathématique et Physique, 10, 1838, pp. 113-121.