Freni, Giuseppe and Gozzi, Fausto and Salvadori, Neri (2010): Existence of optimal strategies in linear multisector models with several consumption goods.
This is the latest version of this item.

PDF
MPRA_paper_21809.pdf Download (285kB)  Preview 
Abstract
In this paper we give a sufficient and almost necessary condition for the existence of optimal strategies in linear multisector models when time is continuous and the the instantaneous utility function of the representative agent has two properties: (a) the intertemporal elasticity of substitution is constant over time and (b) preferences are concave and homothetic.
Item Type:  MPRA Paper 

Original Title:  Existence of optimal strategies in linear multisector models with several consumption goods 
English Title:  Existence of optimal strategies in linear multisector models with several consumption goods 
Language:  English 
Keywords:  Endogenous growth; optimal control with mixed constraints; von Neumann growth model 
Subjects:  O  Economic Development, Innovation, Technological Change, and Growth > O4  Economic Growth and Aggregate Productivity > O41  One, Two, and Multisector Growth Models C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium 
Item ID:  21809 
Depositing User:  Neri Salvadori 
Date Deposited:  05. Apr 2010 02:30 
Last Modified:  25. Feb 2015 08:46 
References:  [1] Acemoglu, D. and Guerrieri, V.: Capital Deepening and Nonbalanced Economic Growth. Journal of Political Economy, 116(3), 467498 (2008). [2] Balder, E. J.: Existence of Optimal Solutions for Control and Variational Problems with Recursive Objectives. Journal of Mathematical Analysis and Applications, 178, 418437 (1993). [3] Bardi, M., Capuzzo Dolcetta, I.: Optimal Control and Viscosity Solutions of HamiltonJacobiBellman Equations. Boston, Birkhauser, 1997. [4] Becker, R. A., Boyd III, J. H., Sung, B. Y.: Recursive Utility and Optimal Capital AccumulationI: Existence. Journal of Economic Theory, 47, 76100 (1989). [5] Cesari, L.: Optimization Theory and Applications. New York, Springer Verlag, 1983. [6] Freni, G., Gozzi, F., Pignotti, C.: A Multisector AK Model with Endogenous Growth: Value Function and Optimality Conditions. J. Math. Ec., 2008. [7] Freni, G., Gozzi, F., Salvadori, N.: Existence of Optimal Strategies in linear multisector models. Economic Theory, 29 2548, 2006. [8] Freni, G., Gozzi, F., Salvadori, N.: Existence of Optimal Strategies in linear Multisector Models. Discussion papers, Collana di Epapers del Dipartimento di Scienze Economiche  Universit a di Pisa, No. 29, 2004. http://wwwdse.ec.unipi.it/discussionpapers/lavori/freniGozziSalvadori.pdf [9] Gale, D.: The Closed Linear Model of Production. Paper 18 in Kuhn, H., and A. W. Tucker, eds., Linear Inequalities and Related Systems. Princeton U. Press, 1956. [10] Gale, D.: The Theory of Linear Economic Models. New York, McGrawHill, 1960. [11] Kongsamut, P., Rebelo, S., and Xie, D.; Beyond Balanced Growth. Review of Economic Studies, 68(4), 86982 (2001). [12] Magill, M. J. P.: In nite Horizon Programs. Econometrica, 49, 679711 (1981). [13] Magill, M. J. P.: On a Class of Variational Problems Arising in Mathematical Economics, J. Math. Anal. Appl., 82, 6674 (1981). [14] Mangasarian, O. L.: Nonlinear Programming. BombayNew Delhi: Tata McGraw Hill, reprinted as vol. 16 of the series Classics in Applied Mathematics, Philadelphia: SIAM, 1994. [15] Motzkin, T. S.: Beiträge zur Theorie der Linearen Ungleichungen. Inaugural Dissertation, Jerusalem, Base, 1936. [16] von Neumann, J.: A Model of General Economic Equilibrium. Review of Economic Studies 13, 19 (1945). [17] Ngai, L.R. and Pissarides, A.: Structural Change in a Multisector Model of Growth, American Economic Review, 97(1), 429443 (2007). [18] Seierstad, A.: Nontrivial Multipliers and Necessary Conditions for Optimal Control Problems with In nite Horizon and Time Path Restrictions. Memorandum from Department of Economics, University of Oslo, 24, (1986). [19] Seierstad, A., Sydsaeter, K.: Optimal Control Theory with Economic Applications. Amsterdam, North Holland, 1987. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/21809 
Available Versions of this Item

Existence of Optimal Strategies in Linear Multisector Models with several consumption goods. (deposited 21. Nov 2009 11:56)

Existence of optimal strategies in linear multisector models with several consumption goods. (deposited 27. Nov 2009 10:31)

Existence of optimal strategies in linear multisector models with several consumption goods. (deposited 01. Mar 2010 12:17)
 Existence of optimal strategies in linear multisector models with several consumption goods. (deposited 05. Apr 2010 02:30) [Currently Displayed]

Existence of optimal strategies in linear multisector models with several consumption goods. (deposited 01. Mar 2010 12:17)

Existence of optimal strategies in linear multisector models with several consumption goods. (deposited 27. Nov 2009 10:31)