Freni, Giuseppe and Gozzi, Fausto and Salvadori, Neri (2010): Existence of optimal strategies in linear multisector models with several consumption goods.
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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 more than one consumption good exists.
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, 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:  20963 
Depositing User:  Neri Salvadori 
Date Deposited:  01. Mar 2010 12:17 
Last Modified:  18. Feb 2013 20:14 
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/20963 
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) [Currently Displayed]

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