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The Lagrange multipliers and existence of competitive equilibrium in an intertemporal model with endogenous leisure

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This paper proves the existence of competitive equilibrium in a single sector dynamic economy with elastic labor supply. The method of proof relies on some recent results (see Le Van and Saglam [2004]) concerning the existence of Lagrange multipliers in infinite dimensional spaces and their representation as a summable sequence

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  • Nguyen Manh Hung & San Nguyen Van, 2005. "The Lagrange multipliers and existence of competitive equilibrium in an intertemporal model with endogenous leisure," Cahiers de la Maison des Sciences Economiques b05041, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:b05041
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    1. Le Van, Cuong & Cagri Saglam, H., 2004. "Optimal growth models and the Lagrange multiplier," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 393-410, June.
    2. Peleg, Bezalel & Yaari, Menahem E, 1970. "Markets with Countably Many Commodities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 369-377, October.
    3. Datta, Manjira & Mirman, Leonard J. & Reffett, Kevin L., 2002. "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Journal of Economic Theory, Elsevier, vol. 103(2), pages 377-410, April.
    4. Cuong Le Van & Yiannis Vailakis, 2003. "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 743-771, November.
    5. Greenwood Jeremy & Huffman Gregory W., 1995. "On the Existence of Nonoptimal Equilibria in Dynamic Stochastic Economies," Journal of Economic Theory, Elsevier, vol. 65(2), pages 611-623, April.
    6. Cuong Le Van & Yiannis Vailakis, 2004. "Existence of competitive equilibrium in a single-sector growth model with elastic labour," Cahiers de la Maison des Sciences Economiques b04123, Université Panthéon-Sorbonne (Paris 1).
    7. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-1053, September.
    8. Le Van, Cuong & Cagri Saglam, H., 2004. "Optimal growth models and the Lagrange multiplier," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 393-410, June.
    9. Florenzano, Monique, 1983. "On the existence of equilibria in economies with an infinite dimensional commodity space," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 207-219, December.
    10. Cuong Le Van & Yiannis Vailakis, 2003. "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," Post-Print halshs-00119095, HAL.
    11. Coleman, Wilbur II, 1997. "Equilibria in Distorted Infinite-Horizon Economies with Capital and Labor," Journal of Economic Theory, Elsevier, vol. 72(2), pages 446-461, February.
    12. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898, Elsevier.
    13. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    14. Dechert, W. D., 1982. "Lagrange multipliers in infinite horizon discrete time optimal control models," Journal of Mathematical Economics, Elsevier, vol. 9(3), pages 285-302, March.
    15. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    1. Cuong Le Van & Manh Hung Nguyen, 2005. "Existence of competitive equilibrium in a single-sector growth model with heterogeneous agents and endogenous leisure," Cahiers de la Maison des Sciences Economiques b05092, Université Panthéon-Sorbonne (Paris 1).

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    More about this item

    Keywords

    Optimal growth model; Lagrange multipliers; competitive equilibrium; elastic labor supply;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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