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Nonclassical Brock-Mirman Economies

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Author Info
Manjira Datta () (W. P. Carey School of Business Department of Economics)
Leonard Mirman (University of Virginia)
Kevin Reffett () (W. P. Carey School of Business Department of Economics)

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Abstract

We show that monotone methods, especially, those based on lattice theory and lattice programming can produce results, e.g., on the monotonicity of the optimal programs, as well as on the existence of fixed points, consistent with the current macroeconomics literature, in the absence of continuity, differentiability and concavity. We illustrate the use and power of the lattice theory techniques in two simple and very useful models. First, the Brock-Mirman growth model is studied in a nonclassical setting. Here all the assumptions of the original model are made except that the production function is allowed to be non-concave. The second model is an extension of the Brock-Mirman model that goes beyond the planner's solution and allows for decentralized decisions in equilibrium. JEL Classification: C61, C62, D90, E60

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Paper provided by Department of Economics, W. P. Carey School of Business, Arizona State University in its series Working Papers with number 2179544.

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Handle: RePEc:asu:wpaper:2179544

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  1. Manjira Datta & Leonard J. Mirman & Olivier F. Morand & Kevin L. Reffett, 2002. "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Tinbergen Institute Discussion Papers 02-086/2, Tinbergen Institute. [Downloadable!]
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  2. 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. [Downloadable!] (restricted)
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  3. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September. [Downloadable!] (restricted)
  4. Manjira Datta & Leonard J. Mirman & Olivier F. Morand & Kevin L. Reffett, 2005. "Markovian Equilibrium in Infinite Horizon Economies with Incomplete Markets and Public Policy," Tinbergen Institute Discussion Papers 05-013/2, Tinbergen Institute. [Downloadable!]
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  5. Mark Huggett, 2003. "When Are Comparative Dynamics Monotone?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(1), pages 1-11, January. [Downloadable!] (restricted)
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  6. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January. [Downloadable!] (restricted)
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  7. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February. [Downloadable!] (restricted)
  8. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, vol. 66(2), pages 409-426, March.
  9. Amir, Rabah, 1997. "A new look at optimal growth under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 67-86, November. [Downloadable!] (restricted)
  10. Le Van, C. & Morhaim, L., 2000. "Optimal Growth Models with Bounded or Unbounded Returns : a Unifying Approach," Papiers d'Economie Mathématique et Applications 2000.64, Université Panthéon-Sorbonne (Paris 1).
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  11. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-406, November. [Downloadable!] (restricted)
  12. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
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  14. Amir, Rabah & Mirman, Leonard J & Perkins, William R, 1991. "One-Sector Nonclassical Optimal Growth: Optimality Conditions and Comparative Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 625-44, August. [Downloadable!] (restricted)
  15. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September. [Downloadable!] (restricted)
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  16. Coleman, Wilbur II, 2000. "Uniqueness of an Equilibrium in Infinite-Horizon Economies Subject to Taxes and Externalities," Journal of Economic Theory, Elsevier, vol. 95(1), pages 71-78, November. [Downloadable!] (restricted)
  17. Marco LiCalzi & Arthur F. Veinott, 2005. "Subextremal functions and lattice programming," GE, Growth, Math methods 0509001, EconWPA. [Downloadable!]
  18. David Levhari & Leonard J. Mirman, 1980. "The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 322-334, Spring. [Downloadable!] (restricted)
  19. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July. [Downloadable!] (restricted)
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  20. Manjira Datta & Leonard Mirman & Olivier Morand & Kevin Reffett, . "Lattice Methods in Computation of Sequential Markov Equilibrium in Dynamic Games," Working Papers 2179545, Department of Economics, W. P. Carey School of Business, Arizona State University. [Downloadable!]
  21. 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. [Downloadable!] (restricted)
  22. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141. [Downloadable!] (restricted)
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  23. Leonard J Mirman & Olivier F. Morand & Kevin L. Reffett, 2004. "A Qualitative Approach to Markovian Equilibrium in Infinite Horizon Economies with Capital," Levine's Bibliography 122247000000000224, UCLA Department of Economics. [Downloadable!]
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  24. Robert E. Lucas, Jr. & Nancy L. Stokey, 1987. "Money and Interest in a Cash-in-Advance Economy," NBER Working Papers 1618, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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