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Nonclassical Brock-Mirman Economies

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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  1. 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.
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  3. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
  4. 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.
  5. Stachurski, J., 2001. "Stochastic Optimal Growth with Unbounded Shock," Department of Economics - Working Papers Series 777, The University of Melbourne.
  6. Datta, Manjira & Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2005. "Markovian equilibrium in infinite horizon economies with incomplete markets and public policy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 505-544, August.
  7. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
  8. Robert E. Lucas, Jr. & Nancy L. Stokey, 1985. "Money and Interest in a Cash-in-Advance Economy," NBER Working Papers 1618, National Bureau of Economic Research, Inc.
  9. Olivier F. Morand & Kevin L. Reffett, 2001. "Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies," Working papers 2001-02, University of Connecticut, Department of Economics.
  10. 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.
  11. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  12. 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.
  13. Kevin Reffett & Manjira Datta & Leonard Mirman & Olivier Morand, . "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Working Papers 2133476, Department of Economics, W. P. Carey School of Business, Arizona State University.
  14. Marco LiCalzi & Arthur F. Veinott, 2005. "Subextremal functions and lattice programming," GE, Growth, Math methods 0509001, EconWPA.
  15. Jeremy Greenwood & Gregory W. Huffman, 1993. "On the existence of nonoptimal equilibria in dynamic stochastic economies," Research Paper 9330, Federal Reserve Bank of Dallas.
  16. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
  17. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
  18. Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
  19. Le Van, Cuong & Morhaim, Lisa, 2002. "Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach," Journal of Economic Theory, Elsevier, vol. 105(1), pages 158-187, July.
  20. 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.
  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.
  22. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
  23. 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.
  24. Manjira Datta & Leonard Mirman & Kevin Reffett, . "Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor," Working Papers 2132846, Department of Economics, W. P. Carey School of Business, Arizona State University.
  25. Amir, R., 1991. "Sensitivity analysis of multi-sector optimal economic dynamics," CORE Discussion Papers 1991006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  26. 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.
  27. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-82, September.
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