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Mathematics for Stability and Optimization of Economic Systems

Editor

Listed:
  • Shell, Karl

Author

Listed:
  • Murata, Yasuo

Abstract

Economic Theory and Mathematical Economics: Mathematics for Stability and Optimization of Economic Systems provides information pertinent to the stability aspects and optimization methods relevant to various economic systems. This book presents relevant mathematical theorems sufficient to develop important economic systems, including Leontief input–output systems, Keynesian dynamic models, the Ramsey optimal accumulation systems, and von Neumann expanding economic systems. Organized into two parts encompassing nine chapters, this book begins with an overview of useful theorems on matrices, eigenvalue problems, and matrices with dominant diagonals and P-matrices. This text then explores the linear transformations on vector spaces. Other chapters consider the Hawkins–Simon theorem concerning non-negative linear systems. This book discusses as well the dual linear relations and optimization methods applicable to inequality economic systems. The final chapter deals with powerful optimal control method for dynamical systems. This book is a valuable resource for mathematicians, economists, research workers, and graduate students.

Suggested Citation

  • Murata, Yasuo, 1977. "Mathematics for Stability and Optimization of Economic Systems," Elsevier Monographs, Elsevier, edition 1, number 9780125112505 edited by Shell, Karl.
  • Handle: RePEc:eee:monogr:9780125112505
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    References listed on IDEAS

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    1. D. Cass & J. E. Stiglitz, 1972. "Risk Aversion and Wealth Effects on Portfolios with Many Assets," Review of Economic Studies, Oxford University Press, vol. 39(3), pages 331-354.
    2. Bhagwati, Jagdish N. & Srinivasan, T. N., 1976. "Optimal trade policy and compensation under endogenous uncertainty: The phenomenon of market disruption," Journal of International Economics, Elsevier, vol. 6(4), pages 317-336, November.
    3. Batra, Raveendra N & Russell, William R, 1974. "Gains from Trade Under Uncertainty," American Economic Review, American Economic Association, vol. 64(6), pages 1040-1048, December.
    4. Ruffin, Roy J., 1974. "International trade under uncertainty," Journal of International Economics, Elsevier, vol. 4(3), pages 243-259, August.
    5. Ethier, Wilfred, 1974. "Some of the theorems of international trade with many goods and factors," Journal of International Economics, Elsevier, vol. 4(2), pages 199-206, May.
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    7. Kemp, Murray C. & Ohyama, Michihiro, 1978. "The gain from free trade under conditions of uncertainty," Journal of International Economics, Elsevier, vol. 8(1), pages 139-141, February.
    8. Stephen J. Turnovsky, 1974. "Technological and Price Uncertainty in a Ricardian Model of International Trade," Review of Economic Studies, Oxford University Press, vol. 41(2), pages 201-217.
    9. K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," Review of Economic Studies, Oxford University Press, vol. 31(2), pages 91-96.
    10. Anderson, James E & Riley, John G, 1976. "International Trade with Fluctuating Prices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 76-97, February.
    11. Steinar Ekern & Robert Wilson, 1974. "On the Theory of the Firm in an Economy with Incomplete Markets," Bell Journal of Economics, The RAND Corporation, vol. 5(1), pages 171-180, Spring.
    12. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    13. Sandwip K. Das, 1977. "Uncertainty and the Heckscher-Ohlin Theorem: A Comment," Review of Economic Studies, Oxford University Press, vol. 44(1), pages 189-190.
    14. Ruffin, Roy J., 1974. "Comparative advantage under uncertainty," Journal of International Economics, Elsevier, vol. 4(3), pages 261-273, August.
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