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Comparative Dynamics via Envelope Methods in Variational Calculus

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  • Caputo, Michael R

Abstract

The primal-dual methodology of P. A. Samuelson (1965) is extended and applied to a nonautonomous variational calculus problem with a fixed vector of initial stocks, fixed initial and terminal time values, a free vector of terminal stocks, and a time-independent vector of parameters. It is shown that, if the solution of the variational problem is smooth enough, the qualitative effects of parameter perturbations on the entire optimal arcs can be represented by a generalized Slutsky-type matrix, which holds in integral form and is symmetric negative semidefinite. Sufficient conditions for the optimal value function to be convex in the parameters are also given. Copyright 1990 by The Review of Economic Studies Limited.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Review of Economic Studies.

Volume (Year): 57 (1990)
Issue (Month): 4 (October)
Pages: 689-97

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Handle: RePEc:bla:restud:v:57:y:1990:i:4:p:689-97

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Cited by:
  1. Micahel Caputo & Chen Ling, 2012. "The Intrinsic Comparative Dynamics of Locally Differentiable Feedback Nash Equilibria of Autonomous and Exponentially Discounted Infinite Horizon Differential Games," Working Papers 2012-03, University of Central Florida, Department of Economics.
  2. Caputo, Michael R. & Wilen, James E., 1995. "Optimality conditions and comparative statics for horizon and endpoint choices in optimal control theory," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 351-369.
  3. Löfgren, Karl-Gustaf, 2011. "On Envelope Theorems in Economics: Inspired by a Revival of a Forgotten Lecture," UmeÃ¥ Economic Studies 830, Umeå University, Department of Economics.
  4. Barney, L. Jr., 1997. "Uncertainty and the comparative dynamics of stock price," International Review of Economics & Finance, Elsevier, vol. 6(4), pages 405-419.
  5. YIlmaz, Ensar, 2011. "Income distribution, efficiency and rationing," Economic Modelling, Elsevier, vol. 28(3), pages 1247-1255, May.
  6. Ngo Long & Horst Siebert, 1992. "A model of the socialist firm in transition to a market economy," Journal of Economics, Springer, vol. 56(1), pages 1-21, February.
  7. Jeffrey T. LaFrance, 1992. "Do Increased Commodity Prices Lead To More Or Less Soil Degradation?," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 36(1), pages 57-82, 04.
  8. Favard, Pascal & Karp, Larry, 2004. "How many cake-eaters? Chouette, on a du monde a diner !," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 801-815, January.
  9. Caputo, Michael R., 2003. "The comparative dynamics of closed-loop controls for discounted infinite horizon optimal control problems," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1335-1365, June.
  10. Yilmaz, Ensar & Ünveren, Burak, 2011. "Income distribution and exchange in a dynamic search model," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 665-678, October.
  11. Lichtenberg, Erik, 2004. "Cost-Responsiveness of Conservation Practice Adoption: A Revealed Preference Approach," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 29(03), December.
  12. Krysiak, Frank C., 2006. "Stochastic intertemporal duality: An application to investment under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 30(8), pages 1363-1387, August.

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