Acyclicity and Dynamic Stability: Generalizations and Applications
We study the asymptotic stability of infinite horizon concave programming problems. Turnpike theorems for this class of models generally have to assume a low level of discounting. By generalizing our precedent work we provide a one-parameter family of verifiable conditions that guarantee convergence of the optimal paths to a stationary state. We call this property theta-acyclicity. In the one-dimensional case we show that supermodulatity implies our property but not viceversa. In the multidimensional case supermodularity has no relevant implications for the asymptotic behavior of optimal paths. We apply theta-acyclicity to a pair of models which study firms' dynamic behavior as based on adjustment costs. The first is the familiar model of competitive equilibrium in an industry in the presence of adjustment costs. IN the second case firms act strategically and we study the dynamic evolution implied by the closed-loop Nash equilibria. In both instances our criteria apply and allow us to obtain stability results that are much more general than those already existing in the literature.
(This abstract was borrowed from another version of this item.)
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Milgrom, P. & Shannon, C., 1991.
"Monotone Comparative Statics,"
11, Stanford - Institute for Thoretical Economics.
- McKenzie, Lionel W, 1976.
Econometric Society, vol. 44(5), pages 841-865, September.
- Robert E. Lucas & Jr., 1967. "Adjustment Costs and the Theory of Supply," Journal of Political Economy, University of Chicago Press, vol. 75, pages 321-321.
- Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
- Araujo, A & Scheinkman, Jose A, 1977. "Smoothness, Comparative Dynamics, and the Turnpike Property," Econometrica, Econometric Society, vol. 45(3), pages 601-620, April.
- Chaim Fershtman & Eitan Muller, 1984.
"Turnpike Properties of Capital Accumulation Games,"
604, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Flaherty, M Therese, 1980. "Industry Structure and Cost-Reducing Investment," Econometrica, Econometric Society, vol. 48(5), pages 1187-1209, July.
- J. P. Gould, 1968. "Adjustment Costs in the Theory of Investment of the Firm," Review of Economic Studies, Oxford University Press, vol. 35(1), pages 47-55.
- Brock, William A. & Scheinkman, JoseA., 1976.
"Global asymptotic stability of optimal control systems with applications to the theory of economic growth,"
Journal of Economic Theory,
Elsevier, vol. 12(1), pages 164-190, February.
- William A. Brock & Jose A. Scheinkman, 1974. "Global Asymptotic Stability of Optimal Control Systems with Applications to the Theory of Economic Growth," Discussion Papers 85, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Fershtman, Chaim & Muller, Eitan, 1984.
"Capital accumulation games of infinite duration,"
Journal of Economic Theory,
Elsevier, vol. 33(2), pages 322-339, August.
- Treadway, Arthur B, 1971. "The Rational Multivariate Flexible Accelerator," Econometrica, Econometric Society, vol. 39(5), pages 845-855, September.
- Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-681, September.
- Dechert, Dee, 1978. "Optimal control problems from second-order difference equations," Journal of Economic Theory, Elsevier, vol. 19(1), pages 50-63, October.
- Mortensen, Dale T, 1973. "Generalized Costs of Adjustment and Dynamic Factor Demand Theory," Econometrica, Econometric Society, vol. 41(4), pages 657-665, July.
- Uzawa, H, 1969. "Time Preference and the Penrose Effect in a Two-Class Model of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 77(4), pages 628-652, Part II, .
- McKenzie, Lionel W., 1979. "Optimal Economic Growth and Turnpike Theorems," Working Papers 267, California Institute of Technology, Division of the Humanities and Social Sciences.
- Vives, X., 1988.
"Nash Equilibrium With Strategic Complementarities,"
UFAE and IAE Working Papers
107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Magill, Michael J P & Scheinkman, Jose A, 1979. "Stability of Regular Equilibria and the Correspondence Principle for Symmetric Variational Problems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(2), pages 297-315, June.
- DasGupta, S., 1985. "A local analysis of stability and regularity of stationary states in discrete symmetric optimal capital accumulation models," Journal of Economic Theory, Elsevier, vol. 36(2), pages 302-318, August.
- Alexandre Scheinkman, Jose, 1976. "On optimal steady states of n-sector growth models when utility is discounted," Journal of Economic Theory, Elsevier, vol. 12(1), pages 11-30, February.
- Fumio Hayashi, 1981.
"Tobin's Marginal q and Average a : A Neoclassical Interpretation,"
457, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Hayashi, Fumio, 1982. "Tobin's Marginal q and Average q: A Neoclassical Interpretation," Econometrica, Econometric Society, vol. 50(1), pages 213-224, January.
- Boldrin, Michele & Montrucchio, Luigi, 1988. "Acyclicity and Stability of Intertemporal Optimization Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 137-146, February.
When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:65:y:1995:i:2:p:303-326. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.