The Second Fundamental Theorem of Positive Economics
Welfare Economics is fortunate that there are two Fundamental Theorems of Welfare Economics. Positive Economics on the other hand is seemingly endowed with none. One of the fundamental results of Positive Economics is that a competitive equilibrium exists under fairly general conditions; this then may be called the First Fundamental Theorem of Positive Economics (FFTPE). The existing results on uniqueness and stability of competitive equilibrium are far too restrictive to be up for consideration as a Fundamental Theorem. It is to re-examine this question that we revisit the question of stability of competitive equilibrium. It is shown that if, for all distributions of the aggregate endowment, the matrix sum of the Jacobian of the excess demand function plus its transpose, evaluated at the equilibrium, have maximal rank then equilibria will be locally asymptotically stable. When this condition is not met, it is shown how redistributing resources will always make a competitive equilibrium price configuration stable and this need not involve redistributing endowments so that trades do not exist at equilibrium. This last result is quite general and the only requirement is that the rank condition referred to earlier hold at zero trade competitive equilibria and consequently may qualify to be called the Second Fundamental Theorem of Positive Economics (SFTPE).
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.:
- Hirota, Masayoshi, 1981. "On the Stability of Competitive Equilibrium and the Patterns of Initial Holdings: An Example," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 461-67, June.
- Herings, P.J.J., 1994.
"A globally and universally stable price adjustment process,"
1994-52, Tilburg University, Center for Economic Research.
- Jean-Jacques Herings, P., 1997. "A globally and universally stable price adjustment process," Journal of Mathematical Economics, Elsevier, vol. 27(2), pages 163-193, March.
- Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
- Antoine Billot, 2009. "How to shake the invisible hand (when Robinson meets Friday)," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(3), pages 257-270.
- Van Der Laan, G. & Talman, A. J. J., 1987.
"A convergent price adjustment process,"
Elsevier, vol. 23(2), pages 119-123.
- Anjan Mukherji, 2003. "Global Stability Conditions on the Plane," ISER Discussion Paper 0589, Institute of Social and Economic Research, Osaka University.
- Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
- Mukherji, Anjan, 1973. "On the Sensitivity of Stability Results to the Choice of the Numeraire," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 427-33, July.
- Mukherji, Anjan, 1995. "A Locally Stable Adjustment Process," Econometrica, Econometric Society, vol. 63(2), pages 441-48, March.
- Hirota, Masayoshi, 1985. "Global stability in a class of markets with three commodities and three consumers," Journal of Economic Theory, Elsevier, vol. 36(1), pages 186-192, June.
- Hirota, Masayoshi & Hsu, Ming & Plott, Chrales R. & Rogers, Brian W., 2005. "Divergence, closed cycles and convergence in scarf environments: Experiments in the dynamics of general equilibrium systems," Working Papers 1239, California Institute of Technology, Division of the Humanities and Social Sciences.
- Anderson, Christopher M. & Granat, Sander & Plott, Charles R. & Shimomura, Ken-Ichi, 2000.
"Global Instability in Experimental General Equilibrium: The Scarf Example,"
1086, California Institute of Technology, Division of the Humanities and Social Sciences.
- Anderson, Christopher M. & Plott, Charles R. & Shimomura, K.-I.Ken-Ichi & Granat, Sander, 2004. "Global instability in experimental general equilibrium: the Scarf example," Journal of Economic Theory, Elsevier, vol. 115(2), pages 209-249, April.
- repec:ner:tilbur:urn:nbn:nl:ui:12-154936 is not listed on IDEAS
- Anjan Mukherji, 2008. "Stability of a competitive economy: A reconsideration," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(2), pages 317-336.
- Venkatesh Bala, 1997. "A pitchfork bifurcation in the tatonnement process," Economic Theory, Springer, vol. 10(3), pages 521-530.
- Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
When requesting a correction, please mention this item's handle: RePEc:npf:wpaper:12/98. 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: (S.Siva Chidambaram)
If references are entirely missing, you can add them using this form.