The second fundamental theorem of positive economics
AbstractWelfare 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).
Download InfoIf 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.
Bibliographic InfoArticle provided by The International Society for Economic Theory in its journal International Journal of Economic Theory.
Volume (Year): 8 (2012)
Issue (Month): 2 (06)
Contact details of provider:
Web page: http://www.blackwellpublishing.com/journal.asp?ref=1742-7355
Other versions of this item:
- Mukherji, Anjan, 2012. "The Second Fundamental Theorem of Positive Economics," Working Papers 12/98, National Institute of Public Finance and Policy.
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.
- 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.
- 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.
- 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.
- 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.
- Antoine Billot, 2007. "How to shake the Invisible Hand (when Robinson meets Friday)," PSE Working Papers halshs-00588081, HAL.
- Anjan Mukherji, 2003. "Global Stability Conditions on the Plane," ISER Discussion Paper 0589, Institute of Social and Economic Research, Osaka University.
- 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.
- 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.
- Van Der Laan, G. & Talman, A. J. J., 1987.
"A convergent price adjustment process,"
Elsevier, vol. 23(2), pages 119-123.
- 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.
- Herings, P.J.J., 1994. "A globally and universally stable price adjustment process," Discussion Paper 1994-52, Tilburg University, Center for Economic Research.
- Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
- Venkatesh Bala, 1997. "A pitchfork bifurcation in the tatonnement process," Economic Theory, Springer, vol. 10(3), pages 521-530.
- Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
- Mukherji, Anjan, 1995. "A Locally Stable Adjustment Process," Econometrica, Econometric Society, vol. 63(2), pages 441-48, 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
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.