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).
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Bibliographic InfoPaper provided by National Institute of Public Finance and Policy in its series Working Papers with number 12/98.
Date of creation: Mar 2012
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Note: Working Paper 98, 2012
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Stability of equilibrium ; Redistribution of resources ; Rank condition ; Fundamental theorems;
Other versions of this item:
- Anjan Mukherji, 2012. "The second fundamental theorem of positive economics," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(2), pages 125-138, 06.
- NEP-ALL-2012-03-21 (All new papers)
- NEP-HPE-2012-03-21 (History & Philosophy of Economics)
- NEP-MIC-2012-03-21 (Microeconomics)
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- Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
- 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.
- 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.
- 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.
- Antoine Billot, 2007.
"How to shake the Invisible Hand (when Robinson meets Friday),"
PSE Working Papers
- 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.
- Venkatesh Bala, 1997. "A pitchfork bifurcation in the tatonnement process," Economic Theory, Springer, vol. 10(3), pages 521-530.
- Laan, G. van der & Talman, A.J.J., 1987.
"A convergent price adjustment process,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-154936, Tilburg University.
- 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.
- 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.
- 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.
- 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.
- 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.
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