On "sectoral supply functions" and some critical roles for the consumptions and leisure arbitrages in the stability properties of a competitive equilibrium with heterogeneous goods
AbstractAbstract This article appraises a pareto-optimal competitive equilibrium with heterogeneous consumption goods through a new representation of competitive prices and the building of a pair of new aggregate structures labelled "sectoral supply functions" -- SSF -- that are defined over the aggregate values of the inputs and the relative price of the capital good. An alternative dual appraisal of a class of preferences that take explicit account of heterogeneous consumptions and leisure arbitrages then allows for an unrestricted class of general statements on the stability properties of an optimal accumulation environment that subsumes earlier results as special cases. These are based upon the features of Hicksian demands and it is argued that the retainment of a given sectoral configuration in factors shares and the imposition of concavity and positive income elasticities do not suffice to rule out optimal cycles if consumptions or leisure considered by pairs happen to exhibit complementaries. The SSF approach is finally argued to outshine the PPF protocole because it allows for a simple explicit derivation in the Cobb-Douglas case that have become, since the seminal contribution of Benhabib and Farmer in the nineties, the cornerstone of macroeconomic analysis.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 46 (2010)
Issue (Month): 6 (November)
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Web page: http://www.elsevier.com/locate/jmateco
Sectoral supply functions Production possibility frontier Hicksian demands Saddlepoint property Consumption-leisure arbitrages Cobb-Douglas technologies;
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- Jess Benhabib & Roger E.A. Farmer, 1992.
"Indeterminacy and Increasing Returns,"
UCLA Economics Working Papers
646, UCLA Department of Economics.
- Becker, Robert A. & Tsyganov, Eugene N., 2002. "Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households," Journal of Economic Theory, Elsevier, vol. 105(1), pages 188-225, July.
- Nishimura, Kazuo, 1985. "Competitive equilibrium cycles," Journal of Economic Theory, Elsevier, vol. 35(2), pages 284-306, August.
- Emmanuel M. Drandakis, 1963. "Factor Substitution in the Two-Sector Growth Model," Cowles Foundation Discussion Papers 154R, Cowles Foundation for Research in Economics, Yale University.
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