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The competitive equilibrium: A qualitative analysis

Quirk, James P. (1969) The competitive equilibrium: A qualitative analysis. In: Economic Models, Estimation and Risk Programming: Essays in Honor of Gerhard Tintner. Lecture Notes in Operations Research and Mathematical Economics. No.15. Springer , Berlin, Heidelberg, pp. 58-85. ISBN 9783540046387.

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In value and Capital, Hicks [1] discussed the comparative statics properties of the competitive equilibrium in two qualitatively specified cases: (i) the case in which all commodities are “gross substitutes,” i.e., an increase in the price of commodity i leads to an increase in excess demand for commodity j (i ≠ j); (ii) the “Morishima” case in which all commodities obey the rules “substitutes of substitutes are substitutes, complements of substitutes and substitutes of complements are complements, and complements of complements are substitutes.” In his comparative statics analysis, Hicks assumed that equilibrium positions of the competitive economy were characterized by Hicksian perfect stability. Following Hicks’ work, Mosak [2] extended certain of the Hicksian propositions concerning the gross substitute case, Metzler [3] proved the equivalence of Hicksian perfect stability and local dynamic stability in the sense of Samuelson [4] for the gross substitute case, and Arrow, Block and Hurwicz [5] established global stability of the competitive equilibrium for this case. McKenzie [6] proved that local stability occurs in the gross substitute case if and only if the coefficient matrix of the system is quasi-dominant diagonal. Arrow and Hurwicz [7], and McKenzie [6] established results similar to those noted above for the gross substitute case for the more general case of indecomposable systems involving weak gross substitutes (an increase in the price of commodity i leads to either an increase or to no change in excess demand for commodity j (i ≠ j)).

Item Type:Book Section
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URLURL TypeDescription ItemBook
Alternate Title:Qualitative Economics & Competitive Equilibrium
Additional Information:© Springer-Verlag Berlin · Heidelberg 1969. Originally issued as Social Science Working Paper 4, entitled "Qualitative Economics & Competitive Equilibrium". This work was supported in part under a grant from the National Science Foundation. This paper will be presented at the meetings of the Western Economics Association in Boulder, Colorado, August 24, 1967.
Group:Social Science Working Papers
Funding AgencyGrant Number
Subject Keywords:Sign Pattern ; Excess Demand ; Competitive Equilibrium ; Competitive Condition ; Frobenius Theorem
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Social Science Working Paper4
Series Name:Lecture Notes in Operations Research and Mathematical Economics
Issue or Number:15
Record Number:CaltechAUTHORS:20171207-155215494
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83744
Deposited By: Jacquelyn Bussone
Deposited On:21 Dec 2017 18:39
Last Modified:15 Nov 2021 20:13

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