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The second fundamental theorem of positive economics
Author(s) -
Mukherji Anjan
Publication year - 2012
Publication title -
international journal of economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.351
H-Index - 11
eISSN - 1742-7363
pISSN - 1742-7355
DOI - 10.1111/j.1742-7363.2012.00181.x
Subject(s) - competitive equilibrium , mathematical economics , economics , zero (linguistics) , endowment , jacobian matrix and determinant , rank (graph theory) , function (biology) , mathematics , combinatorics , linguistics , philosophy , epistemology , evolutionary biology , biology
The paper examines what result, apart from the existence of competitive equilibrium, may be called a Fundamental Theorem of Positive Economics. It is shown first that if, for any distribution of the aggregate endowment, the matrix sum of the Jacobian of the excess demand function plus its transpose, evaluated at equilibrium, has maximal rank, then equilibrium will be locally asymptotically stable. It is next shown that redistributing resources will always make a competitive equilibrium price configuration stable provided that the rank condition referred to earlier holds at zero‐trade competitive equilibria: this is the Second Fundamental Theorem of Positive Economics.