Hyun Park () (Department of Economics, University of Essex, Colchester, CO4 3SQ, UK)
Abstract
This paper demonstrates global stability of a competitive equilibrium in a multi-sector model of many firms, each of which exhibits constant returns to scale technology, and of infinitely lived consumers, whose preferences are recursive but not necessarily additively separable. In the topology induced by a sup-norm, the dominant diagonal blocks condition (Araujo and Scheinkman (Econometrica 45, 1977)) allows us to apply the implicit function theorem to obtain continuity of the equilibrium path. If a stationary equilibrium is locally asymptotically stable, then the continuity of the equilibrium path and smoothness of a weight function on heterogeneous consumers imply that all equilibrium paths converge to the steady state. The dominant diagonal blocks condition is also shown to be sufficient for the local asymptotic turnpike property.
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Article provided by Springer in its journal Economic Theory.
Find related papers by JEL classification: C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models