Premium
Stability of Spatial Equilibrium *
Author(s) -
Tabuchi Takatoshi,
Zeng DaoZhi
Publication year - 2004
Publication title -
journal of regional science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.171
H-Index - 79
eISSN - 1467-9787
pISSN - 0022-4146
DOI - 10.1111/j.0022-4146.2004.00352.x
Subject(s) - diseconomies of scale , jacobian matrix and determinant , eigenvalues and eigenvectors , stability (learning theory) , economies of agglomeration , economics , class (philosophy) , public good , equilibrium solution , externality , mathematical economics , general equilibrium theory , mathematics , exponential stability , microeconomics , computer science , physics , quantum mechanics , machine learning , artificial intelligence , economies of scale , nonlinear system
Abstract. Asymptotic stability of equilibrium is often difficult to know when the number of variables exceeds four, since all eigenvalues of the Jacobian matrix are not analytically solvable. However, we obtain stability conditions for a general class of migration dynamics without computing eigenvalues. We show that a spatial equilibrium is stable in the presence of strong congestion diseconomies, but unstable in the presence of strong agglomeration economies. We also show existence of a stable equilibrium in the case of negligible interregional externalities, which is applicable to club goods, local public goods, and new economic geography.