Existence, uniqueness, and computation of short-run and long-run equilibria of the Dixit–Stiglitz–Krugman model in an urban setting

• Published in: Applied mathematics and computation Vol. 234; pp. 339 - 355
• Main Authors: Tabata, Minoru, Eshima, Nobuoki, Sakai, Yuusuke
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.05.2014
• Subjects: Computation; Dixit–Stiglitz–Krugman model; Economics; Fixed point theorem; Long-run equilibrium; Mathematical analysis; Mathematical models; Movements; Short-run equilibrium; Uniqueness; Urban environments; Urban setting; Wages; Short-run equilibrium; Fixed point theorem; Dixit–Stiglitz–Krugman model; Urban setting; Long-run equilibrium
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2014.02.014

•The Dixit–Stiglitz–Krugman model is studied in an urban setting.•The model has a unique short-run equilibrium.•The model has a unique long-run equilibrium.•Short-run equilibria are obtained numerically. This study analyzes the short-run and long-run equilibria of the Dixit–Stiglitz–Krugman model, without accounting for agriculture. The model, within the branch of New Economic Geography, describes the real wage distribution and worker movements motivated by the disparity in real wages in an urban setting. No restriction is imposed on the total number of locations where economic activities are conducted. We prove that this model has a short-run equilibrium, obtain a sufficient condition for its uniqueness, and construct an iteration scheme to obtain numerical short-run equilibria whose approximation errors are sufficiently small. Moreover, we prove that if the elasticity of substitution and the transport costs are sufficiently large, then the model has a unique long-run equilibrium.