Existence and Uniqueness of Competitive Equilibrium in Input-Output Models with Neoclassical Production Functions

• Published in: Lobachevskii journal of mathematics Vol. 46; no. 1; pp. 264 - 272
• Main Author: Lavrin, O. I.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.01.2025; Springer Nature B.V
• Subjects: Algebra; Analysis; Geometry; Lipschitz condition; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Probability Theory and Stochastic Processes; Uniqueness; global uniqueness; Lagrange multipliers; fixed point theory; competitive equilibrium; convex analysis; 2010 Mathematics Subject Classification: 93A30, 97M40; Young transform; production function; input-output model
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S1995080224608191

In this paper, sufficient conditions for the existence and uniqueness of the equilibrium price index in the model of nonlinear input-output balances were established. These conditions were shown to be natural and applicable in practical settings. Moreover, for certain cases, it was possible to prove the Lipschitz continuity of the dependence of the equilibrium price index on the prices of primary resources. In the absence of capacity constraints, the uniqueness of the price index is ensured by the inability to completely substitute primary resources in the production functions.