AN ABSTRACT MODEL OF ECONOMIC DYNAMICS FOR SECOND ORDER DISCRETE INCLUSIONS


Mahmudov E., Güloğlu B., Mastalieva D.

Advanced Mathematical Models and Applications, vol.7, no.3, pp.292-305, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 3
  • Publication Date: 2022
  • Journal Name: Advanced Mathematical Models and Applications
  • Journal Indexes: Scopus
  • Page Numbers: pp.292-305
  • Keywords: Conjugate, duality, Euler-Lagrange, fixed-point, infimal convolution, Neumann-Gale, polyhedral
  • Istanbul Technical University Affiliated: Yes

Abstract

© 2022, Jomard Publishing. All rights reserved.The paper deals with the abstract model of economic dynamics described by second order discrete inclusions. Then based on the concept of infimal convolution, we construct dual problems for discrete inclusions and prove the duality results. It seems that the Euler-Lagrange type inclusions are ”duality relations” for both primal and dual problems. For a set-valued mapping, the graph of which is a cone, the locally adjoint mapping is calculated, and then the necessary and sufficient conditions of optimality are formulated in terms of prices. The Neumann-Gale model is investigated in detail. For the optimal trajectory, there are such prices that when choosing the intensities of the technological capacity of production at a given moment in time, the optimal trajectory corresponds to the one that provides the maximum income in the prices of the next instant time. Finally, in term of prices duality in problems with second order model with polyhedral discrete inclusions are considered.