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Optimization of Economic Renovation

In: Mathematical Modeling in Economics, Ecology and the Environment

Author

Listed:
  • Natali Hritonenko

    (Prairie View A&M University)

  • Yuri Yatsenko

    (Houston Baptist University)

Abstract

This chapter analyzes optimization problems in the economic models with heterogeneous capital and labor of Chap. 4 . Such models are important in explaining economic modernization under improving technology. Section 5.1 provides a qualitative analysis of the continuous-time optimization problem of one-machine replacement from Sect. 4.4 using standard tools of nonlinear optimization. Section 5.2 explores the optimal modernization of vintage capital in a profit-maximizing firm under environmental constraints. Section 5.3 investigates an optimization problem with nonlinear utility in the Ramsey vintage capital model of Sect. 4.2 . A balanced growth regime is established and analyzed under exponential technology and labor. It possesses new properties compared to the linear utility case. Section 5.4 contains a mathematical appendix that derives extremum conditions for vintage capital models using variation techniques and Lagrange multipliers.

Suggested Citation

  • Natali Hritonenko & Yuri Yatsenko, 2013. "Optimization of Economic Renovation," Springer Optimization and Its Applications, in: Mathematical Modeling in Economics, Ecology and the Environment, edition 2, chapter 0, pages 105-130, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-9311-2_5
    DOI: 10.1007/978-1-4614-9311-2_5
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