Optimization of Economic Renovation
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.
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