From Linear to Nonlinear Utility in Vintage Capital Models

Abstract

Optimization problems with nonlinear utility and endogenous capital lifetime are investigated in one- and two-sector modifications of the Solow vintage capital model. Both models have the same balanced growth path in the case of exponential technological change and labour. Turnpike theorems in normal form are proved for the optimal capital lifetime in both models. The differences between the cases of the linear and nonlinear utility are highlighted.

Keywords:

• balanced growth path
• capital lifetime
• nonlinear utility
• optimization
• turnpike theorems
• vintage capital models

Notes

¹The authors are thankful to Renan Goetz (University of Girona, Spain) for bringing their attention to the equivalence of problems (30) and (31)–(35).