Dynamic optimization with a nonsmooth, nonconvex technology: The case of a linear objective function

Takashi Kamihigashi and Santanu Roy

No 175, Discussion Paper Series from Research Institute for Economics & Business Administration, Kobe University

Abstract: This paper studies a one-sector optimal growth model with linear utility in which the production function is only required to be increasing and upper semicontinuous. The model also allows for a general form of irreversible investment. We show that every optimal capital path is strictly monotone until it reaches a steady state; further, it either converges to zero, or reaches a positive steady state in finite time and possibly jumps among different steady states afterwards. We establish conditions for extinction (convergence to zero), survival (boundedness away from zero), and the existence of a critical capital stock below which extinction is possible and above which survival is ensured. These conditions generalize those known for the case of S-shaped production functions. We also show that as the discount factor approaches one, optimal paths converge to a small neighborhood of the capital stock that maximizes sustainable consumption.

Keywords: Nonconvex; nonsmooth; and discontinuous technology; Extinction; Survival; Turnpike; Linear utility (search for similar items in EconPapers)
Pages: 21 pages
Date: 2005-08
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Citations: View citations in EconPapers (2)

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https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp175.pdf First version, 2005 (application/pdf)

Related works:
Journal Article: Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function (2006)
Working Paper: Dynamic Optimization with a Nonsmooth, Nonconvex Technology: The Case of a Linear Objective Function (2004)
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