Critical Capital Stock in a Continuous-Time Growth Model with a Convex-Concave Production Function

Ken-Ichi Akao, Takashi Kamihigashi and Kazuo Nishimura

No DP2015-39, Discussion Paper Series from Research Institute for Economics & Business Administration, Kobe University

Abstract: The critical capital stock is a threshold that appears in a nonconcave aggregate growth model such that any optimal capital path from a stock level below the threshold converges to a lower steady state, whereas any optimal capital path from a stock level above the threshold converges to a higher steady state. Unlike a concave model with wealth effect, the threshold is not necessarily an optimal steady state, which makes its characterization difficult. In a continuous-time growth model with a convex-concave production function, we show that: a) the critical capital stock is continuous and strictly increasing in the discount rate; b) as the discount rate increases, it appears at the zero-stock level and disappears at a certain level between the stock levels of the maximum average productivity and the maximum marginal productivity; c) at this upper bound, it merges with the higher steady state; d) once the critical capital stock disappears, the higher steady state is no longer an optimal steady state; and e) the disappearing point can be arbitrarily close to either of the these stock levels, depending on the curvature of the utility function.

Keywords: Continuous-time growth model; Convex-concave production function; Critical capital stock (search for similar items in EconPapers)
JEL-codes: C61 D90 O41 (search for similar items in EconPapers)
Pages: 42 pages
Date: 2015-09
New Economics Papers: this item is included in nep-eff and nep-gro
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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