Monotonicity and continuity of the critical capital stock in the Dechert–Nishimura model

Abstract

We show that the critical capital stock of the Dechert-Nishimura (1983) model is a decreasing and continuous function of the discount factor. We also show that the critical capital stock merges with a nonzero steady state as the discount factor decreases to a certain boundary value, and that the critical capital stock converges to the minimum sustainable capital stock as the discount factor increases to another boundary value.

Saddle-node bifurcations in an optimal growth model with preferences for wealth habit

“…Then, k l (β, η, γ) and k h (β, η, γ) are strictly increasing, k c (β, η, γ) is strictly decreasing in β∈[β 0 , 1) and η > 0. Akao, Kamihigashi, and Nishimura (2011) analyzes the monotonicity and the continuity of the critical capital stock in the discount factor in a Dechert and Nishimura (1983) framework. Dechert and Nishimura (1983) concentrates on the effects of non-convex technology on the long-run growth paths.…”

“…Belonging to such classes of models with positive cross partials, we show that the minor differences not only in the weight of wealth in utility but also in the degree of wealth habit lead to permanent differences in the optimal path. Akao, Kamihigashi, and Nishimura (2011) shows that the critical capital stock of the Dechert and Nishimura (1983) model is a decreasing and continuous function of the discount factor so that a small change in the discount factor does not cause a sudden regime shift unless the economy is exactly at the critical capital stock. In this paper, we show the corresponding results in a standard optimal growth model augmented by wealth habit in utility.…”

A simple characterisation for sustained growth

“…Dechert & Nishimura [8] extend their works to a general non-concave production function. These works prove the existence of a critical level of capital stock, usually named "Dechert-Nishimura-Skiba" point 1 . Beginning with a level capital stock under this level, the economy shrinks and collapses to zero, otherwise it increases to a steady state.…”

Optimal Growth Strategy under Dynamic Threshold

“…Consider an economy in which the technology exhibits nonconvexities due to fixed costs associated with production. According to Dechert and Nishimura () and its extensions (e.g., Mitra and Ray ; Kamihigashi and Roy ; Hung, Le Van, and Michel ; Akao, Kamihigashi, and Nishimura ), such an economy can fall into a poverty trap if its initial capital or income falls short of the fixed cost inherent in production. However, to what extent these analyses are robust to the considerations of incentives for investment to decrease the fixed costs in production, still remains unanswered: Can such an underdeveloped economy eventually catch up with the developing ones if endowed with a technology to reduce the fixed costs?…”