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

We show that the critical capital stock of the Dechert and 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. ► We study the critical capital stock of the Dechert–Nishimura model. ► We show that it is a decreasing and continuous function of the discount factor beta. ► It merges with a nonzero steady state as beta decreases to a certain boundary value. ► It converges to a positive value as beta increases to another boundary value.