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

► 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.