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.
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