Discounting Thresholds and Critical Capital Stock in Economic Dynamics
Abstract
We study a class of dynamic economic problems with a general supermodular payoff function and examine how the discount factor determines the existence of a critical capital stock. If the initial capital stock is above this threshold, the economy converges to a positive steady state; if it is below, it converges to zero. We show that, under mild conditions, there exists a non-degenerate interval of discount factors for which such a critical threshold exists. Outside this interval, long-run the dynamics are global: the economy converges either always to zero or always to a positive steady state, regardless of the initial state. We also apply our approach to the classical Ramsey-Cass-Koopmans framework and shed new light on conditions leading to a critical capital stock in that setting.
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