Endogenous Discounting and Economic Dynamics
We study a discrete-time optimal growth model with endogenous discounting.
The discount factor may depend on both consumption and the capital stock,
and intertemporal utility is modeled as a discounted sum of instantaneous
utilities, with the sum of discount factors equal to one. We show that this specification
preserves the invariance of optimal paths and steady states to affine transformations
of the instantaneous utility function, providing a general and flexible framework for
analyzing economic dynamics under endogenous time preference. We prove that
optimal capital paths are monotonic, and steady states depend on initial conditions.
We also show the robustness of poverty traps under endogenous discounting:
in several examples, for a set of parameters with positive measure, the optimal path
converges to a positive steady state only if the initial capital stock exceeds a critical
level and otherwise converges to the origin.
