Endogenous time preference and optimal growth

We adapt the classic one-sector optimal growth model to include an endogenous rate of time preference along the lines of Becker and Mulligan (1997). The resulting model is both time-consistent and analytically tractable. Capital sequences are shown to be globally monotone and stable under very general circumstances using lattice programming techniques and value orders. We analyze a series of examples that exhibit a variety of behaviors, including closed-form solutions, unique steady-states, multiple steady-states, and conditionally sustained growth. The endogenous rate of discount preserves monotonicity and stability while allowing for the possibility of non-global convergence.