To account for the development patterns that differ considerably among economies in the long run, a variety of one-sector models that incorporate some degree of market imperfections based on technological external effects and increasing returns have been presented. This paper studies the dynamic implications of, yet another mechanism, the endogenous rate of time preference depending on the stock of capital, in a one-sector growth model. The planner’s problem is presented and the optimal paths are characterized. We show that development or poverty traps can arise even under a strictly convex technology. We also show that even under a convex-concave technology, the optimal path can exhibit global convergence to a unique stationary point. The multipliers system associated with an optimal path is proven to be the supporting price system of a competitive equilibrium under externality and detailed results concerning the properties of optimal (equilibrium) paths are provided. We show that the model exhibits globally monotone capital sequences yielding a richer set of potential dynamics than the classic model with exogenous discounting.