We consider a general Ramsey model with endogenous discounting, depending on
current consumption or future capital, study the monotonicity properties of
the optimal path, and provide a new narrative for the existence of a poverty
trap, alternative to the literature on convex-concave production functions.
We prove the continuity and differentiability properties of the value
function, as well as the monotonicity of the policy correspondence, which in
turn entails the strict monotonicity of the optimal path. Importantly, the
existence of a poverty trap relies on the existence of a critical level of
capital such that, if the initial condition is lower, the optimal path
converges to the origin, while, if it is higher, this path converges to a
positive steady state. Since it is impossible to compute this critical level
under endogenous discounting when the discount factor is a general function
of current consumption or future capital, in both these cases, we complement
the theoretical analysis with robust corresponding examples and, showing
that a poverty trap exists for a nonzero-measure set of parameter values, we
demonstrate that the poverty trap is a pervasive feature under endogenous
discounting.