  This paper characterizes differentiable subgame perfect equilibria in a
continuous time intertemporal decision optimization problem with non-constant
discounting. The equilibrium equation takes two different forms, one of which
is reminescent of the classical Hamilton-Jacobi-Bellman equation of optimal
control, but with a non-local term. We give a local existence result, and
several examples in the consumption saving problem. The analysis is then
applied to suggest that non constant discount rates generate an indeterminacy
of the steady state in the Ramsey growth model. Despite its indeterminacy, the
steady state level is robust to small deviations from constant discount rates.
