Dynamic choices of hyperbolic consumers: the continuous time case.
This paper characterizes the set of differentiable subgame perfect equilibria in a continuous time intertemporal decision optimization problem with non-constant discounting. The idea of an infinitesimal self is formalized and the equilibrium characterization takes the form of an integral equation (IE) which is reminiscent of the
Hamilton-Jacobi-Bellman equation. Beginning with a local existence proof of IE, we analyze some equilibria of the consumption saving problem. We then use the equation IE to suggest a critical indeterminacy in the Ramsey growth model with non-constant discounting
Hyperbolic discount, consumption saving decision, growth theory
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