The stable manifold for the discrete-time, one-sector optimal growth model is shown to be constructed by solving a functional equation for an implicit programming problem based on the planner's Euler equation. The implicit programming problem is described by a minimum-gain operator, and its...

Ramsey equilibrium models with heterogeneous agents and borrowing constraints are shown to yield efficient equilibrium sequences of aggregate capital and consumption. The proof of this result is based on verifying that equilibrium sequences of prices satisfy the Malinvaud criterion for efficiency.