On Optimality, Endogenous Discounting and Wealth Accumulation

We endogenize the discount rate via a broad measure of wealth and provide empirical evidence that wealth affects the discount rate negatively. We demonstrate that the Pontryagin conditions require positive felicity for intuitive results, whereas the concavity of the Hamiltonian requires negative felicity for optimality. This dilemma also holds for the endogenizations of Obstfeld (1990) and followers. We solve the model with positive felicity and resolve when optimality is possible. We discuss the impact on technological change, savings and convergence which are more in line with empirics. Finally, we discuss time consistency of a planner who cannot predict his preferences.