We study a dynamic savings game in continuous time, where decision makers rotate in and out of power. Agents value consumption more highly while in power. Our setup applies to individuals under a behavioral interpretation, or to governments under a political-economy interpretation. We prove existence of Markov equilibria by construction and provide tight characterizations. Our analysis isolates the importance of a local disagreement index b(c) which we define as the ratio of marginal utilities for those in and out of power. If disagreement is constant our setup specializes to hyperbolic discounting and we provide novel results even in this context, but we also allow disagreement to vary with spending. When disagreements are sufficiently high we show that an equilibrium with savings exists; conversely, when disagreement are sufficiently low, an equilibrium with positive savings emerges. When disagreements vary sufficiently with spending rich dynamics are possible. In particular, an equilibrium with poverty traps--dissaving at low levels of wealth and savings at high levels of wealth--exists when disagreements decrease with spending. In contrast, when disagreements increase with spending, wealth may convergence to a unique interior steady state. We also investigate conditions for continuous, discontinuous and multiple equilibria. Finally, we show how the model can be solved in reverse, inverting to find primitives that support an equilibrium.
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