Nick Guo

Optimal Control Problems with State Specific Jumps in the State Equation

Abstract An important class of control problems in economics are those in which the state equation switches (jumps) whenever the state variable crosses a threshold. An example is a life-cycle problem in which a household faces higher rates on borrowing than on lending, and therefore the interest rate on the households asset balance switches discretely each time the asset balance switches signs [6]. The existing method for solving such a problem is notoriously difficult to compute because the first-order conditions include a continuum of complementary slackness conditions. In this paper we provide an easy solution method that utilizes the standard Maximum Principle for unconstrained optimization problems. No inequality constraints (and therefore no complementary slackness conditions) are required.

Roosevelt And Prescott Come To An Agreement

Edward C. Prescott has argued that mandatory saving is socially desirable because it solves the problem of people intentionally free riding and becoming a welfare burden. Inspired by Prescotts argument, we develop a model in which rational individuals choose between saving and free riding. We find that free riding is a robust outcome for a significant share of the population and that everyone, including the free riders, benefits from the elimination of free riding through mandatory saving. Our results strengthen Prescotts position that free riding is a serious problem and that mandatory saving is socially desirable.