We offer a new proof of the maximum principle, by using the envelope theorem that is frequently used in the standard microeconomic theory. Copyright Springer-Verlag Berlin Heidelberg 2003

Consider the optimal time path of a tax on capital income, the proceeds of which are transferred to labor in a lump sum. It is known from earlier open-loop formulations that, if the optimal rate of tax converges to a point, it converges to zero, implying that, in the long run, a tax on capital...

We derive a new transversality condition (which we prove to be necessary) for a class of infinite horizon optimal control problems.

We consider a class of differential games with transition equations that are homogeneous of degree one. For any game G with a discount rate r, consider a Markov perfect equilibrium (MPE) with strategies that are linear in the state variables. We show that the time paths of the control variables...

We show that, if relative wealth appears in the utility function, for example due to status seeking, then under certain conditions on the curvature of the utility function and the production function, the poor will eventually catch up with the rich. We give sufficient conditions for the final...

We consider the class of differential games with transition dynamics and constraints that are homogeneous of degree one. We show that if the integrand of the objective function is homogeneous of degree , then best replies to linear homogeneous Markov strategies are linear homogeneous, and the...