Non-Convexities in a Continuous-Time Capital Theory Problem

In a continuous-time model of capital accumulation, there are convexity or concavity conditions on benefit and cost functions which ensure that dynamical necessary conditions for optimality are also sufficient. Non-convexities can occur in various ways: the Hamiltonian can fail to be concave either in its state variable or in the control variable, and the objective function may not be continuous over time. While stock non-convexities can give rise to multiple equilibria, flow non-convexities can be convexified by averaging over time. A problem of start-up costs is studied to exemplify discontinuous objective functionals.