Dynamic Optimization of the Controlled Model of the Kaldor Business Cycle

We investigate a controlled version of the well-known business cycle model proposed by Nicholas Kaldor. The control is introduced by a parameter that characterizes demand stimulation by the state. The cost of the stimulating policy is a quadratic function; the instantaneous utility function is defined as the national income less demand-stimulation costs. We show that with nearly-maximal demand, an asymptotically stable stationary state always exists in the model. Under fairly general assumptions, we prove existence and uniqueness of the optimal stationary state. The problem of the shortest-time transition of the system to a given stationary state is considered. Numerical simulation results are reported. Keywords: dynamic models in economics, Kaldor business-cycle model, stability, optimality, stationary state, minimum-time problem.