Mathematical and Numerical Analysis of a Type of Monetary Model

This paper examines a type of monetary model of open-market operations using both analytical and numerical tools. Numerical simulation proves particularly important here because of the complexity of the model. Theoretical results are inspired and supported by the numerical investigations. The model employed is based on one by Julio Rotemburg (1984). The equilibrium is a solution to a system of third-order, nonlinear difference equations: F(K_{t-1}, K_t, K_{t+1}, K_{t+2}) = 0 with but one initial condition. The existence and uniqueness of this equilibrium were not established in the original paper, but here, using a different approach, I am able to establish the existence and uniqueness of the equilibrium -- first numerically and then theoretically. Finally I provide a general numerical analysis for a relevant class of dynamic economic problems.