A local analysis of stability and regularity of stationary states in discrete symmetric optimal capital accumulation models (Q1069842)

The paper examines the local stability of stationary states towards which the optimal path of capital accumulation asymptotically converges. The analysis is for the special case where the second order cross partial derivatives of the utility function are symmetric, in which case necessary and sufficient conditions for local stability can be provided in terms of characteristic roots of certain submatrices of the Hessian of the utility function. The author extends previous works of Magill and Scheinkman (1979) and Scheinkman (1978) who treated symmetric variational problems in continuous time models by analyzing these problems in discrete time models. In an important theorem (4.1) the author shows that stability implies that the comparative static matrix is negative definite. This, in turn, implies that the stationary state is regular, i.e., the value of the stationary state capital stocks increases with the discount factor.