Dynamic equilibria for linear systems and quadratic costs

Abstract This paper considers the computation of dynamic equilibria from a systems viewpoint. Attention is focused on an economic system governed by a linear production system, quadratic production costs, and a linear demand function. The resulting necessary conditions for a dynamic equilibrium take the form of a linear two-point boundary value problem similar in structure to the conditions of optimal control. However, the conditions are not equivalent to those of optimal control, and the standard Riccati equation approach cannot generally be applied. A new procedure based on descriptor variable theory provides a general solution, which is a generalization of the Riccati equation approach.