Optimal Firm Behaviour in the Context of Technological Progress and a Business Cycle

This book extends the theoretical study of optimal dynamic firm behaviour by introducing technological progress and fluctuating demand in a deterministic Optimal Control model of the firm. The investment, dividend and financing behaviour of a firm is described in a dynamic optimisation model with two state variables and several state constraints. The Maximum Principle is used to derive analytically the optimal policy. In the model with a fluctuating demand for the firm's products, the conditions for and the length of a "zero-investment period" are derived, as well as the role of debt in surviving a depression. For the model with (labour augmenting) technological progress, a new version of the Maximum Principle is derived in order to handle the vintage structure of the model. Conditions are derived under which the optimal lifetime of capital is constant. Special attention is given to the shadow price interpretation of auxiliary variables in optimal control models with pure state constraints. Finally, the merits and demerits of optimisation models as a tool in a dynamic theory of the firm are discussed