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

This book applies Optimal Control Theory to dynamic firm behaviour. In a deterministic context, the optimal investment and financing policy of a firm which is confronted with technological progress or with a fluctuating demand is studied. A new version of the Maximum Principle is derived in order to handle vintage models. Special attention is given to the shadow price interpretations and the (de-)merits of optimisation models of firm behaviour.

Contenu
One Introduction.- Two A Selective Literature Survey.- Three On Dynamic Optimisation Models of the Firm as a Branch of 'Pure Theory' and on the Use of Mathematics.- Four The Basic Model.- Five A Model with a Business Cycle.- Six Shadow Prices in a Model with Pure State Constraints.- Seven Technological Progress in Vintage Models of the Firm: Scrapping Condition and Steady State.- Eight Optimal Policies in Models with Technological Progress, with and without a Business Cycle.- Nine Summary and Conclusions.- Appendix One Optimality Conditions for the Basic Model of Chapter 4.- A1.1 Necessary and sufficient conditions.- A1.2 The coupling procedure.- A1.2.1 The paths.- A1.2.2 Derivation of the final paths.- A1.2.3 The coupling procedure.- Appendix Two The Mathematical Details of Chapter 5.- A2.1 General remarks.- A2.2 The details of section 5.3.3.- A2.3 The details of section 5.3.4.- A2.4 The details of section 5.3.5.- A2.5 Uniqueness of the solution.- A2.6 Numerical illustrations.- A2.7 The details of section 5.4.- Appendix Three On the Shadow Price Interpretation of the Multipliers of Pure State Constraints in Optimal Control Problems.- A3.1 Introduction.- A3.2 The class of models to be considered.- A3.3 An outline of the proof.- A3.4 A general sensitivity result.- A3.6 The Kuhn-Tucker conditions and Theorem 1 for problem II.- Appendix Four Necessary and Sufficient Conditions for an Optimal Control Problem with an Endogeneously Determined 'Lag-Structure'.- A4.1 Introduction.- A4.2 The model.- A4.3 The tric.- A4.4 Derivation of the necessary conditions for optimality for a special case.- A4.5 Sufficient conditions for the general model.- Appendix Five Various Derivations.- A5.1 The details of section 7.4.- A5.1.1 Existence of a steady state solution in section7.4.1.- A5.1.2 Derivation of equation (7.57).- A5.1.3 Convergence of the upper and lower bounds on M and T.- A5.2 The optimal policy of section 8.2.2.- A5.3 The pattern of investments in section 8.4.2.- A5.4 Discussion of 'zero investment'-periods.- References.