This work deals with optimal company behaviour in the context of technological progress and fluctuating demand in an "optimal control model" of a company. The investment, dividend and financing behaviour of a firm is described in a dynamic optimization model and the "maximum principle" is used to deduce optimal policy after two government variables and some government constraints have been added to it. In the aspect of 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 aspect of the model with labour-augmenting technological progress, a new version of the maximum principle is derived in order to handle the old structure of the model. Conditions are derived under which the optimal lifetime of capital is constant and special attention is given to the shadow price interpretation of auxiliary variables in optimal control models with pure state constraints. In the final section of the book, the merits and weaknesses of optimization models for use as tools in a dynamic theory of companies and business are discussed.
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 section 7.4.1.- 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.
Series: Lecture Notes in Economic and Mathematical Systems
Number Of Pages: 233
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.41 x 16.99
Weight (kg): 0.4