Dynamic Models of the Firm: Determining Optimal Investment, Financing and Production Policies by Computer

by Mark W.J. Blok, A.T. Kearney

Overview

This book contributes to the scientific field of optimal control theory applied to dynamic models of the firm. It discusses optimal investment, financing and production policies of the firm, that have to deal with a variety of aspects, such as financial constraints, start-up costs, business cycles, increasing returns to scale, production life cycles and experience curves. In contrast to many other publications on this subject, here, in combination with an analytical approach, the dynamic optimization problems are solved numerically with the aid of a powerful computer and specific programs for optimizing non-linear functions of a finite number of variables and non-linear constraints.

Product Details

ISBN-13:	9783540608028
Publisher:	Springer Berlin Heidelberg
Publication date:	03/07/1996
Series:	Lecture Notes in Economics and Mathematical Systems , #434
Edition description:	Softcover reprint of the original 1st ed. 1996
Pages:	193
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1 Introduction.- 2 Mathematical Background to Dynamic Optimization.- 2.1 Introduction.- 2.2 Analytical approach to the optimization problem.- 2.3 Numerical approach to the optimization problem.- 2.4 Economic interpretation of the adjoint variables.- 2.5 General procedure.- 3 The Basic Model.- 3.1 Introduction.- 3.2 The model and its assumptions.- 3.3 Examination of the paths.- 3.4 Case study.- 3.5 Conclusions.- 4 A Model with Start-up Costs.- 4.1 Introduction.- 4.2 The model and its assumptions.- 4.3 Examination of the paths.- 4.4 Case study.- 4.5 Conclusions.- 5 Models with a Business Cycle.- 5.1 Introduction.- 5.2 The basic model.- 5.3 A model with a variable utilization rate.- 5.4 A model with a cash balance.- 5.5 A model with an inventory of finished goods.- 5.6 Conclusions.- 6 A Model with Increasing Returns to Scale, an Experience Curve and a Production Life Cycle.- 6.1 Introduction.- 6.2 Description of the model.- 6.3 Case study.- 6.4 Conclusions.- Appendices.- A Mathematical Details for Chapter 3.- A.1 Problem formulation.- A.2 Necessary conditions for optimality.- A.3 Elaborating the transversality conditions.- A.4 Further examination of some paths.- B Mathematical Details for Chapter 4.- B.1 Problem formulation.- B.2 Necessary conditions for optimality.- B.3 Elaborating the transversality conditions.- B.4 Further examination of some paths.- C Mathematical Details for Chapter 5.- C.1 The basic model.- C.1.1 Determining the coupling points for Subsection 5.2.2.- C.1.2 Determining the coupling points for Subsection 5.2.3.- C.1.3 Deriving relationships (5.22) and (5.27).- C.1.4 Determining the coupling points for Subsection 5.2.4.- C.l.5 Determining the coupling points for Subsection 5.2.5.- C.1.6 Deriving relationships (5.45) and (5.49).- C.2 A model with a variable utilization rate.- C.2.1 Necessary conditions for optimality.- C.2.2 Further examination of some paths.- C.2.3 Determining the coupling points for Subsection 5.3.2.- C.2.4 Determining the coupling points for Subsection 5.3.3.- C.2.5 Determining the coupling points for Subsection 5.3.4.- C.3 A model with a cash balance.- C.3.1 Necessary conditions for optimality.- C.3.2 Further examination of some paths.- C.3.3 Determining the coupling points for Subsection 5.4.2.- C.3.4 Determining the coupling points for Subsection 5.4.3.- C.3.5 Determining the coupling points for Subsection 5.4.5.- C.4 A model with an inventory of finished goods.- C.4.1 Necessary conditions for optimality.- C.4.2 Further examination of some paths.- C.4.3 Determining the coupling points for Subsection 5.5.2.- C.4.4 Determining the coupling points for Subsection 5.5.3.- D Mathematical Details for Chapter 6.- D.1 Necessary conditions for optimality.- Symbols and Notation.- Summary.