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

ISBN-13: 9783540608028 / Angielski / Miękka / 1996 / 193 str.

Mark W. J. Blok; A. T. Kearney

Opis

This text aims to contribute 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, which has to deal with a variety of aspects, such as financial constraints and business cycles.

Spis treści

1 Introduction.- 2 Mathematical Background to Dynamic Optimization.- 2.1 Introduction.- 2.2 Analytical approach to the optimization problem.- 2.2.1 Problem formulation.- 2.2.2 Solving through path coupling.- 2.3 Numerical approach to the optimization problem.- 2.3.1 Discretization.- 2.3.2 Method 1.- 2.3.3 Method 2.- 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.- 3.3.1 Introducing the adjoint variables.- 3.3.2 Determining the feasible paths.- 3.3.3 Economic interpretation of paths 4, 8 and 10.- 3.4 Case study.- 3.4.1 The case of i < (1 — f)r.- 3.4.2 The case of i > (1 — f)r.- 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.- 4.3.1 Introduction of the adjoint variables.- 4.3.2 Further examination of the stationary paths.- 4.4 Case study.- 4.4.1 The case of i < (1 — f)r.- 4.4.2 The case of i > (1 — f)r.- 4.5 Conclusions.- 5 Models with a Business Cycle.- 5.1 Introduction.- 5.2 The basic model.- 5.2.1 Description of the model.- 5.2.2 Severe recession in the case of i < (1 — f)r and m (1 — f)r and m < m°.- 5.2.5 Severe recession in the case of i > (1 — f)r and m > m°.- 5.3 A model with a variable utilization rate.- 5.3.1 Description of the model.- 5.3.2 Moderate recession in the case of i < (1 — f)r.- 5.3.3 Moderate recession in the case of i > (1 — f)r.- 5.3.4 Severe recession in the case of i > (1 — f)r.- 5.4 A model with a cash balance.- 5.4.1 Description of the model.- 5.4.2 Severe recession in the case of i < (1 — f)r and m < m*.- (1 — f)r and m < m°.- 5.4.5 Severe recession in the case of i > (1 — f)r and m > m°.- 5.5 A model with an inventory of finished goods.- 5.5.1 Description of the model.- 5.5.2 Severe recession in the case of i m*.- 5.5.3 Severe recession in the case of i > (1 — f)r and m > m°.- 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.- 6.2.1 The production function.- 6.2.2 The price function.- 6.2.3 Problem formulation.- 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.