Dynamic Policies of the Firm: An Optimal Control Approach

ISBN-13: 9783642778865 / Angielski / Miękka / 2011 / 445 str.

Onno Van Hilten; Peter M. Kort; Paul J. J. M. Van Loon

Opis

In this book we open our insights in the Theory of the Firm, obtained through the application of Optimal Control Theory, to a public of scholars and advanced students in economics and applied mathematics. We walk on the micro economic side of the street that is bordered by Theory of the Firm on one side and by Optimal Control Theory on the other, keeping the reader away from all the dead end roads we turned down during our 10 years lasting research. We focus attention on the expressiveness and variety of insights that are obtained through studying only simple models of the firm. In this book mathematics is our tool, insight in optimal corporate policy our goal. Therefore most of the mathematics and calculations is put into appendices and in the main text all attention is on modelling corporate behaviour and on analysing the results of the calculations. So, the main text focusses on micro economics, even more specific: on Theory of the Firm. In that way this book is contrasted from such famous text books in applied Optimal Control with a much broader portfolio of applications, like Feichtinger & Hartl (1986) or with a more rigorous introduction into theory, like Seierstad & Sydsaeter (1987).

Spis treści

A. State of the Art.- 1. Introduction.- 1. Scope of the book.- 2. Nature of the theory of the firm and of this book.- 3. Outline of the book.- 2. A Survey of Dynamic Theories of the Firm.- 1. Introduction.- 2. Shareholders.- 3. Management.- 4. Employees.- 5. Labour market.- 6. Output market.- 7. Competitors.- 8. Lenders of debt money.- 9. Suppliers of assets.- 10. Government.- 11. Macro-economic data.- 12. Summary.- 3. Some Predecessors.- 1. Introduction.- 2. Investments and depreciation (Jorgenson).- 3. Investments and adjustment costs (Gould).- 4. Production and finance I (Leland).- 5. Finance and the value of the firm (Ludwig).- 6. Production and finance II (Lesourne & Leban).- 7. Optimal firm behaviour during a business cycle (Leban & Lesourne).- 8. Technological progress in vintage models of the firm.- 9. Summary.- B. Investment and Finance.- 4. A Dynamic Model of the Firm.- 1. Introduction.- 2. Production, sales and operating income.- 3. Financing and taxes.- 4. Policy of the firm.- 5. The model.- 6. Further assumptions.- 7. The Maximum Principle.- 8. Optimal solution.- 9. Basic trajectory.- 10. Consolidation.- 11. Summary.- 5. Investment and Finance.- 1. Introduction.- 2. Personal Taxation.- 2.1. The model.- 2.2. Optimal solution.- 2.3. Summary.- 3. Net present value concept.- 3.1. Corporate finance theory.- 3.2. NPV concept and the model of Chapter 4.- 3.3. Summary.- 4. Adjustment costs.- 4.1. The theory of adjustment costs.- 4.2. A self-financing firm facing convex adjustment costs.- 4.2.1. The model and its solution.- 4.2.2. NPV concept and further analysis.- 4.3. Summary.- 5. Summary.- C. Production.- 6. Production, Employment, Finance and Investment.- 1. Introduction.- 2.The model.- 3. Further assumptions.- 4. Optimal solution.- 5. Basic trajectory and consolidation.- 6. Depth investments.- 7. Depth investments and consolidation.- 8. Summary.- 7. A Further Analysis.- 1. Introduction.- 2. Optimal decision rules.- 2.1. Production.- 2.2. Financial structure.- 2.3. Investment and dividend.- 3. Environmental influence on the trajectory of the firm.- 3.1. Reallocations.- 3.2. Final output.- 3.3. Consolidation.- 3.4. Expansion.- 3.5. Substitution.- 3.6. Financial substitution.- 4. Inluence of (sets of) environmental parameters.- 4.1. Corporation profit tax rate.- 4.2. Investment grant rate.- 4.3. Abolishing investment grants.- 4.4. Financial parameters.- 4.5. Wage rate.- 5. Summary.- 8. Production, Pollution, Finance and Investment.- 1. Introduction.- 2. The model.- 3. Optimal trajectories.- 3.1. Introduction.- 3.1.1. Financing costs.- 3.1.2. Technology.- 3.1.3. Environmental policy.- 3.2. Weak environmental policy of the government.- 3.3. Strong environmental policy of the government.- 3.4. Total set of trajectories.- 4. Conclusions.- D. Dynamic and Risky Environment.- 9. Production, Finance and Investment During a Business Cycle.- 1. Introduction.- 2. Assumptions.- 3. The model and relevant paths.- 4. Optimal solution.- 4.1. Introduction.- 4.2. A ‘light’ recession.- 4.3. A ‘moderate’ recession.- 4.4. A ‘severe’ recession.- 5. Summary.- 10. Production and Investment with Technological Progress.- 1. Introduction.- 2.The model and its optimality conditions.- 2.1. Vintages and taxes.- 2.2. The model.- 2.3. Lifetime of the eldest vintage.- 2.4. Optimization problem.- 2.5. Optimality conditions.- 3. Scrapping condition.- 3.1. A general scrapping condition.- 3.2. Interpretation.- 3.3. Another derivation.- 4. Steady state solution.- 5. Limitations to the coupling procedure.- 6. Summary.- 11. Production, Finance and Investment When Demand is Uncertain.- 1. Introduction.- 2.The model.- 3. Solution.- 4. Summary.- 12. Epilogue.- Appendix 1. An Interpretation of the Maximum Principle.- 1. Introduction.- 2. Technical terms.- 3. The Maximum Principle of Pontryagin.- 4. Mixed control constraints.- 5. Pure state constraints.- 6. Problems with infinite horizon.- Appendix 2. Solutions of the Models of Chapter 3.- 1. Introduction.- 2. A general solution procedure.- 3. The model of Jorgenson.- 4. The model of Gould.- 5. The model of Ludwig.- 6. The model of Lesourne and Leban.- 7. The model (s) of Leban and Lesourne.- 8. The model of Nickell.- 9. Summary.- Appendix 3. Solution of the Model of Chapter 4: A Step by Step Description.- 1. A reduced form of the model.- 2. Optimality conditions.- 3. Infeasible paths.- 4. Feasible paths.- 5. Final paths.- 6. Coupling procedure.- 6.1. Strings ending with path 5.- 6.2. Strings ending with path 4.- 7. Summary.- Appendix 4. Solutions of the Models in Chapters 5, 6 and 8: The Main Lines.- 1. Personal taxation model.- 2. NPV formulas of the model of Chapter 4.- 3. Convex adjustment costs.- 3.1. Optimal trajectories.- 3.2. Net present value formulas.- 3.3. Extension of the planning period.- 3.4. Infinite time horizon.- 4. The model of Chapter 6.- 5. Pollution model.- 5.1. Reformulation of the model.- 5.2. Solution procedure.- Appendix 5. Specific Problems in Solving the Models of Chapters 9 and 10.- 1. Solution of the model of Chapter 9.- 1.1. Optimality conditions.- 1.2. String 1002D2-1.- 1.3. String 1-2-3-2-1.- 2. The Maximum Principle for the model in Chapter 10.- 2.1. The model.- 2.2. The trie.- 2.3. Necessary optimality conditions for a special case.- 2.4. Necessary conditions for the general model.- 3. Existence of steady state solution in Section 10.4.- Appendix 6. Stochastic Dynamic Programming and the Additional Solutions and Mathematical Proofs of Chapter 11.- 1. Stochastic dynamic programming.- 2. Additional solutions and mathematical proofs.- List of Symbols.- References.- Author Index.

O autorze

The book is a contribution to the dynamic theory of the firm. It provides production, finance and investment decision rules, taking into account subjects like adjustment costs, financial constraints, costs of environmental pollution, technological progress, business cycles and uncertain demand.