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).
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This is a contribution to the dynamic theory of the firm. It discusses optimal investment, financing and production policies of the firm that have to deal with a diversity of aspects, such as alternative production techniques, financial constraints, technological progress, business cycles, uncertainty and environmental constraints. The book studies how debt financing may facilitate expansion and how cost prices, prices of capital goods and investment grants influence depth investment decisions. Optimal investment decisions are analyzed, taking into account taxation on environmental pollution, business cycles, adjustment costs and technological progress. Results are obtained by using optimal control theory. The models lead to descriptions of growth and decline patterns of firms as in practice, with distinctive stages succeeding each other, each with its own emphasis on specific management policies (growth consolidation, depth investments, abatement efforts, etc).
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