This volume collects research papers addressing topical issues in economics and management with a particular focus on dynamic models which allow to analyze and foster the decision making of firms in dynamic complex environments. The scope of the contributions ranges from daily operational challenges firms face to strategic choices in dynamic industry environments and the analysis of optimal growth paths. The volume also highlights recent methodological developments in the areas of dynamic optimization, dynamic games and meta-heuristics, which help to improve our understanding of (optimal) decision making in a fast evolving economy.

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).

1.1. Scope of the Book This book is a contribution to the area of "dynamic models of the firm." The motivation for this kind of research is the following: Empirical studies (e.g. Albach (1976)) have shown that the development of the firm over time can be divided into different stages. such as growth. stationarity and contraction. In order to understand and evaluate these stages in a proper way. it is important to develop a suitable theoretical framework. To that end. economists have applied dynamic mathematical techniques. such as optimal control theory. calculus of variations and dynamic programming to design and analyse dynamic models of the firm. In this way. the economic theory of the firm is extended to a dynamic context. Within the field of the dynamics of the firm this book - develops a general investment decision rule. based on the concept "net present value of marginal investment." which is applicable in deterministic dynamic models of the firm; - studies the influence of adjustment costs of investment on optimal dynamic firm behavior; - extends the stochastic dynamic theory of the firm by connecting it with a dynamic version of the Capital Asset Pricing Model. Before elaborating on "the dynamics of the firm." we first review the subject of net present value in the classical analysis.