The Basic Model

Abstract

The model to be presented in this chapter will serve as the core of the more complicated models in the next chapters. It is in fact also the core of most of the models in Van Loon [1983], Van Schijndel [1988] and Kort [1989]. Their analysis of this model is extended in three directions. Firstly, bringing into practice one of the guidelines of chapter 3 (section 3.3.3), Musgrave’s advice concerning the background of assumptions is followed (section 4.2). Secondly, a feedback decision rule is derived (section 4.4), which gives the optimal policy for (almost) all possible initial conditions (the exceptions are treated in section 4.6). It will be argued that this decision rule is a very convenient and useful shorthand way to characterise the optimal solution. In the following chapters it will be investigated if and why this decision rule is still valid in more complicated models. Thirdly, whereas Kort, Van Loon and Van Schijndel are primarily focussed on the analysis of the growth of the firm, section 4.5 also studies how the firm reduces its size in an optimal way (which is used in the next chapter). The necessary and sufficient conditions for optimality are given in section 4.3. Section 4.7 discusses the difference between the ‘book value’ and the ‘market value’ of equity in the model. Section 4.8 summarises this chapter and gives conclusions.