PART I

 

Special Field Theory

 

4 Special Field Theory of Macroeconomics

Even simple correlations of the art are often already non-linear in nature. This principle applies to the macro economy as well, if only because of the direct mutual interdependencies of the essential factors, so of capital and gross domestic product. But also of prices, interest and trading volume and velocity of money expenditure. This must result at last in a self-consistent model of nonlinear dependencies.

The special field theory of macroeconomics is therefore, as the first step, a non-self-consistent model since important parameters, such as the interests of capital, must be taken from measured values. A self-consistent model however, i.e. the later in this book treated General Field Theory of macroeconomics, should be able to explain even these parameters by itself from fundamentals. In the special field theory, we therefore first ask the simpler question: "What kind of development the function of capital stock and gross domestic product will take under a given return on capital ?” The solution to this, for most practical problems of growth theory however entirely satisfactory question, finally gives us the entrance to the complex non-linear theory.

The overall balance of sources11 and sinks naturally plays here, as with any viable field theory, the most important role. For such a balance or continuity equation at any field theory is immanent. It is clear that in all such structures, errors in the accounting equation will have a significant impact on the consistency of any model to the larger, the less precisely the balance sheet is. A "field" may be in the general case of course an abstract, arbitrary dimensional, mathematical space. In the simplest case, therefore, also one-dimensional. To provide about the answer to e.g. the question: How develops the field

   (4.1)

along our space, the time line

    (4.2) ?

The required balance equations, as we shall see, will be given by the long-known economic balance equation

    (4.3),

the so-called quantity equation of the macro economy. However, we will have to define this much more precisely.