PART II

 

General Field Theory

 

37 General Field Theory of Macroeconomics

The first part dealt with the Special Macroeconomic Fieldtheory (SMF) which is a usable, and thus in the broadest sense, ready-theory. Because it is already sufficient to describe the essential problems of the economies and, more importantly in the future to make predictions for the development of economic production and trade as a function of capital stock and its use. This can be achieved but only using statistically significant ⁷⁷ numbers which must be accrued in the international statistical offices on a matchable basis, so the total capital stock and GDP and other required ratios, and then needs just a powerful database server and of course some software development. The already very extensive range of validity of linear SMF, even in its simplest form, can be well recognized by the consistency check of the quantity equation: It is seen that only some time after the onset of the crisis, the solution of the linear SMF gets questionable, as the source equation then gets more and more away from balance. For the sample of the FRG one can see that with year 2015 the balance begins to diverge slightly, and from 2020 significant deviations are increasingly apparent. The reason for this discrepancy is that the linear approximations are no longer sufficient to keep the continuity straight for a then strongly decreasing GDP.

In the real economy can be seen this error before, because from the time when an increasingly nervous market is no longer willing to buy any loan or financial product. So it comes to depreciation on the capital stock, which because of feared repercussions on the financial system for can lead by example to self-purchases of government bonds by their own central banks. But this means the loss of balance of the source equations. As there is generated a cash flow , which is contrary to any real products. Mathematically, this means that the continuity equation would be described not only by divergence fields, but additionally by rotating fields.

For the use of SMF, we need only the values for empirically. These can be determined both from statistical data, as well as suitably adapted analytical functions to generate. But it would be nice, if we could also derive such parameters self-consistently out of theory. The purpose of the thus ensuing General Macroeconomic Fieldtheory (GMF) is the investigation of the fundamental structures of the economy and should thus help to see how one can predict in self-consistent way these important factors. In principle, this should be widely available.

It's obvious a size such as population growth is not easy to predict. Because this is dependent for example of social and religious structures, which we can treat hardly as part of the economy. Nevertheless are useful estimation formulas for this possible and can also be used. However, the economist will prefer to leave this to other sciences, which can provide suitable models if necessary. Otherwise, we just choose to use statistical data, of course. The other three variables, however, should be deductible as part of economic modeling in a good accuracy from first principles. Thus, for it is clear that not only the price level for goods, but also about the nominal interest rates on assets and liabilities are a function of supply and demand for such financial products. So in about

    (37.1),

if we want to guess at this point just once. Because the demand for loans comes from the current GDP, and the more capital is available, the sooner will reduce the interest rate. In a complete theory, as should also the difference between the interest rate of real loans (consumptive and investment purposes; commercial bank model) and bank proprietary trading and derivatives (investment banking) enter into, because they are not necessarily identical and are in accordance with their specific laws to model. Similarly, the savings rate, as a function of the GDP's and its growth

    (37.2)

should be represented. Because the people need not only saving surpluses (from), but also confidence in the future potential of the system (from ). In parallel, would be to find an analytical solution for the relative share orof the commercial bank model and and investment banking model, which essentially

    (37.3)

the reciprocal value of the capital-coefficient is likely to be dependent. One may recognize these parameters and functions, although suitable like andand then fit it using andto the measured data and finally invest these functions into the basic equations, thus giving:

(37.4 a and b)

After that one has to check this nonlinear⁷⁸ ODE's for suitability. But this procedure is generally not advisable. Safer and more useful, however, is the derivation of such relationships from elementary principles. In contrast to the SMF the GMF is less intuitive, and in this edition, will still not be a complete theory, as it still requires a lot of theoretical research. This introduction to the GMF is therefore even more of an ideas-box and an invitation to all scholars of macroeconomics, to address as part of their research with these new subjects from SMF and GMF and supplemented in the future and develop it further.
The generalization described below, however, requires a lot of structural mathematical knowledge, as it is mainly taught only on physical science subjects to be studied. Therefore, I try to briefly explain the most important things and the methods used. Thus, the following notation of differentials are familiar, such as for the derivation of a size A to the variables of time t or a (local) x coordinate:

wherein means the total andthe partial derivatives and these may be also withandabbreviated. Accordingly, the double and triple derivative of  A in respect to the time are , and the last abbreviations may be for the multiple mixed derivatives with respect to x and t.  
The latter is a particularly rough shortening and called index-notation⁷⁹ . Although it can lead to confusion here and there, as there are other indices often used only for easy identification of identifiers, they are often needed for shortness in very complex systems of nonlinear differential equations. In such places, therefore, always a bit of attention of the reader to the actual context is necessary.