Heribert Genreith

Economic Engineering - 

Field Theory of Macroeconomics

Preprint of the English translation

of the German book

Makroökonomische Feldtheorie”

ISBN: 978-3842380295


with some advances.


Refer to:

Heribert Genreith

Economic Engineering

General Field Theory on Economic Growth

in Substitutional Competition

Editor and Author:

Heribert Genreith



Economic Engineering. Academic Preprint; Books on Demand, Norderstedt, Germany, 2012.


BoD Book Number: 949158


V 1.0 - HTML



All rights reserved:  Copyright 2012 Heribert Genreith

H. Genreith, Makroökonomische Feldtheorie, ISBN 978-3-8423-8029-5, Books on Demand, Norderstedt, 2011

D. Peetz and H. Genreith, The financial sector and the real economy, Real-World Economics Review, issue no. 57, 6 September 2011, pp. 40-47

H. Genreith, Economic Engineering, Academic Preprint, English Translation of  "Makroökonomische Feldtheorie" with some advances, Preprint, Books on Demand, Nr. 949158, Norderstedt, August 2012.

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Foreword to the Preprint Version

1 Foreword to the Classical Economist

2 Introduction

3 Definition of the Main Problem


4 Special Field Theory of Macroeconomics

5 Derivation of Basic Equations

6 The Parameter Functions

7 Determination of the Net Business Rate

8 Basic Example Calculations for the FRG

9 Some Remarks about Units

10 Capital Coefficients in the Model and Reality

11 Monetary Inflation Correction and Calibration

12 Real, Nominal or Hedonic Numbers?


13 Classical Growth Models

14 AK-Models and Others

15 Cobb-Douglas Production Function

16 Uzawa-Lucas and Solow-Swan-Models

17 General Criticism of the Classical Growth Models


18 Analysis of the Basic Equations

19 Discussion of the Analytical Solution

20 Rule of Thumb: the Economic half-life Time


21 The Quantity Equation

22 Conformity to Quantity Equation

23 The Enhanced Quantity Equation

24 Supply and Demand - Substitution

25 Marginal Utility and Gossen's Law


26 Substitution Laws

27 Macro- and Microeconomic Substitution Rules

28 Macroeconomic Savings

29 Comparison with Classical Economics

30 Remarks on Technology, Productivity and Education


31 Analysis of Inflation

32 Substitution Competition and Public Debt

33 Short Remark on the Economic Cycle

34 Effects of Globalization

35 Sustainable Environmental Performance


36 Summary of the Special Field Theory




37 General Field Theory of Macroeconomics

38 Invariants and Euler-Lagrange-Equations

39 The General Quantity Equation

40 Field Equations of Economics

41 Example: Investment Banking

42 Introducing Labor and Wages

43 The Predator-Prey Symmetry

44 Spiral Symmetry of Economy

45 Preservation of the Tangent Angle

46 Higher Orders of the Tangent

47 Rotational-Stretching-Symmetry

48 Commutator Symmetry


49 Summary of the General Field Theory




Some Sample Calculations



Errata, Addenda, and Preview


Acknowledgements and Dedication

Foreword to the Preprint Version:

The German edition of this book was published in 2011 with the title “Makroökonomische Feldtheorie: Allgemeine Theorie des ökonomischen Wachstums in Substitutionskonkurrenz”, ISBN 978-3-8423-8029-5, Books on Demand, Norderstedt, 2011. The most simplest linearized model was first introduced in literature a little bit earlier in D. Peetz, H. Genreith, “Neues Makromodell: Die Grenzen des Wachstums: Finanz- vs. Realwirtschaft,” Die Bank, Zeitschrift für Bankpolitik und Praxis, Ausgabe 3/2011, S. 20-24. An English translation of this article appeared in D. Peetz and H. Genreith, “The financial sector and the real economy”, Real-World Economics Review, issue no. 57, 6 September 2011, pp. 40-47.

In the meantime the first Master Thesis using the new theory was delivered at the University of Luzern, Switzerland: Hochschule Luzern – Wirtschaft & Zürcher Hochschule für Angewandte Wissenschaft, MSc in Banking & Finance, Selvi Basci, “Betrachtung von Wachstumsdynamiken unter Berücksichtigung von sozioökonomischen Entwicklungen am Beispiel der Türkei”, Masterthesis, June 2012. Further academic works are in progress.

Im still working on an approved edition of this fundamental economic book in English language. Producing high quality academic books with layout standards and correct translated language like it is requested by the eminent international academic publishing companies is a very time and cost intensive task. Time that we don't have due to the actualities and not enough money for fast publishing in standard academic press due to lack of sponsorship.

Due to the dramatically increasing financial crisis, not just in the EU, but also in the US and mainly most developed countries, I have to publish this somehow raw preprint. Although the maths is on actually high standard, the graphics and the language are not yet finished to standard academic book quality. Especially the graphs have to be redesigned. Although the graphs are partly still with German markers, they are mostly self-explanatory and also provided with detailed english description.

The book's preprint is published to enable international university scientist, which are no German language readers, to use and cite the new theory much earlier. I hope the worldwide much larger community of economists reading english literature will pardon me for my sometimes fragile English.

The final (ISBN listet) edition will appear after a lot of fine tuning in later 2012 or 2013.

Footnotes as appearing in the text:


1    For quantum dynamics e.g. CERN Accelerator. The largest machine ever build in history. The goal of this machine is to find the smallest differences between theory and reality. For example in 2012 there was a big rumor about the seemingly measured small difference in the speed of neutrinos. The difference between measurement and theory was of the order of just 10-5, which means the thousandth part of a percent. No other science would even be able to predict any measurable number with this precision from their theories, nor even would be able to measure such small differences reliable.

2    Distinct means, that any other formulation of the correct theory may somehow look a little bit others, but it has to be mathematically of the same principle structure. As an example one may remember the different formulations of quantum dynamics made independent by Schrödinger, Heisenberg and Dirac. Although at first glance they were different in their special formulations, it soon was proved that they all mathematically represent the exact same structures.

3    Creating money from nothing means, that money isn't associated with (internal) GDP. This are things like buying government bonds by the own central banks, but also the inflow of investment money from abroad.

4    Holonom Systems are seemingly closed systems, anholonom Systems open ones. GDP value-free money creation leads to anholonom Lagrangians, which are characterized by an additional external source:with .

5    Except mathematics itself, which goes back partly at least 5000 years in time. But mathematics is the science of pure logics and structures and has despite of its age entered technical and natural sciences much later.

6    GDR means German Democratic Republic. The German abbreviation is DDR (Deutsche Demokratische Republik).

7    The 1990s boom was an exceptional effect based solely on the sharp increase in the population by the GDR inclusion.

8    The brokered loans by commercial banks, both investment and consumption loans in the real economy.

9    Marked 1 = 100 % in Figure 2.

10    Except for short-term cyclical fluctuations without medium-or long-term significance.

11    In the general case can be divided into so-called sources and sinks of the divergence and rotation fields.

12   Also unpaid services are in kind such donations.

13   As each function can also be represented as a Taylor-series, we may write in our case:


As a the first approach, we can take the numerically leading linear terms. It is a well-established fact that this works at least locally, and if the higher-grade terms are indeed almost negligible, are also works even globally:


The basic structure of our differential-linear analytical model of two dependent functions is thus:


The functions of the parameters p and q are already here replaced by the following names needed. Non-linear terms such asoretc. drop off fast. So they play at least locally no role as the implicit factor usually goes quickly to zero.

14    Time series OU0115, loans to domestic non-banks

15    Introduction of the Deutschmark on 21 June 1948.

16    With an implicit assumption here is that the rates of return do not differ from real economic investment and economic transactions substantially. One could consider a slightly extended approach although, in the first approximation,    but this is of no decisive importance.

17    "Phenomenological" means that you put the real course of a function due to obvious assumptions. Instead an exponential, you can of course take any other customized functions (eg polynomials) or even take the measurements themselves. For a customized analytic view a phenomenological function is much more substantial, because the causal link will go along with analytical analysis then. For numerical considerations the kind of the adjustment function however is of lesser importance.

18   The Euler constant is. After the Time the ratio drops to which is about 36.8 % percent. The exponential half-lifetime is always greater than the decimal half-lifetime, which accounts for a drop to 1/2=0.5 which equals to the higher level of 50 % percent.

19    We get a system of two dependent differential equations due to considering the two most important parts of capital driven economy, GDP Y and capital K. Introducing further parts, e.g. like labor L and wages W, will give further interdependent differential equations, e.g. dY=f(Y,L,K); dL=g(L,Y,K); dK=h(K,Y,L). In principle this can be done by expanding the products under consideration to any number, while also expanding the differential system to any complexity. How this must be done in full consistency, will be shown in the general field theory in the second part of the book. Besides, from the fact that economy is capital driven and also underlies the inner substitutional symmetry MV=HP, such larger systems will give a lot of additional benefit to the researcher, but will not alter the solution for Y and K in the main.

20    In sums this is important, but not in products. However even more features can be sum, such as the sine or exponential functions etc., can be represented as a polynomial. For example holds. Because of the exponent n has any value from zero to infinity, the physical unit of the argument will always have to be dimensionless. So x= t as time in seconds does not work, as it returns in unitswhich can not been added. Correct is, which means a dimensionless argument of time t in respect to some unit of time. Mostlyis chosen as 1 year.

21    This fact often leads to problems, be it in the literature that satisfy this condition not actually, or because the formulas there are not explained in the correct manner.

22    At least theoretically. In practice this may not be possible, due to a lack in enough goods to buy.

23    For the relative development of K and Y, it has no meaning.

24     In the use of hedonic methods in the national price statistics, the United States is playing a pioneering role. So there in the mid-1980s, a hedonic price index for computers has been implemented. Since been found in the United States also the use of hedonic quality adjustment methods for many other products, e.g including since 1987 for rentals, since 1991 in apparel, since 1993 in multi-family homes since 1997 in digital telephone systems, television sets since 1999. In addition to that, also the official growth rate of GDP is effected by hedonic methods in the US. (source: www.destatis.de)

25    In classical macroeconomics is, however, distinguish between nominal and real interest rates. The nominal interest rate is calculated correctly by the model. The so-called real interest rate, however, is what remains after deducting the inflation determined statistically from the shopping basket. Although the amount of the real interest rate is important for savers and investors, however for macroeconomics only the nominal rate does matter. The real interest rate is just a derived number from two separate calculable effects. The inflation rates calculated by the statistical institutes using shopping baskets data are already in barely comprehensible manner changed data. They are more or less good “house numbers”, but largely useless for exact analytical computations. You may try to calculate in return the raw data from already statistically processed data. However, this is usually only approximately possible because the algorithms used by the statistical institutes usually are not bijective.

26    The level of inflation is perceived differently by consumers. One reason for the deviations of the "perceived inflation" to the measured inflation is the fact that in the cart, which is used to measure inflation, both products of daily use (as food) and consumer durables (like cars) are included and the products selection or weighting of individual consumers do not agree with any individual or any group of consumers. The perception of price changes for the goods of daily demand were higher than that for consumer durables. Thus, the perceived inflation is higher than that measured when the prices of everyday goods rising faster than consumer durables (and vice versa). The phenomenon of "perceived inflation" has been widely discussed especially after the introduction of the euro. 2002 occurred in some countries of the EU a divergence between inflation rates, as they were perceived by the population according to surveys, and those as the statistical offices e.g. in Germany determined. The "perceived" inflation was significantly higher than the official rate of inflation. (translated from german wikipedia “inflation”). Also in the US there are a lot of different definitions of special inflation rates.

27    I.e. on average, the relatively higher technical inflation is 80% away from the official value. In the long term average that means a value about 4.1% instead of the official rate around 2.5% in FRG.

28    The total assets of all credit institutions of the FRG on the data of the Bundesbank and the Federal Statistical Office. The assets account for similar amounts of liabilities corresponding to the deposits and assets. Time series OU0308 of the Federal Bank, which is the balance sheet total for all categories of banks. Available at http://www.bundesbank.de/statistik/statistik_zeitreihen.php?lang=de&open=&func=row&tr=OU0308 ("General: Business volume = Balance sheet total plus endorsement liabilities arising from rediscounted discounted bills, the borrowers own drawings in circulation and the bill portfolio before maturity for collection of bills sent. ")

29    That is, that per generated € or $ increase of capital or debt less and less volume growth of GDP is found. By 1950 in the FRG the ratio was better than 1:1, but by 1980 only 50 cent GDP growth can be found per 1 euro capital increase. In 2010 there is zero or even below GDP growth per one € capital growth. At last it can be found empirically that capital growth even begins to shrinks the GDP.

30    These are the approaches used in the IMF 2005 model, from which various conclusions were then drawn. These are not considered in detail here, since they can contribute little to the cause. Because consequences of unsuitable conditions are completely independent of its mathematical rigor of little significance. Literature [IMF 2005].

31    The possible variationdoes not change the singularity of the function with respect to the two-to-find functions Y and K. It simply means that a selectable portionoris introduced as an additional playing parameter in the right side of the equation.

32    Linearly independent means that the (at least) two necessary equations, which itself may be on Y and K dependent, can not been transferred into one another by a linear arithmetic operation. This is a fundamental and universally known fact.

33    Although with diminishing marginal utility, but it is always growing.

34   Of course, you can instead use any other production factor. For example, the quota of an ethnic group, so as L=uF. The result is always the same.

35    Basically one can constitute that all singular approaches can be rearranged as an AK-model.

36    The german word for the great time of rapidly growing economy was „Wirtschaftswunderjahre“.

37    At the very beginning, the savings rate must even be positive, otherwise the economic capital would immediately "dry up", unless external (foreign countries, central bank) money will be shot in. Such a start-up financing took place in the FRG, the so called Marshall Plan after the end of WW II.

38    Simple calculations can be done already by an Excel spreadsheet. However, its accuracy in differential calculation is low. Much better is to use higher mathematics software, such as the freely available Scilab environment.

39    As a tool for integration the computer algebra system Maxima version 5.22.1 (or http:wxmaxima.sf.net http:maxima.sf.net) was used, which is freely available on the Internet under the GNU GPL license. As a fee-based program Maple 9 was used to.

40    The linear scaling is only due to the better comparison of the functions in the graphic, it does nothing to the basic mathematical profile of the functions.

41    Percentages used in this work as a rule with the symbolandas the index specifier of the specific percentage. Note that percentages are always used (per cent lat.= hundredth) in the natural mathematical way, i.e. 5% = 5/100 = 0.05.

42    In fact, the state plays a major role. For he draws from effective. See in later chapters on government debt.

43    Thus, the German Wikipedia cites an example to the problem of empirical money in circulation: "Thus, an economy to work smoothly, the velocity of money has to be constant. But actually the velocity of circulation decreases in Germany ever since 1981 ...", a behavior that in the basic model can already be well recognized. It continues: "The velocity has been demonstrated for a number of OECD countries as a long U-shaped curve ...". Even this basic course is very easy to see in our model.

44    "The question is disputed, what long-term trend, the income velocity of money shows. The answer to this question depends, among other things, on the amount of the chosen money concept. In many developed economies today V3 shows a falling trend for individual nations (such as Great Britain) but there were earlier periods longer-term stability. For V2 was demonstrated for a number of OECD countries, a long U-shaped curve. V1 shows a rising trend partly ...." (Source: http://de.wikipedia.org /wiki/ Umlaufgeschwindigkeit_(Geld))

45    If one breaks the range down to the smallest levels, then.holds. Otherwise, this must not necessarily be the case, but it can be assumed in general.

46    Which of course includes all financial products and foreign transfers and also money creation through equity purchases of government bonds and other financial constructs.

47    Such a thing is at best an approximate number by detailed statistical works in practice.

48    decreasing, as if the trade is no longer willing to trade products and services against the weakening currency.

49    This applies generally also in times with a positive economic growth, not always in absolute numbers but in relative terms. And the latter is here essentially.

50    In marginal utility theory the so-called "indirect utility function."

51    As we will see later, with the exception of "system-relevant" products.

52    As the operatorpicks out of the sumalways the j-th element.

53    Even with wage increases, the approximation is usually justified as a general increase in the money supply via the levy on the goods is entitled inflated accordingly. The net effect will be regularly close to zero.

54    Remember, it is not only the competition of similar products such as cars from Ford or GM, but also the question of car or bread and butter?

55    With a sufficiently large number of products we can do this without great error.

56    As long as the net foreign contributions are approximately zero.

57    The course can be taken also from financial products. Financial products are basically nothing more than another competitor. But special are the interests, which may represent an additional source Q, which will be examined in more detail later.

58    In fact, it is incorporated economically in both. This is due to the spiral symmetry of classical economics, which we treat in the general theory section. It is the symmetry under rotational-expansion.

59    i=j is not mandatory, but can mostly be accepted.

60    In a closed economy, there is a direct link between national saving and investment. This follows from the definition of the total demand function:Y=C+I+G. After conversion of the demand function it is obtained: I =Y-C-G. Substituting these with the national savings, then it follows: I = Y-C-G = (Y-C-T) + (T-G) = Sp + Sg = S and so I = S . (see e.g. http://de.wikipedia.org/wiki/Sparen )

61    Remember thatis negative in our notation at the beginning and in the end gets positive.

62    A “jump” is characterized by an increase in slope of the function (which means in df/dt) and not just in the function f itself.

63   In 1971 was introduced BaFöG as student loans not paid back to full funding under Chancellor Willy Brandt for needy students. It guaranteed a wider circle of those entitled to receive a guaranteed and enforceable education funding.Under Chancellor Kohl, it was taken back to 1998 successively. Since 2001 it lives in a reduced form.

64    First PC's were manufactured by Apple for the mass market. But only providing a freely available and not protected by patents cumbersome hardware platform from IBM, and a garage company called Microsoft for the operating system, made possible the triumph of the PC's from 1981 to today.

65    Hedonic regression is used to calculate CPI (inflation) and GDP in the US, GB, AUS and New Zealand since the 1990ies. For example, the processor speed of computers hasincreased in 2005 due to improved techniques of 2,000 MHz to 3,000 MHz. On average for theCPU prices have remained constant. Here expect the statistician as follows: The increase in the frequency for the processor is a quality improvement of 50 percent. This means that prices for CPUs, taking account of quality improvements during 2005 falls in the Consumer Price Index by a third. With the growth and productivity levels, this process is reversed.So it is assumed that the real prices in the determination of the value has to be corrected according to the quality improvement of 50 percent upwards.So, although there during the year was no statistically significant changes, the CPI in our sample for processors gets a reduction of one third (inflation reduction) and the growth of GDP is increased by 50 percent of the real numbers. In addition there is always a subjective decision as to whether there is a qualitative improvement of a product or mot. Strictly speaking one must also take account of quality deterioration, which is almost never the case. For economic calculations hedonic regression can never be of any use, as the demand and supply of capital does not vary with quality of products but just with real prices and real trade.

66    There is a famous quote: "Differentiation is a craft, integration is an art." Differentiation is true in general, but in this case there is already some work to do. Therefore one should seek help from ananalytics programs like Maple or Maxima.

67    As we consideronly, we may set.

68    This is because the increase of the assets or liabilities of the banks grow even more exponentially if the GDP is already stagnating

69    The knowledge of Chapter 26 ff. is provided here.

70    The individual actionsare of course the respective trades . In the case of wages or taxes are this, as usual, the annual number of actions. Actions are purchases, specifically the acts of each payment, which are the representative of a purchase.

71    Instead of the expression "from labor" is more accurate "from general trading activities" should be used.

72    To clarify: The above figure is all about real values​​, and not to model values​​!

73    Today money is covered solely to debt. Each property has to face in the same amount of debt.The balance sheets of financial institutions on asset side (assets) and liabilities side (deposits) is always balanced.

74    In this case all values of the national debt are simply multiplied by the same number

c= 1/21,1% = 1/0,211 =4.74.

75   The auction of the mobile phone licenses by the federal government of the FRG to the public sector.

76    Currency effects are also not considered here. These are but of course also financial derivatives, and so can be accounted for as a financial product too.

77   The better the information about the national parameters, the more precisely one can predict the future. An accuracy of less than one half a percentage point in the prediction of the capital and GDP growth is not art but a lot work to be done. This should not be underestimated, because many statistical agencies determine their figures incomplete or qualitatively deficient for our purpose. Moreover, these figures are mostly not published as nominal numbers, but presented already in statistical processing. Often therefore, one must appreciate or correct the official numbers. In the worst case we have to deal with hedonic processed data. So there is still much to do in this area.

78    This one can drive up to very complex nonlinear ODE systems. However, should always be observed, that such schemes must be always suited to real numbers for consistency tests and may possibly be rejected. Because if such designs are not based on fundamental principles, such as a conservation law or symmetry, then but at least their general validity is very much doubtful. ( They are often then just locally valid.)

79    Sometimes referred to as Einstein-notation, since it was introduced by him to shorten the cumbersome writing of nonlinear differential calculus.

80    ...in theoretical physics...she provided extraordinary with the Noether-theorem laid in 1918, the cornerstone for a new examination of conserved quantities. In the last quarter of the 20th Century the Noether-theorem developed to one of the most important foundations of physics. The Noether-theorem associates basic physical concepts such as charge, energy and momentum with geometric properties, the invariance of the action under symmetry transformations. It states: For every continuous symmetry of a physical system there is a conserved quantity. This symmetry may be a transformation, for example, a rotation or displacement, which does not change the behavior of the physical system... (Q:http://de.wikipedia.org/wiki/Emmy_Noether)

81   A sample from physics is location and velocity, and resulting acceleration from forces:

82    With “complex” we mean here just for shortness “pseudo-riemanian-complex”. In the simplest two-dimensional case the difference doesn't matter very much.

83   For discussion of this complex-vector-formula one has to remark, that in this case the numbers under the square roots may be also negative, as the resulting imaginarymay be divided away! And by the way, growing rate of complex inflation may result under suitable conditions in less additional net real business.

84    Of course one may integrate over any period of time, then the spiral is only growing wider.

85    The logarithmic spiral has several unique characteristics, so it was one of her biggest fans, Jakob Bernoulli, who referred to it as spiral mirabilis ("miracle spiral") . The logarithmic spiral is invariant with respect to a central dilation by the factor exp(kγ) with simultaneous rotation of angle γ.

86     Economic stagnation in the absence of credit trade.

87    Sincethe terms for n=0 to 2 must be subtracted. This results in .

88    Of course today one uses the help of analytical software like Maple and others.

89     This section will be expanded to a lot more samples, international and USA too, theoretically and practically. Which is no big problem, but due to lack in time, will be done in the later official version.

90    As PDF-files in the same format as this book, so that they can be entered in your copy. Web address see under literature and references.


© Heribert Genreith, E.E. Acad. Preprint, V1.0 - HTML