36 Summary of the Special Field Theory
Capital productivity
GDP with respect to productivity of capital:
total capital-output ratio or capitalcoeffizient:
The ratio
of all national bank assets to gross domestic product.
traditional capital-output ratio
direct capital investment
The proportion of the total capital stock, which is introduced in a direct manner to the GDP
indirect use of capital:
The difference between the sum total of all
bank assets K (example U0308 series of Bundesbank)
and(example: U0115
series of Bundesbank).
indirect capital-coefficient
Basic Macroeconomic Equation System
with
and 
and
is the net investment ratio and
the net business rates of the banking industry
Capital Yield Equation
Percentage of direct capital investment:
Re-investment-equation (capital to GDP loans)
phenomenological exponential form
phenomenological net business rate
simplified basic model:
approximate ansatz for productivity increase
(30.1)
where
is the function of effective productivity increase (decrease) .
Carts or basket for CPI
Inflation rate of the i-th basket
monetary calibration
linear monetary calibration
monetary exponential calibration
Capital productivity for the basic model:
Inflation rate from capital productivity
with 
Cobb-Douglas production function CDPF:
:
CDPF is special AK-model with 
Simplified system basis
and
End of direct GDP growth
(for FRG data approximatly:
years
)
indirect growth
for idg-GDP-growth
for idg-CAP-growth
for idg-GDP-growth
for idg-CAP-growth
for idg-GDP-growth
for idg-CAP-growth
with 
.
complete analytical system of equations
Growth frequency
Analytical solution
Growth path
(
negativ)
Maximum path
(null)
Crisis path
(positiv)
specific growth forms
(negativ (D1) )
(positiv (D2) )
bzw. 
bzw. 
(Null (D3) )
and/or 
and
with the following abbreviations used:
Approximation for small arguments
:
Characteristic frequency
Characteristic time
(For FRG approximately 
years.)
General immediate growth condition
Rule of thumb for macroeconomic half-life-time
Thumb formula for moderate values of 
and 
:
with =
5% gives
years
half-life-time
Classical Quantity Equation
extended quantity equation
simplified monetary velocity
Extended form of the balance equation
with
and 
(Real trade and investment interests)
Prices of real goods, depending on investment products
with 
For
and 
:
In times before crisis
for 
and
In times of crisis
In the final stage for 
and
macroeconomic supply-demand equation
Business management success
Business substitution competition
if
Marginal utility theory
Second law of Gossen
Gossen second law of economic conservation equation
with the conversion
and 
Diminishing marginal utility with economic competition
Competitive pricing with substitution
price change
The marginal benefit
is achieved when
Trading volume in the substitutional competition
Substitutional Competition
Trade substitution
Rates of change of trade substitution
Because of 
one
needs 
and
to
achieve the changes.
General substitutional relationship
Systemic Importance
Damage comparison
Interest income of financial products
Total stock of all derivatives:
Macroeconomic Savings
enhanced savings:
Inflation-related price change
Critical Trading Term
Inflation
Trading volume
Trading volume on growth path
Trading volume on crisis path
Change in price level
with 
and
Trading volume in normal times approximate formula
Progressive form of inflation in normal times
Analytical Core Inflation
expressed in growth rates:
actual inflation rate
with 
for the FRG data.
State Substitutional Competition
with 
and
State budget balance
Deficient State
Ideal State
Profitable
State
Public Debt
Resource orientation of the public debt
and 
Dependent Economies
and 
World Economic System
dimensional matrices:
and 
Balanced external relations
and 
and 
Maximum imbalance
and 
World energy and resources balance sheet
World Sustainability Coefficient
National Sustainability Coefficient
Sustainable boundary of national growth
