Geoscience Reference
In-Depth Information
The model allows for joint production and substitution of inputs.
Von Neumann proved that for the economic system (
5.7
) a sustainable equili-
brium exists and is a saddle-point solution determining the equilibrium price and
quantity vector. At the equilibrium point the minimum rate of interest
β
and the
maximum sustainable rate of growth
are equalized.
von Neumann's theory does not presume utility maximization by the decision
makers. This assumption probably stems from Gustav Cassel, who dismissed
individual utility functions as necessary for the existence of demand functions.
Von Neumann and Wald had by then initiated modern mathematical economics
with the use of saddle point and fixed point theorems. These ideas were later to be
used in game theory as created by John von Neumann and Oscar Morgenstern
(
1944
) and much later in general equilibrium theory as reformulated by Debreu
(
1959
). von Neumann's introduction of inequalities in the formulation of saddle
point theory also became one of the main preconditions for the development of
linear and non-linear programming theory. The other important set of mathematical
theorems to be used as a basis of programming theory was the topic
Inequalities
by
Hardy, Littlewood and Polya (HLP) (1933). Hardy, Littlewood and Polya proved
all theorems behind the Constant Elasticity of Substitution (CES) function, which
was much later to be used in the formulations of neoclassical economic growth
theory (mostly without any references to HLP). Spatial analysis based on these
theories later became important in theoretical and applied Regional Science.
α
5.5
Growth, Institutions, Uncertainty and Risk
in the Determination of the Rate of Interest and the Value
of Capital
It has been shown in the former section that a dynamic equilibrium in a determi-
nistic economy requires equality of the growth rate and the rate of interest.
However, Wicksell (
1914
) and later Keynes showed that institutional factors
may make the rate of interest deviate from this rule. The interest rate, as charged for
loanable funds is a macroeconomic variable, determined by central banks, often
using the interest rate as an instrument of monetary policies, sometimes in an
international game between different governments. This monetary policy deter-
mined rate of interest can thus easily deviate from the “natural rate of interest” as
determined by general equilibrium requirements. Such a deviation would then lead
to inflation, deflation or unemployment, depending on the sign and size of the
deviation and the institutional conditions ruling in the region.
Beside disregarding monetary institutions, most of the early analysis of the
relation between the rates of growth and interest was based on deterministic
equilibrium modelling. However, it is quite obvious that there could be uncertainty
about the future among decision makers, for example as a consequence of
variations in the conditions influencing production or demand. There would then
be a required risk compensation in the form of a higher rate of interest in order to
bridge the gap between lenders and borrowers. In the real world there will always
