Continuous dynamic systems
59
Given linear demand and supply then there is only one fixed point. The system
is either globally stable or globally unstable. It is apparent from figure 2.16 that the
fixed point is an attractor, as illustrated in figure 2.16(b). Furthermore, the differ
ential equation is negatively sloped for all values of
p
.
In other words, whenever
the price is different from the equilibrium price (whether above or below), it will
converge on the fixed point (the equilibrium price) over time. The same
qualita
tive
characteristics hold for example 2.5, although other possibilities are possible
depending on the value/sign of the parameter
f
.
Example 2.6 on population growth, and example 2.7 on radioactive decay, also
exhibit linear differential equations and are globally stable/unstable only for
p
=
0 and
n
=
0, respectively. Whether they are globally stable or globally unstable
depends on the sign of critical parameters. For example, in the case of Malthusian
population, if the population is growing,
k
>
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 Fall '11
 Dr.Gwartney
 Economics

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