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Economics Dynamics Problems 75

Economics Dynamics Problems 75 - Continuous dynamic systems...

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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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