Economics Dynamics Problems 116

Economics Dynamics Problems 116 - discussed in chapter 2,...

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100 Economic Dynamics Figure 3.10. and smaller over time, tending to zero in the limit. If a is negative, then the series will alternate between positive and negative numbers. However, if 1 < a < 0 the values of the alternating series becomes smaller and smaller, tending to zero in the limit. While if a < 1, then the series alternates but tends to explode over time. The various solution paths are plotted in Fgure 3.10. Example 3.3 A number of systems satisfy this general form. Consider the Malthusian population
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Unformatted text preview: discussed in chapter 2, but now speciFed in discrete form. Between time t and t + 1 the change in the population is proportional to the population size. If p t denotes the population size in period t , then p t + 1 = p t + 1 p t is proportional to p t . If k denotes the proportionality factor, then p t + 1 = kp t Or p t + 1 = (1 + k ) p t which has the analytical solution p t = (1 + k ) t p...
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