Economics Dynamics Problems 108

Economics Dynamics Problems 108 - 92 Economic Dynamics...

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Unformatted text preview: 92 Economic Dynamics Given this system, the first few terms in the sequence are readily found to be: yt+1 = −yt + k yt+2 = −yt+1 + k = −(−yt + k) + k = yt yt+3 = −yt+2 + k = −yt + k yt+4 = −yt+3 + k = −(−yt + k) + k = yt It is apparent that this is a repeating pattern. If y0 denotes the initial value, then we have y0 = y2 = y4 = . . . and y1 = y3 = y5 = . . . We have here an example of a two-cycle system that oscillates between −y0 + k and y0 . There is still a fixed point to the system, namely y∗ = −y∗ + k k y∗ = 2 but it is neither an attractor nor a repellor. The situation is illustrated in figure 3.4, where again the line L denotes the difference equation and the line E gives the equilibrium condition. The two-cycle situation is readily revealed by the fact that the system cycles around a rectangle. Return to the linear cobweb model given above, equation (3.5). Suppose the slope of the (linear) demand curve is the same as the slope of the (linear) supply Figure 3.4. ...
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.

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