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Unformatted text preview: 90 Economic Dynamics Figure 3.2. Consider ﬁrst ﬁgure 3.3(a). We require an initial value for y to start the sequence,
which is denoted y0 . Given y0 in period 0, then we have y1 in period 1, as read off
from the line L. In terms of the horizontal axis, this gives a value of y1 as read off
the 45◦ -line (i.e. the horizontal movement across). But this means that in period 2
the value of y is y2 , once again read off from the line L. In terms of the horizontal
axis this also gives a value y2 , read horizontally across. Regardless of the initial
value y0 , the sequence converges on y∗ , and this is true whether y0 is below y∗ , as in
the ﬁgure, or is above y∗ . Using the same analysis, it is clear that in ﬁgure 3.3(b),
starting from an initial value of y of y0 , the sequence diverges from y∗ . If y0 is
below y∗ then the system creates smaller values of y and moves away from y∗
in the negative direction. On the other hand, if y0 is above y∗ , then the sequence
diverges from y∗ with the sequence diverging in the positive direction. Only if ...
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- Fall '11