## Exercise 166

1 In difference-equation models, the variable t can only take integer values. Does this imply that in the phase diagrams of Fig. 16.4 the variables v, and y,+ , must be considered as discrete variables?

2 As a phase line, use the left half of an inverse U-shaped curve, and let it intersect the 45° line at two points L (left) and R (right).

(a) Is this a case of multiple equilibria?

(b) If the initial value yn lies to the left of L, what kind of time path will be obtained?

(c) What if the initial value lies between L and R1

(d) What if the initial value lies to the right of R?

(<?) What can you conclude about the dynamic stability of equilibrium at L and at R, respectively?

3 As a phase line, use an inverse U-shaped curve. Let its upward-sloping segment intersect the 45° line at point L, and let its downward-sloping segment intersect the 45° line at point R. Answer the same five questions raised in the preceding problem. (Note: Your answer will depend on the particular way the phase line is drawn; explore various possibilities.)

4 In Fig. 16.5, rescind the legal price ceiling and impose a minimum price Pm instead.

(a) How will the phase line change?

(b) Will it be kinked? Nonlinear?

(c) Will there also develop a uniformly oscillatory movement in price?

5 With reference to (16.17') and Fig. 16.5, show that the constant k can be expressed as

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