2.9. Using the phase diagram to analyze the impact of an anticipated change. Consider the policy described in Problem 2.8, but suppose that instead of announcing and implementing the tax at time 0, the government announces at time 0 that at some later time, time t, investment income will begin to be taxed at rate r.

(a) Draw the phase diagram showing the dynamics of c and k after time t.

(b) Can c change discontinuously at time t? Why or why not?

(c) Draw the phase diagram showing the dynamics of c and k before t.

(d) In light of your answers to parts (a), (b), and (c), what must c do at time 0?

(e) Summarize your results by sketching the paths of c and k as functions of time.