11.18. Consider the situation analyzed in Problem 11.16, but assume that there is only some finite number of periods rather than an infinite number. What is the unique equilibrium? (Hint: Reason backward from the last period.)

11.19. The political business cycle. (Nordhaus, 1975.) Suppose the relationship between unemployment and inflation is described by πt = πt −1 −α(ut −u )+

εS t , α > 0, where the εS t ’s are i.i.d., mean-zero disturbances with cumulative distribution function F (•). Consider a politician who takes office in period 1, taking π0 as given, and who faces reelection at the end of period 2. The politician has complete control over u1 and u2, subject only to the limitations that there are minimum and maximum feasible levels of unemployment, uL and uH. The politician is evaluated based on u2 and π2; specifically, he or she is reelected if and only if π2+βu2 < K, where β > 0 and K are exogenous parameters. If the politician wants to maximize the chances of reelection, what value of u1 does he or she choose?