Problewm
The political business cycle. (Nordau's, 1975.) Suppose the relationship between unemployment and inflation is described by yt = y‾ + b (πt - Et-1 πt), where the εst'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 u1and 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?
(a) Given Et-1πt, what value of yt will a liberal leader choose? What value will a conservative leader choose?
(b) What is E0π1? If a liberal is elected, what are π1 and Y1? If a conservative is elected, what are π1 and y1?
(c) If a liberal is elected, what are π2 and y2? If a conservative is elected, what are π2 and y2?