Problewm

The political business cycle. (Nordau's, 1975.) Suppose the relationship between unemployment and inflation is described by y_t = y‾ + b (π_t - E_t-1 π_t), where the ε^s_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 u₁and u₂, subject only to the limitations that there are minimum and maximum feasible levels of unemployment, u_L and u_H. 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 E_t-1π_t, what value of y_t 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?