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Consider a country with two political parties, Democrats and Republicans. Democrats care more about unemployment than Republicans, and Republicans care more about inflation than Democrats. When Democrats are in power, they choose an inflation rate of $πœ‹_D$, and when Republicans are in power, they choose an inflation rate of $πœ‹_R$. We assume that $πœ‹_D > πœ‹_R$. The Phillips curve is given by $πœ‹_t = πœ‹_t^e βˆ’ 𝛼(𝑒_t βˆ’ 𝑒_n)$. An election is about to be held. Assume that expectations about inflation for the coming year (represented by $πœ‹^e_t$) are formed before the election. (Essentially, this assumption means that wages for the coming year are set before the election.) Moreover, Democrats and Republicans have an equal chance of winning the election.


a) Solve for expected inflation, in terms of $πœ‹_R$ and $πœ‹_D$.

$πœ‹^e_t=0.5(πœ‹_R+πœ‹_D)$

b) Suppose the Democrats win the election and implement their target inflation rate, $πœ‹_D$. Given your solution for expected inflation in part a), how will the unemployment rate compare to the natural rate of unemployment?

The unemployment rate will be less than the natural rate. Inflation will be higher than expected.

c) Suppose the Republicans win the election and implement their target inflation rate, $πœ‹_R$. Given your solution for expected inflation in part a), how will the unemployment rate compare to the natural rate of unemployment?

The unemployment rate will be greater than the natural rate. Inflation will be lower than expected.

d) Now suppose that everyone expects the Democrats to win the election, and the Democrats indeed win. If the Democrats implement their target inflation rate, how will the unemployment rate compare to the natural rate?

The unemployment will equal the natural rate, because $Ο€ = Ο€^e$,and there will be high inflation.

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