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Suppose that an economy has the following relationship between output and inflation: (SEE IMAGE FOR FORMULAS) Y = Y¯ +α(π−Eπ) and that Okun’s Law, relating output and unemployment by Y − Y¯ = −2(u−u¯), holds.

(a) Derive the Phillips Curve for this economy. (That is, find the relationship between unemployment and inflation)

(b) Suppose the government observes that unemployment is very high and wants to reduce it. To achieve this, it increases the money supply to raise inflation by by 3 percentage points, which is a surprise to individuals in the economy. How much does unemployment go down? (Your answer should be in terms of α).

(c) Now suppose several years later, unemployment has gotten to be quite high again, and the government wants to reduce it again. If individuals in the economy have rational expectations, can the government use the same procedure in part (a) to lower unemployment?

3 . Chapter 14 , Inflation , the Phillips Curve and Rational Expectations ( 2 points ) :Suppose that an economy has the following relationship between output and inflation :"Y = Y ta ( IT – ETC ) and that Okun’s Law , relating output and unemployment by Y -Y = – 2 ( 4 – 1 ) , holds .( a ) Derive the Phillips Curve for this economy . ( That is , find the relationship be -tween unemployment and inflation )( b ) Suppose the government observes that unemployment is very high and wantsto reduce it . To do this , it increases the money supply to raise inflation by by3 percentage points , which is a surprise to individuals in the economy . Howmuch does unemployment go down ? ( Your answer should be in terms of Q ) .( C ) Now suppose several years later , unemployment has gotten to be quite highagain , and the government wants to reduce it again . If individuals in the econ -omy have rational expectations , can the government use the same procedure inpart ( a ) to lower unemployment ?

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