is the output gap with no cost push shock for simplicity aShow that inflation

# Is the output gap with no cost push shock for

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𝑡 is the output gap (with no cost-push shock for simplicity). a. Show that inflation 𝜋 𝑡 is given by: 𝜋 𝑡 = κ𝐸 𝑡 [? 𝑡 + β? 𝑡+1 + β 2 ? 𝑡+2 + ⋯ ] b. Suppose that the central bank would like to reduce inflation. It announces a contractionary policy whereby it will reduce the output gap starting from some point in the future (brought about by higher interest rates). What happens to current inflation after the announcement, but before the policy is implemented? c. Now suppose that many politicians are known to oppose the policy in part b. Might this change the effects of the policy? Explain. d. The IS curve is: ? 𝑡 = 𝐸 𝑡 [? 𝑡+1 ] − (𝐸 𝑡 [𝑟 𝑡+1 ] − δ) σ . Putting δ = 0 for simplicity, show that the output gap ? 𝑡 is given by: ? 𝑡 = −𝐸 𝑡 [𝑟 𝑡+1 + 𝑟 𝑡+2 + 𝑟 𝑡+3 + ⋯ ]/σ e. Now suppose the central bank announces today that it will raise the nominal interest rate in the future. What happens to the current output gap after the announcement, but before the policy is implemented? f. Given the effect of the output gap on inflation found in part a, can we say what happens to the real interest rate?

• Fall '19
• Kevin Sheedy

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