Assume that consumers and firms use the currently observed inflation rate as their best guess about inflation next year, and that the central bank follows the Taylor rulei= ̄r+π+ 0.5(π−π⊗) + 0.5ˆYwhereiis the nominal interest rate set by the central bank, ̄ris (the central bank’sestimate of) the long-run real interest rate,πis current inflation,π⊗is the inflation target of the central bank, andˆYis the output gap. Assume further that the centralbank has the inflation targetπ⊗= 1%, the output gap isˆY= 0, and that the centralbank estimates the the long run equilibrium real interest rate to ̄r= 3% per year.

(a) What is the nominal interest rate if current inflation isπ= 1%?

(b) Then, what is the expected real interest rate (r)?

(c) What is the nominal interest rateiif current inflation isπ= 3%?

(d) Then, what is the expected real interest rate (r)?

(e) What is the expected real interest rate (r) if current inflation isπ=−1%?