Extra Credit Assignment: Exercises

1. (a) Suppose that the central bank has an inflation target of π
T = 2.5. Compute the loss L
to the central bank when the actual inflation rate is 0, 1, 2.5, and 3. You don’t have to
(b) When π
T = 2.5, what is the value of π that minimizes the central bank’s loss function
given in equation (3)? You don’t have to show your work.
1
2. (a) Rewrite the aggregate supply equation (2) to express the output gap y as a function of
π and π
e
. You don’t have to show your work.
(b) Use your answer to part (a) to eliminate y from the IS equation (1) and solve for the
real interest rate r as a function of π, π
e
, and . You don’t have to show your work.
2
(c) Suppose that the public expects that the inflation rate will equal the central bank’s
target (i.e., π
e = π
T
). Use the equation for the real interest rate that you derived in
2(b) to compute the appropriate real interest rate for each combination of π
T
, π
e
, and
.
π
T π
e
 r
2.5 2.5 0
2.5 2.5 0.5
2.5 2.5 1
2.5 2.5 -0.5
2.5 2.5 -1
3
(d) Now, suppose that the public expects that the inflation rate will equal the central bank’s
target plus 1 percent. (i.e., π
e = π
T + 1). Use the equation for the real interest rate that
you derived in 2(b) to compute the appropriate real interest rate for each combination
of π
T
, π
e
, and .
π
T π
e
 r
2.5 3.5 0
2.5 3.5 0.5
2.5 3.5 1
2.5 3.5 -0.5
2.5 3.5 -1