## Extra Credit Assignment

## 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

show your work.

(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.

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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.

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(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

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(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

(e) Compare your answers to part (d) with your answers to part (c). How does the increase

in the expected inflation rate affect the appropriate value of the real interest rate?

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