Econ 100C: Intermediate Economics III Name: Spring 2018 ID#:
Extra Credit Assignment: Exercises
May 30, 2018
1. (a) Suppose that the central bank has an inflation target of πT = 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 πT = 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.
2. (a) Rewrite the aggregate supply equation (2) to express the output gap y as a function of
π and πe. 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, πe, and �. You don’t have to show your work.
(c) Suppose that the public expects that the inflation rate will equal the central bank’s
target (i.e., πe = πT ). 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 πT , πe, and
πT πe � 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
(d) Now, suppose that the public expects that the inflation rate will equal the central bank’s
target plus 1 percent. (i.e., πe = πT +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 πT , πe, and �.
πT πe � 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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