Econ 100B: Economic Analysis { Macroeconomics
Problem Set #6 { Solutions
Due Date: August 7, 2020
General Instructions:
• Please upload a PDF of your problem set to Gradescope by 11:59 p.m.
• Late homework will not
...
Econ 100B: Economic Analysis { Macroeconomics
Problem Set #6 { Solutions
Due Date: August 7, 2020
General Instructions:
• Please upload a PDF of your problem set to Gradescope by 11:59 p.m.
• Late homework will not be accepted.
• Please put your name, student ID & your GSI’s name at the upper right corner of the front page.
1. Some supply-side economists argue that decreasing taxes will result in higher output
at current target inflation with no change in the policy rate.
(a) What changes in investment and potential output are supposed to follow from a
decrease in taxes according to supply-side economics?
Solution: A reduction in taxes is supposed to increase both autonomous
investment and potential output.
(b) If the assumptions of supply-side economics hold, is is possible for a loss-functionoptimizing central bank to not raise the policy rate? Refer to the optimal-policy
rate equation in your answer.
Solution:
If the economy was in steady-state an increase in autonomous investment
would, it an of itself, be inflationary. An increase in I would result in an
increase in Y which, via the IS curve, would increase output. An increase in
output would result in a positive output gap which, via the Phillips curve,
would be inflationary. If, however, there was at the same time an increase in
potential output that exactly offset the increase in output due to the increase
in I, then the output gap would be zero and there would be no inflation source
in the Phillips curve.
From the perspective of the optimal-policy rate equation:
r(t) = r∗ + 1
ζy
γ + βγ 1
π(t) − πT (1)
where
r∗ = 1
ζY
Y − Y P (2)
we see that this offset would (i) keep the inflation gap closed and (ii) leave r∗
unchanged. Thus, there would be no need to chang
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