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DEPARTMENT OF ECONOMICS
FALL 2009
UNIVERSITY OF CALIFORNIA, BERKELEY
ECON 182
Problem Set 8
Due in class on Thursday, November 5
th
at the beginning of lecture
.
Students that show their work and write neatly will be graded favorably.
Please write your full name,
GSI, and section time on your problem set.
1.
The Sustainability of Public Debt
This question asks you to explore the important issue of public debt sustainability, using
an analogous framework developed in the lecture for current account sustainability. Define $B
as total government debt in nominal terms, $PS the primary surplus in nominal terms and $FS
the fiscal surplus in nominal terms. Note that $FS = $T  $G – i$B and $PS = $T  $G. Note also
that $FS
t
= $B
t+1
 $B
t
.
a). Derive the primary surplus (as a fraction of GDP) required to stabilize the ratio of
public debt to GDP at its current level. (Hint: Think about the analogous quantities for the fiscal
surplus and primary surplus in the international context.)
PS/Y = (r – g) B/Y
b). Interpret the sustainability rule you found above.
When interest rates are high, the country needs to run a larger primary surplus to stabilize
the debt/GDP ratio. With faster growth, the country needs a lower primary surplus to stabilize
the debt/GDP ratio.
c). Obtain the most recent data on B/Y for the US and Japan (Hint: The Economist
readings for this week is a good place to look!). Assuming a real interest rate of 5% and a real
output growth rate of 2% for both countries, calculate the primary surplus/GDP ratios required
to keep the debt/GDP ratios constant in each case.
In 2008, the B/Y ratios for the US and Japan were 75% and 175% respectively. Plugging
these, and the assumed interest rate and growth rate, into the sustainability rule we found in part
(a), we have the following numbers:
US:
PS/Y = (0.05 – 0.02) * 0.75 = 0.03 * 0.75 = 0.0225 = 2.25%
Japan: PS/Y = (0.05 – 0.02) * 1.75 = 0.03 * 1.75 = 0.0525 = 5.25%
d). How do those ratios change if we use the projected debt/GDP ratios reported in the
article in The Economist this week titled “America’s public debt: Tomorrow’s burden”?
Using the projected government debt to GDP ratios for 2010:
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View Full DocumentUS:
PS/Y = 0.03 * 1 = 3%
Japan: PS/Y = 0.03 * 2.3 = 6.9%
e). Are the fiscal surplus/deficit projections for the US in next few years made by the
Congressional Budget Office consistent with your answers to parts c) and d)?
From the projections made by the CBO, it seems that the US will be running primary
deficits in the next few years, with the result being a rising debt to GDP ratio. This is inconsistent
with what we found in parts (c) and (d).
f). Given your answer to part e), what will be the impact on aggregate demand today of
the planned US fiscal outlays in the next few years? Suppose that the government decides to
implement a fiscal stabilization. Given your answer to the previous question, explain whether
and how it could have an
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 Spring '08
 Kasa
 Economics

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