This preview shows pages 1–3. Sign up to view the full content.
Economics 102 Introductory Macroeconomics  Spring 2006, Professor J. Wissink
Problem Set 5 – ANSWERS
1.
Consider the super simple linear frugal governed open economy with the marginal propensity to consume
being the
only
nonzero marginal propensity.
Ralph understands why the multiplier for G’ is opposite in
sign of the multiplier for T’, but he can’t seem to intuitively figure out why its
value
would be smaller.
That is, why would a change in G’ work “better” or be “stronger” than an equivalent and opposite change in
T’?
Help Ralph out.
Changes in government spending (∆G) directly boost the economy. By the full amount in the first period, by
c ∆G in the second period (assuming the super simple model), etc. (To get the total change in output at the end
of the day, just sum the infinite series.)
On the other hand, changes in taxation (∆T) boost economy indirectly and less. The reason is that households
save part of their tax rebate. Thus, in the first period, (assuming the super simple model) output changes by
c∆T, in the second period by c
2
∆T, etc. (To get the total change in output at the end of the day, just sum the
inifinite series.)
2.
The MerriamWebster Online Dictionary defines a spendthrift as, “a person who spends improvidently or
wastefully.”
Suppose this actually means a person who never saves. Suppose we had a linear spendthrift
UNgoverned closed economy with no investment.
What is the value of the aggregate desired expenditure
multiplier in this world?
The multiplier would be infinite.
Initial change in autonomous consumption will increase output by the whole amount in each period. There will
be no “equilibrium” level of output, it will grow till infinity.
3.
In a governed model, if taxes are not lumpsum, but depend on income, what happens to the size of the
government spending multiplier, and why?
The easiest answer is to derive the multiplier.
Denoting by C
’
an autonomous consumption and by t a marginal tax rate, let us write:
'
*
*
*
'
*
*
'
(1
)
(
)
(1
)
1
(C +I+G)
1
(1
)
d
d
AE
C
I
G
C
c
t Y
I
G
Y
AE Y
Y
C
c
t Y
I
G
Y
c
t
=
+ +
=
+

+ +
=
=
+

+ +
=


This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document1
1
As long as 0< t < 1,
.
1
1
(1
)
c
c
t



If taxes are not lumpsum, the multiplier is smaller.
The reason is that the effect of a change in government
expenditures on equilibrium output is dampened by taxation.
(So, the initial ∆G will change output by ∆G in
the first period, but only by c(1t)∆G in the second period, etc. Sum the series to get the total change in output
at the end of the day on your own.)
4.
Explain what will happen to the size of both M1 and M2 in each of the following situations.
Assume that all
This is the end of the preview. Sign up
to
access the rest of the document.