Homework #4 - Answers The IS-LM Model Due Mar 18
SPP/Econ 556 Winter Term 2004
Alan Deardorff Homework #4 - Answers
Page 1 of 12
Homework #4 - Answers The IS-LM Model Due Mar 18
1. Fun with the Keynesian Cross:
E
a. Use the geometry of the Keynesian Cross diagram shown at the right to derive that the government purchases multiplier is 1/(1?MPC), where MPC is the slope of the planned expenditure line, E. In the figure, planned expenditure has increased (for any given income) by the amount of an increase in government purchases, G. Use the labels in the figure (a, b, c,...) to denote the distances involved (e.g., ab is the distance from Y1 to Y2, or Y). First, identify the following:
c
45?
a
Y1
Y
G
MPC Two other distances that =ab
ab ef de/cd cd, df
E' E f e
d
b
Y2
Y
Then use these to derive the government purchases multiplier:
Y = ab = cd =
1
=1
G ef (df - de) df - de 1 - MPC
cd cd
SPP/Econ 556 Winter Term 2004
Alan Deardorff
Homework #4 - Answers
E
Page 2 of 12
E
b. In the diagram at the right,
suppose that the economy starts, in
time period t=0, out of equilibrium
at income Y0. Suppose also the
following dynamic process for
adjusting when out of equilibrium:
in each period, t, the economy
produces an output equal to the
level of planned expenditure from
the previous period. Find and
label in the figure the levels of
income for time periods 1, 2, and
3.
45?
Y0 Y1 Y2 Y3 Ye
Y
c. In the diagram at the right, draw
E
the new planned expenditure curve
that will exist if there is a cut in
taxes of T=? inch. Label T so
as to show how you determined
where the new curve should be.
(Hint: If taxes are cut by some
E
amount, say $1000, then at any
=? in.
total income Y consumers will buy
T
the same amount that they would
have bought before if their income
had been Y+1000.) Identify also
the old and new equilibrium levels
of income, Y1 and Y2 and the change in income Y.
45?
Y
Here Y is quite a bit smaller than T. Note that the multiplier for a
Y1 Y2
Y
tax cut is ?MPC/(1-MPC), which
is smaller (in absolute value) than ?1 if MPC ................
................
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