Equating these, we can solve for
r
:
1,700 – 100
r
= 500 + 100
r
1,200 = 200
r
r
= 6.
Now that we know
r
, we can solve for
Y
by substituting it into either the
IS
or the
LM
equation. We find
Y
= 1,100.
Therefore, the equilibrium interest rate is 6 percent and the equilibrium level of
output is 1,100, as depicted in Figure 11–11.
d.
If government purchases increase from 100 to 150, then the
IS
equation becomes:
Y
= 200 + 0.75(
Y
– 100) + 200 – 25
r
+ 150.
Simplifying, we find:
Y
= 1,900 – 100
r
.
This
IS
curve is graphed as
IS
2
in Figure 11–12. We see that the
IS
curve shifts to
the right by 200.
By equating the new
IS
curve with the
LM
curve derived in part (b), we can
solve for the new equilibrium interest rate:
1,900 – 100
r
= 500 + 100
r
1,400 = 200
r
7 =
r
.
We can now substitute
r
into either the
IS
or the
LM
equation to find the new
level of output. We find
Y
= 1,200.
Therefore, the increase in government purchases causes the equilibrium interest
rate to rise from 6 percent to 7 percent, while output increases from 1,100 to
1,200. This is depicted in Figure 11–12.
104
Answers to Textbook Questions and Problems
1,200
500
1,100
LM
200
Y
1,900
1,700
0
6
7
r
Interest rate
Income, output
IS
2
IS
1
8
Figure 11–12