**Unformatted text preview: **quations give us two equations
i quating these, we and r. We found
En two unknowns, Ycan solve for r: the following equations in parts (a) and (b):
1,700 – 100r = 500 + 100r IS: Y = 1,700 – 100r. LM: Y = 500 + 100r. d. 1,200 = 200r
r – 100
Equating these, we can solve for r: 1,700 = 6. r = 500 + 100r so 1,200 = 200r and r = 6.
Now that we know r, for Y by solve for Y by into either theitSintothe LM equation to get Y = 1,100.
Knowing r, we solve we can substituting it substituting I or either the IS or the
LM equation. We find
Therefore, the equilibrium interest rate is 6 percent and the equilibrium level of
Y = 1,100.
output is 1,100.
Therefore, the equilibrium interest rate is 6 percent and the equilibrium level of
d. If governmentas depictedincrease from 100 to 150, then the IS equation becomes:
output is 1,100, purchases in Figure 11–11.
If government purchases increase from 100 to 150, then the IS equation becomes: Y = 200 + 0.75(Y – 100)=+200 +–0.75(+ 150. Simplifying, we find:
200 25r Y – 100) + 200 – 25r + 150.
Y
Simplifying, we find: Y = 1,900 – 100r. Y = 1,900 – 100r. This IISccurve is graphed as 2S2 in Figure –12. WeWe see that IS curve shifts to theto
This S urve is graphed as IS I in Figure 11 11–12. see that the the IS curve shifts right by 200.
the right by 200.
r IS1 IS2 Figure 11–12 LM 8
7
Interest rate 04 6
200 0 500 1,100 1,200 1,700 1,900
Income, output Y By equating the new IS curve with the LM curve derived in part (b), we can solve for the new
eBy equating the new IS curve with the LM curve derived in part (b), we can
quilibrium interest rate: solve for the new equilibrium interest rate: 1,900 – 100r = 500 + 100r 1,400 100r = 500 + 100r e can now substitute r into either the IS or the
1,900 – = 200r so r = 7. W
LM equation to find the new level of output. We find
Y = 1,200. 1,400 = 200r
7 = r. We can now substitute r into either the IS or the LM equation to find the new
levelTherefore, the increase in government purchases causes the equilibrium interest rate to rise from
of output. We find 6 percent to 7 percent, while output= 1,200. from 1,100 to 1,200. This is depicted in Figure 11–
Y increases
12. 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
e. If the money supply increases from 1,000 to 1,200, the LM equation is: (1,200/2) = Y – 100r, or
1,200. This is depicted in Figure 11–12. Chapter 11 e. Aggregate Demand II 105 If the money supply increases from 1,000 to 1,200, then the LM equation becomes:
(1,200/2) = Y – 100r, Y or 600 + 100r.This LM curve is graphed as LM2 in Figure 11–13. We see that the LM curve
=
shifts to the right by 100 because of the=increase in r. money balances.
Y 600 + 100 real
This LM curve is graphed as LM2 in Figure 11–13. We see that the LM curve
shifts to the right by 100 because of the increase in real money balances.
r Interest rate IS Figure 11–13 LM1 LM2 6.0
5.5 100 0 500 600 1,100 1,150
Income, output 1,700 Y To determine the new equilibrium interest rate and level of output, equate the IS curve from part
To determine the derived above:
(a) with the new LM curvenew equilibrium interest rate and level of output, equate
the IS curve from part (a) with the new LM curve derived above: 1,700 – 100r = 600 + 100r 1,100 = 200r100r = .600 + 100r
1,700 – 5.5 = r
1,100 = 200r
5.5 = r.
Substituting this into either the I supply causes the interest find
Therefore, the increase in the money S or the LM equation, werate to fall from 6 percent to 5.5 Substituting this into either the IS or the LM equation, we find Y = 1,150. percent, while output increases from 1,100 to 1,150. This is depicted in Figure 11–13.
Y = 1,150.
Therefore, the increase in the money supply causes the interest rate to fall from 6 f. If the price level rises from 2 to 4, then real money balances fall from 500 to 1,000/4 = 250.
percent to 5.5 percent, while output increases from 1,100 to 1,150. This is depicted
The Figure 11–13.
in LM equation becomes:
f. If the price level rises from 2 to 4, then real money balances fall from 500 to Y 1,000/4 = 250. The LM equation becomes:
= 250 + 100r. Y = shifts to the
As shown in Figure 11–14, the LM curve250 + 100r. left by 250 because the increase in the price
level reduces real money balances. Answers to Textbook Questions and Problems As shown in Figure 11–14, the LM curve shifts to the left by 250 because the
in...

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