### Chapter-5-QC-4

```ISL244E
Macroeconomics
Problem Session-6
by
Research Assistant
Serkan Değirmenci
(Ph.D. Candidate)
D202/19.03.2012
# Today #
• Blanchard (2009), Macroeconomics:
#THE SHORT RUN# (CHAPTER 3+4=5)
- Chapter 4: Financial Markets:
(btw pages: 85-106)
Quick Check (page 104-105): 2-3-4
- Chapter 5: Goods and Financial Markets:
(btw pages: 107 -131)
Quick Check (page 127-128): 2-3-4
Chapter-4-QC-2 (Page: 104)
2.
Suppose that a person’s yearly income is \$80,000.
Also, suppose that this person’s money demand function is given
by Md = \$Y(0.30 – i)
a.
b.
c.
d.
e.
What is this person’s demand for money when the interest rate is
4%? 8%?
Explain how the interest rate affects money demand.
Suppose that the interest rate is 4%. In percentage terms, what
happens to this person’s demand for money if her yearly income
is reduced by 50%?
Suppose that the interest rate is 8%. In percentage terms, what
happens to this person’s demand for money if her yearly income
is reduced by 50%?
Summarize the effect of income on money demand. In
percentage terms, how does this effect depend on the interest
rate?
2. a.
b.
i=0.05: Money demand = \$80,000(0.30-0.05) = \$20,000
i=0.10: Money demand = \$80,000(0.30-0.10) = \$16,000
Money demand decreases when the interest rate
increases because bonds, which pay interest, become more
attractive.
c.
The demand for money falls by 50%.
d.
The demand for money falls by 50%.
e.
A 1% increase (decrease) in income leads to a 1%
increase (decrease) in money demand.
This effect is independent of the interest rate.
Chapter-4-QC-3 (Page: 104)
3. Suppose that money demand is given by
Md = \$Y(0.25 – i)
where \$Y is \$100.
Also, suppose that the supply of money is \$20.
a. What is the equilibrium interest rate?
b. If the Federal Reserve Bank wants to increase i by
10 percentage points (e.g., from 2% to 12%), at
what level should it set the supply of money?
3. a.
b.
MD = MS
\$20 = MD = \$100(0.25-i)
i = 5%
i = 5% => i* = 15%
MD = MS = \$100(0.25-0.15)
M = \$10
Chapter-4-QC-4 (Page: 105)
4. Consider a bond that promises to pay \$100
in one year.
a. What is the interest rate on the bond if its
price today is \$75? \$85? \$95?
b. What is the relation between the price of
the bond and the interest rate?
c. If the interest rate is 8%, what is the price of
the bond today?
4.
a.
b.
c.
i = 100/\$PB –1
\$PB = \$75 => i = 33%
\$PB = \$85 => i = 18%
\$PB = \$95 => i = 5%
When the bond price rises, the
interest rate falls.
\$PB = 100/(1+i) = 100/(1.08) ≈ \$93
Chapter-5-QC-2 (Page: 127-128)
2.
Consider first the goods market model with constant investment that we saw in
Chapter 3. Consumption is given by
C = c0 + c1(Y-T)
a.
and I, G, and T are given.
Solve for equilibrium output. What is the value of the multiplier?
Now let investment depend on both sales and the interest rate:
b.
I = b0 + b1Y – b2i
Solve for equilibrium output. At a given interest rate, is the effect of a change in
autonomous spending bigger than what it was in part (a)? Why?
(Assume c1 + b1 <1.)
Next, write the LM relation as
M/P = d1Y – d2i
c.
d.
Solve for equilibrium output. (Hint: Eliminate the interest rate from the IS and LM
relations.) Derive the multiplier (the effect of a change of one unit in autonomous
spending on output).
Is the multiplier you obtained in part (c) smaller or larger than the multiplier you
derived in part (a)? Explain how your answer depends on the parameters in the
behavioral equations for consumption, investment, and money demand.
2. a.
Y* = [1/(1-c1)][c0-c1T+I+G]
The multiplier is 1/(1-c1).
b. Y* = [1/(1-c1-b1)][c0-c1T+b0-b2i+G]
The multiplier is 1/(1-c1-b1).
Since the multiplier is larger than the multiplier in part (a),
the effect of a change in autonomous spending is bigger
than in part (a). An increase in autonomous spending now
leads to an increase in investment as well as consumption.
c.
Substituting for the interest rate in the answer to part (b),
Y* = [1/(1-c1-b1+b2d1/d2)][c0-c1T+b0+(b2/d2)(M/P)+G].
The multiplier is 1/(1-c1-b1+b2d1/d2).
The multiplier is greater (less) than the multiplier in part
(a) if (b1-b2d1/d2) is greater (less) than zero.
2. d.
The multiplier as measured in part (c) measures the marginal effect of an increase
in autonomous spending on equilibrium output. As such, the multiplier is the
sum of two effects: a direct effect of output on demand and an indirect effect of
output on demand via the interest rate.
The direct effect is equivalent to the horizontal shift of the IS curve. The indirect
effect depends on the slope of the LM curve (since the equilibrium moves along
the LM curve in response to a shift of the IS curve) and the effect of the interest
rate on investment demand.
The direct effect is captured by the sum c1+b1, which measures the marginal
effect of an increase in output on the sum of consumption and investment
demand. As this sum increases, the multiplier gets larger.
The indirect effect is captured by the expression b2d1/d2 and tends to reduce the
size of the multiplier. The ratio d1/d2 is the slope of the LM curve, and the
parameter b2 measures the marginal effect of an increase in the interest rate on
investment.
Note that the slope of the LM curve becomes larger as money demand becomes
more sensitive to income (i.e., as d1 increases) and becomes smaller as money
demand becomes more sensitive to the interest rate (i.e., as d2 increases).
Chapter-5-QC-3 (Page: 128)
3.
a.
The response of investment to fiscal policy
Using the IS-LM diagram, show the effects on output and the interest rate of a
decrease in government spending. Can you tell what happens to investment?
Why?
Now consider the following IS-LM model:
C = c0 + c1 (Y-T)
I = b0 + b1Y – b2i
M/P = d1Y – d2i
b.
Solve for equilibrium output. Assume c1 + b1 < 1. (Hint: You may want to work
through problem 2 if you are having trouble with this step.)
c.
d.
Solve for the equilibrium interest rate. (Hint: Use the LM relation.)
Solve for investment.
e.
Under what conditions on the parameters of the model (i.e., c0, c1,
and so on) will investment increase when G decreases? (Hint: If G
decreases by one unit, by how much does I increase? Be careful; you
want the change in I to be positive when the change in G is
negative.)
f.
Explain the condition you derived in part (e).
3. a. The IS curve shifts left. Output and the interest rate fall. The effect on
investment is ambiguous because the output and interest rate effects work in
opposite directions: the fall in output tends to reduce investment, but the fall in
the interest rate tends to increase it.
b.
From the answer to 2(c),
Y* = [1/(1-c1-b1+b2d1/d2)][c0-c1T+b0+(b2/d2)(M/P)+G].
c
From the LM relation, i
= Y(d1/d2)–(M/P)/d2.
To obtain the equilibrium interest rate, substitute for equilibrium Y from part
(b).
i* = Y*(d1/d2)–(M/P)/d2.
d.
I* = b0+b1Y*-b2i* = b0+(b1-b2d1/d2)Y*+(b2/d2)(M/P)
To obtain equilibrium investment, substitute for equilibrium Y from part (b).
3. e. From part (b), holding M/P constant, equilibrium Y decreases by
[1/(1-c1-b1+b2d1/d2)] when G decreases by one unit. From part (d),
holding M/P constant, I decreases by (b1- b2d1/d2)/(1-c1-b1+b2d1/d2)
when G decreases by one unit. So, if G decreases by one
unit, investment will increase when b1<b2d1/d2.
f. A fall in G leads to a fall in output (which tends to reduce
investment) and to a fall in the interest rate (which tends to
increase investment). Therefore, for investment to increase,
the output effect (b1) must be smaller than the interest rate
effect (b2d1/d2).
Note that the interest rate effect is the product of two factors: (i)
d1/d2, the slope of the LM curve, which gives the effect of a oneunit change in equilibrium output on the interest rate, and (ii) b2,
which gives the effect of a one-unit change in the equilibrium
interest rate on investment.
Chapter-5-QC-4 (Page: 128)
4.
a.
b.
c.
d.
e.
f.
g.
Consider the following IS-LM model:
C = 400 + 0,25YD
I = 300 + 0,25Y – 1500i
G = 600
T = 400
(M/P)d = 2Y – 12000i
M/P = 3000
Derive the IS relation. (Hint: You want an equation with Y on the left side and everything
else on the right.)
Derive the LM relation. (Hint: It will be convenient for later use to rewrite this equation
with i on the left side and everything else on the right.)
Solve for equilibrium real output. (Hint: Substitute the expression for the interest rate
given by the LM equation into the IS equation and solve for output.)
Solve for the equilibrium interest rate. (Hint: Substitute the value you obtained for Y in
part (c) into either the IS or LM equations and solve for i. If your algebra is correct, you
should get the same answer from both equations.)
Solve for the equilibrium values of C and I, and verify the value you obtained for Y by
adding C, I, and G.
Now suppose that the money supply increases to M/P = 4320. Solve for Y, i, C, and I, and
describe in words the effects of an expansionary monetary policy.
Set M/P equal to its initial value of 3000. Now suppose that government spending
increases to G = 840. Summarize the effects of an expansionary fiscal policy on Y, i, and C.
4.
a.
Y=C+I+G=400+.25(Y-400)+300+.25Y-1500i+600
Y=2400-3000i => IS relation
b.
M/P = 3000 = 2Y-12000i
i = Y/6000-1/4 => LM relation
c.
Substituting from part (b) into part (a) gives
Y* = 2100
d.
Substituting from part (c) into part (b) gives
i* = 10%
e.
C* = 825; I* = 675; G = 600; C+I+G = 2100
4. f. Y* = 2320; i* = 2,67%; C* = 880; I* = 840.
A monetary expansion reduces the interest rate and
increases output.
Consumption increases because output increases.
Investment increases because output increases and the
interest rate decreases.
g. Y* = ?; i* = ? %; C* = ?; I* = ?. (TRY YOURSELF!)
A fiscal expansion increases output and the interest rate.
Consumption increases because output increases.
Investment is affected in two ways: the increase in output
tends to increase investment, and the increase in the
interest rate tends to reduce investment.
In this example, these two effects exactly offset one another,
and investment does not change.
# Halfway Check List #
GNH (2009): Chapters: 1-5-6-11
Blanchard (2009): Chapters: 1-2-3-4-5
Highlights:
Measuring National Income and Growth
Money, Banking and Financial Markets
Goods and Financial Markets: The IS-LM
Model
to be continued…
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