CHAPTER The Determination of Output in the Short Run

1
CHAPTER The Determination of Output in
the Short Run
8
2
The Determination of Output in the Short Run

• Overview of the Short-Run Model, IS/LM
• The Multiplier Model
• Equilibrium
• The Multiplier Effect
• Fiscal Policy

3
The Determination of Output in the Short Run

• The Goods Market and the IS Curve
• Shifts in the IS Curve
• Shape of the IS Curve
• The Money Market and the LM Curve
• Shifts in the LM Curve
• Shape of the LM Curve
• Monetary Policy and the LM Curve

4
Development of the Short-Run Model

• The long-run model assumes that the economy will
  return to its long-run growth path relatively
  quickly.
• In the 1930s that did not occur
• Real output fell 30 from 1929 to 1933
• Unemployment rose to 25
• J.M. Keynes developed a short-run model that
  focused on aggregate demand, rather than
  aggregate supply.

5
Aggregate Supply when Prices are Fixed
2. High aggregate demand means high output.
1. Low aggregate demand means low output.
Price Level
Short-run aggregate supply
P0
AD1
AD0
Y0
Y1
Real Output
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Short-Run Aggregate Supply and Aggregate Demand

• The short-run aggregate supply curve is perfectly
  horizontal.
• Prices are fixed in the short run
• Changes in aggregate demand cause changes in
  output, not prices
• The aggregate demand (AD) curve differs from the
  demand curve for a single good.
• AD relates the price level of all goods to the
  quantity of all goods in an economy.
• AD shows combinations of price levels and income
  levels where goods and money markets are in
  equilibrium.

7
The Models Behind Aggregate Demand
8
The Multiplier Model

• The multiplier model is a model of the goods
  market.
• Aggregate expenditures (AE) are total
  expenditures are total expenditures on goods and
  services.
• Consumption expenditures by households (C)
• Investment expenditures by firms (I)
• Government expenditures (G)
• Net exports (X-M)

9
Categories of Expenditures

• Induced expenditures are expenditures that vary
  with the level of income of the economy.
• Autonomous expenditures are expenditures that are
  independent of the level of income of the economy.

10
The Consumption Function
C C0 mpc(Y-T)
C0 is autonomous consumption, independent of the
level of income
The marginal propensity to consume (mpc), the
change in consumption for each additional dollar
of disposable income, is induced consumption.
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Aggregate Expenditures
AE C0 mpc(Y-T0) I0 G0 (X0-M0)
Autonomous investment
Autonomous investment
Consumption Function C0 - autonomous mpc(Y-T0)
- induced
Autonomous investment
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Aggregate Expenditures
Aggregate Expenditures Curve
Aggregate Expenditures
The slope of the AE curve equals the mpc
The y-axis inter- cept is the sum of
autonomous expenditures
C0I0G0X0-M0
Aggregate Output
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Aggregate Expenditures and Equilibrium
Aggregate Expenditures Curve
The 45o line shows all points where AE equals
output
Aggregate Expenditures
A
AE0
Equilibrium is where AE equals aggregate productio
n
45o
0
Aggregate Output
Y0
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Equilibrium in the Goods Market

• Assume that
• Autonomous consumption (C0) is 100
• The mpc is 0.9
• Taxes are 50
• Investment (I0) is 200
• Government spending (G0) is 50
• Net exports (X0-M0) are zero
• Aggregate Expenditures (AE) are
• AE 100 .9(Y-50) 200 50
• AE 305 .9Y
• Equilibrium is where Y (output) AE
• Y 305 .9Y so Y 3050 at
  equilibrium

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Equilibrium in the Goods Market
AE Curve
2. Expenditures are 3905 and...
?
C
Aggregate Expenditures
3. Firms cut production, moving the economy
toward point A.
A
?
B
?
1. When production is 4000
45o
0
Aggregate Output
3050
2000
4000
16
Just in Time Inventory Management
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The Multiplier Effect

• The multiplier is the change in output that
  results from a one-dollar change in autonomous
  aggregate expenditures.
• multiplier 1/(1-mpc)
• For mpc 0.9, then the multiplier 1/(1-mpc)
  multiplier 1/(1-.9) 10
• If expenditures decrease by 100, equilibrium
  income decreases by 10 x 100 1000

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The Multiplier Process
Change in Cumulative Change in
Cumulative expenditures change
output income change Step 1
-100 -100 -100 -100 Step 2
- 90 -190 -
90 - 190 Step 3 -
81 -271 - 81 - 271
. . Final Step 0 -1000
0 -1000
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Fiscal Policy and Aggregate Expenditures
AE0
A
AE1
?
Aggregate Expenditures
?
B
1. A 100 decline in autonomous expenditures
45o
0
Aggregate Output
3050
2050
2. causes a 1000 decline in aggregate output
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The Multiplier and the MPC
Multiplier mpc 2.0 .5 2.5
.6 3.3
.67 4.0 .75 5.0
.8 10.0 .9 100.0
.99
As the mpc approaches 1, the multiplier gets
larger.
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A More Realistic Multiplier

• Tax payments and purchases of imports reduce the
  multiplier.
• To include the portion of income paid in taxes
  (t) and spent on imports (m), we replace the mpc
  with the marginal propensity to expend (mpe).
• mpe mpc(1-t) - m
• multiplier 1/(1-mpe) 1/?1-mpc(1-t)m?
• If mpc .8, t .25, and m .1, the multiplier
  is
• multiplier 1/?1-.8(1-.25).1? 2

22
Fiscal Policy and the Multiplier

• Government Spending
• An increase (decrease) in government spending
  will increase (decrease) output by the
  multiplier, 1/(1-mpe), times the change in
  government spending.
• Taxes
• An increase (decrease) in taxes will decrease
  (increase) output by -mpc/(1-mpe) times the
  change in taxes.

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The IS Curve

• The IS curve shows all combinations of real
  interest rates and incomes where the goods market
  is in equilibrium.
• The multiplier model assumes that investment is
  autonomous.
• The IS model assumes that investment is inversely
  related to the interest rate.
• I I0 - I(r)

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Derivation of the IS Curve
AE curve when r4
B
200
?
AE curve when r6
Aggregate Expenditures
?
A
45o
3000
0
1000
Aggregate Output
Real Interest Rate
A
?
6
B
?
IS Curve
4
Aggregate Output
3000
1000
25
Shifting the IS Curve
If the multiplier is 3, an increase in
government spending of 1,000 shifts the IS curve
to the right by 3,000.
Real Interest Rate
A
B
?
?
4
IS1
IS0
Aggregate Output
3000
6000
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Slope of the IS Curve
1. The decline in interest rates increases I0
slightly and the AE curve shifts up by a small
amount.
AE curve when rr0
B
AE curve when rr1
?
?
Aggregate Expenditures
A
2. The multiplier is small, so output rises by
only slightly more than the increase in
autonomous expenditures.
?I
45o
0
Y1
Aggregate Output
Y0
Y0
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Slope of the IS Curve
A
3. The IS is steep because the multiplier is
small and investment is not very sensitive to
the interest rate.
?
r0
B
Real Interest Rate
?
r1
IS (steep)
Y0
Y1
Aggregate Output
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The Money Market and the LM Curve

• The interest rates on the IS curve are determined
  by the demand and supply of money in the money
  market.
• The money market is a financial market where
  highly liquid assets (money) are traded.
• The LM curve shows equilibrium incomes and
  interest rates in the money market.

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The Demand for Money

• The general equation for the demand for money is
• MD MD(Y,i)
• MD represents the demand for money
• Y is income
• MD is positively related to Y
• i is the nominal interest rate
• MD is inversely related to i, the opportunity
  cost of holding money

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Interest Rates, Income, and Money Demand
If income increases from Y0 to Y1, the
quantity of money demanded increases at each
interest rate.
If the interest rate decreases from r0 to r1, the
quantity of money demanded increases from M0 to
M1.
Real Interest Rate
Real Interest Rate
r0
r0
MD (r, Y1)
MD (r)
r1
MD (r, Y0)
Quantity of Money
M0
Quantity of Money
M1
M1
M0
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Autonomous Influences on Money Demand

• Innovation in the financial services industry
• Automatic teller machines decrease the cost of
  transferring funds from one account to another
  and decrease the demand for money
• Expected interest rates
• If higher interest rates are expected in the
  future, the demand for money increases

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Equilibrium Interest Rate in the Money Market
Real Interest Rate
The equilibrium interest rate is determined where
the demand and supply of money are equal, at
point A and r0 and M0.
r2
A

r0
r1
MD (Y0, r)
Quantity of Money
M0
M1
M2
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Derivation of the LM Curve
When Y increases from 2000 to 4000, MD increases
and r increases from 4 to 6.
On the LM curve, a higher r (6) is associated
with a higher Y (4000).
Ms
LM Curve
Real Interest Rate
Real Interest Rate
B
B


6
MD (r, Y4000)
A

4

A
MD (r, Y2000)
Aggregate Output
2000
4000
Quantity of Money
34
Shifts in the LM Curve
LM3
Aggregate Output
Aggregate Output
35
Slope of the LM Curve
Ms
B
B

r1
LM Curve when money demand is very sensitive to
income changes.

Real Interest Rate
MD (r, Y1)
Real Interest Rate

A

r0
A
MD (r, Y0)
Ms
Aggregate Output
Quantity of Money
Y0
Y1
LM Curve when money demand is very sensitive to
interest rate changes.
Real Interest Rate
MD (r, Y1)
D


Real Interest Rate
r1


D
r0
C
C
MD (r, Y0)
Y0
Y1
4
36
Monetary Policy and the LM Curve
Quantity of Money
Aggregate Output