Download Homework for Chapter 10 10-2 (Key Question) What is the multiplier

DEREE COLLEGE
DEPARTMENT OF ECONOMICS
EC 1101 PRINCIPLES OF ECONOMICS II
FALL SEMESTER 2002
M-W-F 13:00-13:50
Office hours:
Wednesdays
15:00-17:00
Dr. Andreas Kontoleon
Contact: [email protected]
Homework for Chapter 10
Homework for Chapter 10
10-2
(Key Question) What is the multiplier effect? What relationship does the MPC bear to
the size of the multiplier? The MPS? What will the multiplier be when the MPS is 0, .4,
.6, and 1? When the MPC is 1, .90, .67, .50, and 0? How much of a change in GDP will
result if businesses increase their level of investment by $8 billion and the MPC in the
economy is .80? If the MPC is .67? Explain the difference between the simple and the
complex multiplier.
The multiplier effect is the magnified increase in equilibrium GDP that
occurs when any component of aggregate expenditures changes. The
greater the MPC (the smaller the MPS), the greater the multiplier.
M=1/MPS
MPS = 0, multiplier = infinity;
MPS = .4, multiplier = 2.5;
MPS = .6, multiplier = 1.67;
MPS = 1, multiplier = 1.
M=1/1-MPC
MPC = 1; multiplier = infinity;
MPC = .9, multiplier = 10;
MPC = .67; multiplier = 3;
MPC = .5, multiplier = 2;
MPC = 0, multiplier = 1.
MPC = .8:
M=1/(1-0.8)? 5
Change in GDP = $40 billion (= $8 billion X multiplier of 5);
1
MPC = .67:
M=1/(1-0.67)? 3
Change in GDP = $24 billion ($8 billion ? multiplier of 3).
The simple multiplier takes account of only the leakage of saving. The
complex multiplier also takes account of leakages of taxes and imports,
making the complex multiplier less than the simple multiplier.
10-3
Graphically depict the aggregate expenditures model for a private closed economy. Next,
show a decrease in the aggregate expenditures schedule and explain why the decrease in
real GDP in your diagram is greater than the initial decline in aggregate expenditures.
What would be the ratio of a decline in real GDP to the initial drop in aggregate
expenditures if the slope of your aggregate expenditures schedule were .8?
The decrease in real GDP in the diagram is greater than the initial
decline in aggregate expenditures because of the multiplier effect.
The multiplier is given by: M=1/(1-0.8) =5
The ratio of decline in real GDP to the initial drop of expenditures would
be a ratio of 5:1. That is, if expenditures declined by $5 billion, GDP
should decline by $20 billion. On the graph it can be seen that a one
unit decline in (C + I) leads to a four-unit decline in real GDP.
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10-3
Suppose that Zumo has an MPC of .9 and real GDP of $400 billion. If investment
spending falls by $4 billion, what will be its new level of real GDP?
The multiplier is 10 or 1/(1-.9) so 10 x -$4 billion = -$40 billion. The new GDP is $400 billion $40 billion = $360 billion.
10-4
(Key Question) The data in columns 1 and 2 of the table below are for a private closed
economy.
(1)
Real
domestic
output
(GDP=DI)
billions
(2)
Aggregate
expenditures
private closed
economy,
billions
$200
$250
$300
$350
$400
$450
$500
$550
$240
$280
$320
$360
$400
$440
$480
$520
(3)
(4)
(5)
(6)
Exports,
billions
Imports,
billions
Net
exports,
private
economy
Aggregate
expenditures,
open
billions
$20
$20
$20
$20
$20
$20
$20
$20
$30
$30
$30
$30
$30
$30
$30
$30
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
$ _____
a. Use columns 1 and 2 to determine the equilibrium GDP for this
hypothetical economy.
b. Now open this economy for international trade by including the export
and import figures of columns 3 and 4. Calculate net exports and
determine the equilibrium GDP for the open economy. Explain why
equilibrium GDP differs from the closed economy.
c. Given the original $20 billion level of exports, what would be the
equilibrium GDP if imports were $10 billion greater at each level of
GDP? Or $10 billion less at each level of GDP? What generalization
concerning the level of imports and the equilibrium GDP do these
examples illustrate?
d. What is the size of the multiplier in these examples?
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(1)
Real
domestic
output
(GDP=DI)
billions
(2)
Aggregate
expenditures
private closed
economy,
billions
$200
$250
$300
$350
$400
$450
$500
$550
$240
$280
$320
$360
$400
$440
$480
$520
(3)
(4)
(5)
(6)
Exports,
billions
Imports,
billions
Net
exports,
private
economy
Aggregate
expenditures,
open
billions
$20
$20
$20
$20
$20
$20
$20
$20
$30
$30
$30
$30
$30
$30
$30
$30
$ -10
$ -10
$ -10
$ -10
$ -10
$ -10
$ -10
$ -10
$230
$270
$310
$350
$390
$430
$470
$510
(a) Equilibrium GDP for closed economy = $400 billion.
(b) See table above
Equilibrium GDP for the open economy is $350 billion, $50 billion below the $400
billion equilibrium GDP for the closed economy. The $-10 billion of net exports is a
leakage which reduces equilibrium GDP by $50 billion.
(c) Imports = $40 billion: Aggregate expenditures in the private open economy would
fall by $10 billion at each GDP level and the new equilibrium GDP would be
$300 billion. Imports = $20 billion: Aggregate expenditures would increase by
$10 billion; new equilibrium GDP would be $400 billion.
Exports constant, increases in imports reduce GDP; decreases in imports increase
GDP.? imports are forms of leakages
(d) Since every rise of $50 billion in GDP increases aggregate expenditures by $40
billion, the MPC is .8
i.e. MPC=change in spending/change in income=40/50=0.8
and then M=1/(1-MPC)=5
4
10-5
Assume that, without taxes, the consumption schedule of an economy is as shown below:
GDP,
billions
Consumption,
billions
$100
200
300
400
500
600
700
$120
200
280
360
440
520
600
a. Graph this consumption schedule and note the size of the MPC.
b. Assume now a lump-sum tax system is imposed such that the government collects
$10 billion in taxes at all levels of GDP. Graph the resulting consumption schedule
and compare the MPC and the multiplier with that of the pretax consumption
schedule.
(a)
The size of the MPC is 80/100 or .8 because consumption changes by 80 when GDP
changes by 100.
(b)
Before we introduced the tax GDP=DI (since we have no taxes). Once we introduce tax
for each level of GDP the DI will fall short of GDP by the amount of the tax. In this case by $10
billion. This decline in DI reduces both C and S at each level of GDP. The MPC and MPS
determine the declines in C and S. In our case MPC is 0.8 and hence we calculate C at every
level by reducing each level of C by 0.8*10=8
The new (after tax C schduel is shown in the table below)
(c)
The multiplier should be 5 because the MPS is .2 and 1/.2 is 5.
The MCP and M are the same for both C-schedules since the slope of the C has not
changed (we only have a shift).
GDP,
billions
$100
200
300
400
500
600
700
Consumption,
billions
$120
200
280
360
440
520
600
DI
GDP-Tax
90
190
290
390
490
590
690
5
After-tax
Consumption
112
192
272
352
432
512
592
10-8
(Key Question) Refer to columns 1 and 6 of the tabular data for question 4. Incorporate
government into the table by assuming that it plans to tax and spend $20 billion at each
possible level of GDP. Also assume that all taxes are personal taxes and that government
spending does not induce a shift in the private aggregate expenditures schedule.
Compute and explain the changes in equilibrium GDP caused by the addition of
government.
Before G is added, open private sector equilibrium will be at 350. The addition of government
expenditures of G to our analysis raises the aggregate expenditures (C + I g +Xn + G) schedule
and increases the equilibrium level of GDP as would an increase in C, Ig, or Xn. Note that
changes in government spending are subject to the multiplier effect which is M=5
The addition of $20 billion of government expenditures and $20 billion of personal taxes
increases equilibrium GDP from $350 to $370 billion. The $20 billion increase in G raises
equilibrium GDP by $100 billion (= $20 billion x the multiplier of 5); the $20 billion increase in
T reduces consumption by $16 billion at every level. (= $20 billion x the MPC of .8). This $16
billion decline in turn reduces equilibrium GDP by $80 billion ( $16 billion x multiplier of 5).
The net change from including balanced government spending and taxes is $20 billion (= $100
billion - $80 billion).
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10-10 (Key Question) Refer to the accompanying table in answering the questions which
follow:
(1)
Possible levels
of employment,
millions
90
100
110
120
130
(2)
Real do mestic
output,
billions
$500
550
600
650
700
(3)
Aggregate
Expenditures
C + Ig +Xn + G
$520
560
600
640
680
a. If full employment in this economy is 130 million, will there be an inflationary or
recessionary gap? What will be the consequence of this gap? By how much would
aggregate expenditures in column 3 have to change at each level of GDP to eliminate
the inflationary or recessionary gap? Explain.
b. Will there be an inflationary or recessionary gap if the full-employment level of
output is $500 billion? Explain the consequences. By how much would aggregate
expenditures in column 3 have to change at each level of GDP to eliminate the
inflationary or recessionary gap? Explain.
c. Assuming that investment , net exports, and government expenditures do not change
with changes in real GDP, what are the sizes of the MPC, the MPS, and the
multiplier?
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(a)
Equilibrium GDP is $600 billion, while full employment GDP is $700 billion? we have
a recessionary gap.
In this situation:
Employment will be 20 million less than at full employment. Aggregate expenditures
would have to increase by $20 billion (= $700 billion -$680 billion) in order to shift the
AE curve up.
(i.e. $20b increase at each level of GDP to eliminate the inflationary gap).
AE0
AE
AE1
Recessionary
gap= $20 million
Real GDP
$600
$700
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(b)
Aggregate expenditures will be excessive, causing demand-pull inflation.? An
inflationary gap.
Aggregate expenditures would have to fall by $20 billion (= $520 billion -$500 billion) in order
to shift the AE curve down.
(i.e. $20b decrease at each level of GDP to eliminate the inflationary gap).
AE
AE1
AE0
Inflationary gap=
$20 million
Real GDP
$500
$600
(c)
MPC = .8 (= $40 billion/$50 billion); MPS = .2 (= 1 -.8); multiplier = 5 (=1/(1MPC)=1/(1-0.8)=1/.2).
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