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Worked Problems
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Problem 16.1 - Equilibrium GDP
Problem:
Answer:
Suppose a private closed economy's consumption
schedule is given by the following:
GDP=DI
C
I
6600
6680
80
6800
6840
80
7000
700
80
7200
7160
80
7400
7320
80
7600
7480
80
7800
7640
80
8000
7800
80
Use the values in the table to answer the following:
a.
b.
c.
If planned investment is R80 and independent of
output, what is the equilibrium level of GDP?
What is the level of saving at the equilibrium
level of GDP?
Suppose GDP is R7600. How much unplanned
inventory change will occur? What will likely
happen to GDP as a result?
a.
b.
c.
Equilibrium GDP occurs where the level of
planned expenditures—consumption and
planned investment in a private closed
economy—equals the level of GDP. In this
example, equilibrium occurs at a GDP of R7400.
R7320 + R80 = R7400.
Saving is the difference between disposable
income and consumption. When GDP = DI =
R7400, saving is R80. 80 = R7400 - 7320.
The unplanned inventory adjustment is the
difference between what is produced and what
is purchased, either as consumption or planned
investment. At a GDP of R7600, planned
expenditures are R7480 + R80 = R7560. The
unplanned inventory adjustment is then R40 =
R7600 - R7560. This unplanned increase in
inventories will likely lead firms to produce less
output in the future.
Problem 16.2 - Complete aggregate expenditures model
Problem:
Suppose a private closed economy has an MPC of .8 and
a current equilibrium GDP of R7400 billion.
a.
b.
c.
d.
What is the multiplier in this economy?
Now suppose the economy opens up trade with
the rest of the world and adds net exports of
R20 billion. What impact will this have on
equilibrium real GDP?
Suppose the government plans to spend R100
billion. By how much will this change in
spending ultimately cause GDP to change, and
in what direction?
In order to finance this expansion of
government spending, suppose the government
decides to levy a lump-sum tax of R100 billion.
By how much will GDP change, and in what
direction?
Problem 16.3 - Expenditure gaps
Answer:
a.
b.
c.
d.
The multiplier is 1/(1 - .8) = 5.
These positive net exports represent an initial
increase in spending. The increase in GDP will
be the multiplier times this initial injection, or
R100 billion. R100 = 5 x R20. Real GDP rises
from R7400 to R7500 billion.
GDP will increase by the multiplier times the
initial amount of government spending, or R500
billion in this instance. R500 = 5 x R100.
A lump-sum tax of R100 billion reduces
disposable income by R100 billion at every level
of real GDP. Since the MPC is .8, consumption
will initially fall by R80 billion. Multiplied by the
multiplier of 5, this translates to a drop in GDP
of R400. R400 = 5 x R80.
Problem:
Answer:
Suppose an economy can be represented by the
following table, in which employment is in millions of
workers and GDP and AE are expressed in billions of
dollars:
Employment
Real GDP
Aggregate
Expenditure
100
1200
1275
105
1300
1350
110
1400
1425
115
1500
1500
120
1600
1575
125
1700
1650
a.
b.
c.
d.
Use the table to answer the following:
a.
b.
c.
d.
What is the equilibrium level of GDP?
What kind of expenditure gap exists if full
employment is 120 million workers? What is its
size?
Suppose government spending, taxes, and net
exports are all independent of the level of real
GDP. What is the multiplier in this economy?
If the economy was at equilibrium R200 billion
below its potential, what is the size of the
recessionary expenditure gap?
Equilibrium GDP is R1500 billion, the level at
which real GDP equals aggregate expenditures.
Equilibrium employment is 115, so the
economy is suffering a recessionary
expenditure gap: equilibrium GDP is R1500
billion while full employment GDP is R1600
billion. The gap is the difference between real
GDP and aggregate expenditures at the full
employment level, or R25 billion (+ R1600 R1575.) Said differently, if expenditures were
to increase by R25 at each level of real GDP,
real GDP and aggregate expenditures would be
equal at full employment.
Aggregate expenditures rise by R75 billion for
each R100 billion in real GDP, so the MPC is
.75. The multiplier is 4. 1/(1- .75) = 4.
With a multiplier of 4, an additional
expenditure of R50 billion is required to return
to full employment. R50 = R200/4.