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Chapter 11: The Multiplier Model
Chapter 11: The Multiplier Model
Questions for Thought and Review
1.
The multiplier model is more appropriate for large fluctuations in aggregate
demand, when the economy tends to be subject to greater feedback effects and is
less self-correcting.
2.
Induced expenditures are $1,000. Autonomous expenditures are $1,000.
3.
If planned expenditures are below actual production, income will decline. Here’s
how: when planned expenditures are below actual production, firms will see that
their inventories are building up faster than they’d like. In response, they cut
production. As production falls, so does income. Consumption falls by a fraction
of the decline in income, leading to a further decline in planned expenditures.
This process continues until planned expenditures equal actual production.
4.
At levels of output above equilibrium inventories are building up because planned
expenditures are below actual production. People are not buying all that is
produced.
5.
The aggregate expenditures curve shifts down by the decline in autonomous
expenditures.
6.
The AE curve becomes steeper when the marginal propensity to expend increases.
Equilibrium income rises.
7.
Equilibrium income is $500 (300/.6= 500).
8.
If the mpe is .8, then the value of the
multiplier is 1/.2 or 5. If autonomous
expenditures are $4,200, the equilibrium level
of income in the economy is 5 x $4,200 =
$21,000. This is demonstrated in the
accompanying graph.
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Chapter 11: The Multiplier Model
9. a. If the mpe is .66, the value of the multiplier is
3. A decrease in autonomous expenditures of
$20 will likely result in a decrease in income
of $60.
b. This is demonstrated in the accompanying
graph.
10.
If withdrawals were immediately translated into expenditures, the size of the
multiplier would be infinite since leakages from the economy would be zero.
However, autonomous expenditures would no longer exist. In short, under these
conditions the multiplier model would break down.
11. a. Given that the mpe is 0.8 and autonomous investment has risen by $20, income
will increase by $100 (the multiplier is 1/.2 or 5, and 5 X 20 is 100).
b. With an mpe of 0.5, the multiplier is now only 2 (1/.5), and so the change in
investment causes income to increase by only $40.
c. The decrease in exports and increase in investment cancel each other out so that
autonomous expenditures in the aggregate are unchanged.
d. See the graphs below. The graph on the left corresponds to (a) and the graph on
the right corresponds to (b). The graph to (c) would show the AE curve not
moving at all.
(a)
12.
(b)
Given that the mpe is 0.6, I0 = 1,000; G0 = 8,000; C0 = 10,000; and (X0 - M0) =
1,000, then:
a. Y = 10,000 + .6Y + 1,000 + 8,000 + 1,000.
Y - .6Y = 20,000; 0.4Y = 20,000; Y = 50,000.
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Chapter 11: The Multiplier Model
Thus, the equilibrium level of income in the country is $50,000.
b. If net exports increase by $2,000, income will increase by $5,000 (the multiplier
is 2.5, or 1/.4).
c. According to Okun’s rule of thumb, a one-percentage-point change in
unemployment will cause a 2 percent change in income in the opposite direction.
Thus, if income has increased by $5,000, which is a 10 percent increase, then
unemployment should drop by 5 percentage points.
d. If the mpe falls from 0.6 to 0.5, the multiplier decreases from 2.5 to 2. The answer
to part (a) would now be $40,000; the answer to part (b) would be $4,000; and the
answer to part (c) is that unemployment should still fall by 5 percentage points.
13.
Shocks to aggregate expenditures are any sudden changes in factors that affect C,
I, G, X, or M. This includes consumer sentiment, business optimism, foreign
income, and government policy. It is possible that people could change their
marginal propensities to consume and save, and this could also have an effect on
the economy.
14.
If the mpe is 0.5, then the multiplier is 2. Every $1 increase in autonomous
expenditures will raise income by $2. To close a recessionary gap of $200 the
government needs to generate $100 of additional autonomous spending. It can
accomplish this by increasing government expenditures by $100, or by cutting
taxes by $200 (assuming mpc = mpe).
15.
Cutting taxes by $100 has a smaller effect on GDP than increasing expenditures
by the same amount because people don’t spend the entire amount of the tax
cut—they save some of it, too. The multiplier begins with the increased individual
spending resulting from the tax cut, or the mpc times the tax cut.
16. a. This is shown as a shift down of the AE curve
from AE0 to AE1 and a decline in real income.
b. An improvement would be graphically
represented by a shift up of the AE curve
shown in the graph as the shift from AE1 to
AE2 and a rise in real income.
17.
Given that income is $50,000, the mpe is .75:
a. To reduce unemployment by 2 percentage points (again, by Okun’s rule of
thumb) requires a 4 percent increase in income, which in this case is $2,000. The
multiplier is 4.0, calculated as [1/(1 - mpe)]. To generate a $2,000 increase in
income, increase government spending by $500 or decrease taxes by $667.
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Chapter 11: The Multiplier Model
b. If the mpe is .67, the multiplier is about 3, which means that to generate a $2,000
increase in income, the government would have to increase spending by $667 or
decrease taxes by $1,000.
c. If the mpe is .5, then the multiplier is 2.0, which means that to generate a $2,000
increase in income, the government would have to increase spending by $1,000 or
decrease taxes by $2,000.
18. a. If the mpe is .5, the multiplier is 2. Because there is a recessionary gap of $800,
government would have to increase spending by $400 or decrease taxes by $800
to bring the economy back to long-run equilibrium.
b. If the mpe is .8, the multiplier is 5. Because there is an inflationary gap of $1500,
government would have to decrease spending by $300 or increase taxes by $375
to bring the economy back to long-run equilibrium.
c. If the mpe is .2, the multiplier is 1.25. Because there is an inflationary gap of
$1,200, the government should reduce expenditures by $960 or increase taxes by
$4,800.
d. If the mpe is .7, the multiplier is 3.33. Because there is a recessionary gap of
$1,500, the government should increase expenditures by $450 or decrease taxes
by $643.
19. a. If the mpe is .5, the multiplier is 2. To eliminate the inflationary gap, the
government should undertake a contractionary fiscal policy. Since the economy is
$36,000 above potential, we would advise decreasing government spending by
$18,000 or increasing taxes by $36,000.
b. Using Okun’s rule of thumb, since income falls by 6 percent, we would expect
unemployment to rise by 3 percentage points to 8 percent.
c. The multiplier now becomes 5, so we would advise decreasing government
spending by $7,200 or increasing taxes by $9,000. We would not change our
answer to b.
20.
A circular flow diagram of the economy that would more accurately describe the
multiplier model would include leakages of savings to investment that cause the
diagram to pulsate as the economy continually overshoots equilibrium in response
to shocks to the economy.
21.
A mechanistic model states the equilibrium independent of where the economy
has been or where people want it to be. A mechanistic model is used as a direct
guide for policy prescriptions. An interpretive model is used as a guide that
highlights dynamic interdependencies and suggests the possible response of
aggregate output to various policy initiatives.
22.
In the multiplier-accelerator model changes in output are accelerated because
changes in investment depend on changes in income, not the level of income. This
new interconnection accelerates the fall in demand and can possibly make the
second shift larger than the first. In some cases output can be pushed into a
freefall.
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Chapter 11: The Multiplier Model
Issues to Ponder
1.
In mid-2009, the government budget was running a huge deficit and the state of
fiscal policy was expansionary (low taxes and extremely high expenditures from
the stimulus package) in an effort to spark a recovery from the deep recession that
started in 2008. Economists differ on whether or not the recession has bottomed
out and whether or not the stimulus will work. (This answer may change as the
economy progresses.)
2.
The effects of this invention on the economy would be manifold and in many
ways unpredictable because such major shocks have social, institutional, and
political effects, as well as economic effects. The obvious effect is that the
demand for the pill would likely be tremendous (after people were sure it was
safe), and so production of the pill would gear up to meet the demand. Market
structure and pricing decisions will play a big role in determining the effect of the
change. Alternative forms of transportation would suffer decreases in demand
(cars, mass transit, airplanes, etc.), and levels of production of those goods and
services would adjust, as would employment in those industries and related
industries. Measured GDP might actually fall.
3.
If there is a delay, it will mean that the initial multiplier effects can be small or
non-existent, and then, suddenly, they become large and fast. Uncertain,
changing, expectations can add to the ambiguity of the model’s result.
Chapter 28: Appendix A
1.
To determine precisely how much we would need to decrease taxes we must
determine what the multiplier is. Assuming all other marginal propensities are
zero, the multiplier is 5. The tax cut would initially affect the economy by only .8
times the tax cut, so to increase output by 400, we would decrease taxes by 100
(.8 X 100 X 5 = 400).
2.
We would recommend increasing expenditures by 80 (80 X 5 = 400).
3.
This makes the multiplier 3.57, which means that we would increase expenditures
by about 112, or cut taxes by about 140.
4.
This makes the multiplier 2.08, which means that we would increase expenditures
by about 192 or cut taxes by about 213.
Colander’s Economics, 8e. McGraw Hill © 2010
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Chapter 11: The Multiplier Model
5.
Making taxes and imports endogenous reduces the size of the multiplier because
they increase the leakages from the expenditure flow. Because of taxes and
imports, increases in income will lead to lower increases in expenditures than
otherwise.
6.
This would make the multiplier = 1/(1 - c + ct + m - mt). It would be a slightly
higher multiplier. (The difference between the two assumptions is whether we are
assuming government imports.)
Chapter 28: Appendix B
1. a. As shown in the left-hand graph below, an increase in autonomous expenditures
shifts the AE curve up and causes a movement along the AP curve to the right and
results in a higher equilibrium income level twice the shift in the AE curve.
b. As shown in the right-hand graph below, an increase in autonomous expenditures
shifts the AD curve to the right by twice the increase in autonomous expenditures.
Since the price level is fixed, real output increases by twice the rise in
autonomous expenditures.
Colander’s Economics, 8e. McGraw Hill © 2010
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Chapter 11: The Multiplier Model
c. Since prices are somewhat flexible,
the rise in expenditures is split
between an upward shift of the AE
curve and a rise in prices that
causes a downward shift of the AE
curve that is smaller than the initial
upward shift. The rise in income is
less than twice the initial shock.
This is shown in the graph to the
right. In the AS/AD model, a
flexible price means that the shift
in the AD curve is split between
increases in the price level and
increases in real output. Real
output rises by less than the
multiplier times the increase in
autonomous expenditures.
2. a. The AD curve will become steeper.
b. An increase in the size of the multiplier makes the AD curve flatter because the
effect of changes in the price level on aggregate demand will be augmented even
more by the multiplier.
c. An increase of $20 in autonomous expenditures has no effect on the slope of the
AD curve; the increase only affects the position of the curve.
d. A decline in the price level disrupting the financial market will make the AD
curve steeper because it decreases the price-level interest rate effect.
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