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Macro1 Problem #4 Answers (
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In this module you can control two fiscal tools that you can only use one at a time –
government spending and taxation.
Open the Macro1 module, and select “Inflation” as the state of the macroeconomy. Print
or copy the “Initial Conditions” table for further reference.
(1)
Decrease government spending by $45 billion. Use the total GDP that you noted
in the “Initial Conditions” table and the resulting long run GDP from the
decreased government spending to calculate the spending multiplier in your
economy. Show all computations in your answer.
This table shows all the results for all questions.
Initial
G=$1405
G=$1435
T=$1470
T=$1480
conditions
Consumption
$2921.93
$2516.93
$2786.18
$2741.93
$2651.93
Investment
$196.25
$196.25
$196.25
$196.25
$196.25
GDP
$4568.18
$4118.18
$4418.18
$4388.18
$4298.18
Unemployment
4.00%
9.00%
6.00%
6.00
7.00%
Inflation
11.32%
1.49%
1.50%
1.50%
1.50%
The spending multiplier, as applied to changes in government spending, is the
change in real GDP caused by the change in government spending divided by the
change in government spending itself. When government spending is cut by $45
that value is the change in G, the change in real GDP is $4568.18 - $4118.18 = $450,
so the spending multiplier is $450/$45 = 10.
(2)
Decrease government spending by $15 billion. Use the total GDP that you noted
in the “Initial Conditions” table and the resulting long run GDP from the
decreased government spending to calculate the spending multiplier in your
economy. Show all computations in your answer.
When government spending is cut by $15 that value is the change in G, the change
in real GDP is $4568.18 - $4418.18 = $150, so the spending multiplier is $150/$15 =
10.
(3)
Why are these the multiplier results in (1) and (2) the same? For this module, and
for any increase or decrease in government spending, will the spending multiplier
always be the same? Why or why not? Using these results determine the value
of the marginal propensity to save? What is the marginal propensity to consume?
Show all computations in your answer.
The results for the spending multiplier is the same in (1) and (2) because its value
depends on the marginal propensity to spend. In this module there are no exports
or imports and the only spending that varies with the level of income is
consumption, so the marginal propensity to spend is the same as the marginal
propensity to consume. Since the marginal propensity to spend (consume) in this
module is constant the spending multiplier is the same no matter what level of
income is. Since the value of the spending multiplier is 10 and the spending
multiplier is (1/(1 – MPC)) where MPC is the marginal propensity to consume:
10 = (1/(1 – MPC)), so 10 – (10* MPC) = 1 and MPC = -9/-10 = 0.9
Since the marginal propensity to consume plus the marginal propensity to save (in
the absence of an income based tax system) must add up to 1:
1 = MPC + MPS and MPS = 1 – MPC = 1 – 0.9 = 0.1
(4)
Increase taxes by $20 billion. Use the total GDP that you noted in the “Initial
Conditions” table and the resulting long run GDP from the increased taxes to
calculate the tax multiplier. Show all the mathematical computations in your
answer.
The tax multiplier is the change in real GDP divided by the change in taxes that
caused the GDP change. Since taxes were increased by $20 that is the change in
taxes. The change in real GDP is $4568.18 - $4388.18 = $180. That means the tax
multiplier is -$180/$20 = -9
(5)
Increase taxes by $30 billion. Use the total GDP that you noted in the “Initial
Conditions” table and the resulting long run GDP from the increased taxes to
calculate the tax multiplier. Show all computations in your answer.
Since taxes were increased by $30 that is the change in taxes. The change in real
GDP is $4568.18 - $4298.18= $180. That means the tax multiplier is -$270/$30 = -9.
(6)
Why are these the amounts in (4) and (5) the same? For this module, and for any
increase or decrease in taxes, will the tax multiplier always be the same? Why or
why not? If the tax multiplier is the same, what is the marginal propensity to
save? What is the marginal propensity to consume? Show all computations in
your answer.
As with the spending multiplier the tax multiplier’s value depends only on the MPC
(or marginal propensity to spend when more types of spending vary with income).
Since the MPC is the same at all income levels in this module the tax multiplier is
the same for all increases and decreases in taxes. Since the tax multiplier is 9 (in
absolute value) and that equals MPC/(1 – MPC):
9 = MPC/(1 – MPC) so 9 – (9*MPC) = MPC
9 = 10* MPC and 0.9 = MPC
Since the MPC is 0.9 the MPS has to be 0.1.
(7)
Why is the tax multiplier different from the spending multiplier? Explain.
With the spending multiplier the initial increase in spending directly increases real
GDP. The this initial increase in real GDP causes more spending, the amount of
that depending on the MPC. In the case of the tax multiplier the initial change in
taxes does not directly affect real GDP, that is only affected when the change in
disposable income affects spending, and the size of that effect depends on the MPC.
In effect each multiplier is the result of infinite series of spending and income
changes and the only difference between the two sets of series is that the spending
multiplier has one more term to it. For example for a government spending increase
of $10 compared to a tax cut of $10 the real GDP changes would be (assuming and
MPC and propensity to spend of 0.9):
Government spending:
$10 + 9 + 8.1 + 7.29 +……………….
Tax cut:
9 + 8.1 + 7.29 +……………….
The absence of the $10 term in the second row, the lack of a direct impact by the tax
change, is the difference between the two multipliers. The top row sums over infinite
terms to $100, the second row sums over one fewer terms to $90.