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Macro1 Problem #1 Answers (
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In this module you control three tools, which you can only use one at a time. The
tools are government spending (part of fiscal policy), taxes (part of fiscal policy),
and the real rate of interest (monetary policy). Your objective is to learn what
effects these tools have on real GDP and its components, and how these effects differ
among the tools.
Begin by choosing the “Recession” scenario, and record the initial conditions
presented. Then change government spending by at least $20 and observe the long
run results.
1)
Derive the spending multiplier using the information you have about the
initial conditions and the long run results you got by changing government
spending. Explain why you got the results you did.
Real GDP
Consumption
Investment
Unemployment
Inflation
Long Run Results
Default G = 1250
4018.18
2589.68
178.50
10.00%
1.47%
G = 1270
4218.18
2669.18
178.50
8.00%
1.49%
To get the spending multiplier:
Method 1:
The change in GDP is 4218.18 – 4018.18 = 200 while the change in
government spending is 1270 – 1250 = 20. The spending multiplier is the
change in GDP divided by the change in spending = 200/20 so the
spending multiplier is 10.
Method 2:
The marginal propensity to consume is the change in consumption divided
by the change in income. The change in consumption is 2769 – 2589 =
180. The change in income is 4218.18 – 4018.18 = 200. The ratio is
180/200 so the MPC is 0.9. The spending multiplier is (1/(1-MPC) =
(1/(1-0.9)) = 1/0.1 = 10.
Also review the “annual” results of your government spending change each
year for four years. Compare the effects with the graph (Keynesian Cross)
and with the arithmetic of the multiplier process. Explain how all these
aspects of the multiplier process are related.
Real GDP
Consumption
Investment
Unemployment
Inflation
Year 1
4018.18
2589.68
178.50
10.00%
1.47%
Year 2
4038.18
2589.68
178.50
10.00%
1.47%
Year 3
4056.18
2607.68
178.50
9.00%
1.47%
Year 4
4072.38
2623.88
178.50
9.00%
1.48%
In the first year none of the variables has changed from the initial conditions. The
government has demanded more goods and services but no more have been produced yet
-- increasing production takes time. This corresponds to the first upward pointing arrow
on the aggregate expenditure graph.
The second year GDP has increased by the amount of the increase in government
spending (the government is getting the products it wants, they have been produced, so
GDP is up). The amount consumed has not changed even though income has risen,
households want more products but they have not gotten them -- it takes time for the
added goods to be produced. The increase in GDP corresponds to the first horizontal
arrow on the graph; the increase in consumer demand (but no further rise in output)
corresponds to the second vertical arrow. There is no change in investment in any of
these years or in the long run, since in this module only interest rates can affect
investment. Since there was no change in the interest rate, there is no change in
investment.
In the third year production rose by 90% of the previous rise in GDP. This represents
the increased consumer demand now expressed in increased production (the MPC is 90%
so 90% of the rise in income has been spent by households). The increase in production
is shown by the second horizontal arrow, the rise in demand by the third vertical arrow.
There is no visible change in the inflation rate, the changes in GDP are too small to have
any visible effect on this variables. Unemployment has started to decrease, however. If
the rise in GDP had been larger the effects would have been like those in the long run,
with higher inflation (with an upward sloping aggregate supply line more demand means
higher prices and, for a while, higher inflation).
In the fourth year GDP rose by 90% of the increase in income from Year 3, as households
succeed in spending 90% of the increase in income from that year. This rise in GDP is
indicated by the third horizontal arrow, the further rise in demand by a (small) fourth
vertical arrow. In this year there was no further visible decrease in unemployment but the
inflation rate has risen slightly.
2)
Now return to the policy tools menu and change taxes by at least $20. View
the long run results of this policy change and compare them with the results
of the government spending change in (1). Explain why these results are
different.
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Real GDP
Consumption
Investment
Unemployment
Inflation
Long Run Results
Default T = 1250
4018.18
2589.68
178.50
10.00%
1.47%
T = 1230
4198.18
2679.18
178.50
8.00%
1.49%
To get the tax multiplier:
Method 1:
The change in GDP is 4198.18 – 4018.18 = 180 while the change in taxes
is 1250 – 1230 = 20. The spending multiplier is the change in GDP
divided by the change in taxes = 180/20 so the spending multiplier is 9.
Method 2:
The marginal propensity to consume is the change in consumption divided
by the change in income. The change in consumption is 2769 – 2589 =
180. The change in income after taxes is (4198.18 – 1230) – (4018.18 1250) = 200. The ratio is 180/200 so the MPC is 0.9. The tax multiplier is
(MPC/(1-MPC) = (0.9/(1-0.9)) = 0.9/0.1 = 9.
The result is a smaller tax multiplier than the government spending multiplier. The
reason for this is that when taxes are changed by 10 spending begins to change, but the
initial change is not 10, is 9 (the rise in disposable income is 10, but only 90% of that
change in income becomes a change in spending since the MPC is 0.9). After that, every
round of increased spending and income corresponds with a similar round in the spending
multiplier process, every term is the same except that the spending multiplier has the
initial rise in spending of 10, while this term did not exist in the tax multiplier process.
3)
Next return to the policy tools menu and change the interest rate by at least 1%
Compare the effects of the interest rate change with those of the other tools.
Explain why one component of real GDP changed this time even though it did not
change when you changed government spending and taxes.
Real GDP
Consumption
Investment
Unemployment
Inflation
Long Run Results
Default Interest Rate = 0.06
4018.18
2589.68
178.50
10.00%
1.47%
New Interest Rate = 0.05
4368.18
2921.93
196.25
6.00%
1.50%
This cut in interest rates had a strong effect on the economy. However this policy tool
changed by 1/6 of its original value, an equivalent cut in taxes would not have been a cut
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of 20, but of about 207 (the same for the government spending rise) so this doesn’t prove
that this tool is vastly more powerful than the others. The cut in the interest rate
increased investment spending, which was unaffected by the other tools. That is because
the rate of interest -- which changes the profitability of investment -- is the only thing
that affects investment in this module, although this is not true in the real world. The
total impact of the interest rate change was the result of a shift in investment spending
and also a shift in consumer spending (since consumer spending also depends on the
interest rate). This one point change in the interest rate cause an overall increase (shift)
in spending of $350/10 = $35. (That is the total change in GDP divided by the spending
multiplier -- to determine the size shift in spending needed to get GDP to change by
$350.)
4)
Now, look at all of your results from (1) (2) and (3), and use them to
determine the relationship between: (a) inflation rate and unemployment in
this module (the “Phillips curve”), and (b) the relationship between inflation
and real GDP. Do the relationships look like you expected?
If the inflation and unemployment rates are related and the inflation rate
and real GDP are related, what does this say about the relationship between
real GDP and the unemployment rate? Should the unemployment rate and
real GDP be related this way? Explain.
While in the range shown the changes were small, the higher real GDP went, the higher
the inflation rate and the lower the unemployment rate. That also means the higher the
inflation rate the lower the unemployment rate, which is the standard Phillips curve
result. It is proper that higher GDP should be associated with lower unemployment,
since to increase production (GDP) usually requires more labor (as long as productivity
does not change significantly -- more jobs usually means a lower unemployment rate.
(In the real world this does not always happen in the short run due to the “discouraged
worker” effect, but in the long run it should happen.)
Now choose the “Inflation scenario.”
Using the information you have
developed thus far regarding the effects of the policy tools, use one of those
tools to create a long run equilibrium result with a zero inflation rate.
Explain how you determined the correct value. (Note: Trial and error is not
an explanation. You must use the information from the previous scenario to
guide your answer).
The initial conditions for the inflation scenario had a real GDP of $4568 and an inflation
rate over 11%. The recession scenario had an inflation rate of 1.47% with a real GDP of
$4018.18. Since there is a correspondence between changes in inflation and changes in
real GDP to get an inflation rate near zero means getting a real GDP lower than the
recession real GDP. To get to the real GDP of the recession scenario requires a drop of
$550. Using the government spending tool, a spending multiplier of 10 means a cut in
government spending of $55. Since the target would be lower than the recession real
GDP, the cut in spending should be larger than $55. A conservative trial would involve
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a cut in government spending of $60, that reduces real GDP to $3968.18 and that yields
an inflation rate of 1.46%, which is too high but getting closer. A cut in government
spending of $150 produces a better result -- an inflation rate of 0.36% (but a 19%
unemployment rate).
Given the relationship between the tax and spending multipliers, a tax increase of about
11% more than the spending increase would give about the same result. This would be a
tax rise of about 166 (it gives an inflation rate of 0.37%). The interest rate change to
reach this neighborhood is -- if a 1% change in the interest rate creates a change of $350
in GDP -- is (550/350) times 1% or about 1.6%. That rise in interest rates gives an
inflation rate of 1.47%. To get very near zero inflation raise the interest rate to 0.095,
which gives an inflation rate of 0.15%. Of course, since the biases in the price indices
exaggerate inflation, the true inflation rate is about zero if the measured rate is about 1%.
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