Download Answers to Practice Problems 2005

FACULTY OF COMMERCE
AUTUMN SESSION PRACTICE PROBLEMS 2005
ECO220 MACROECONOMIC ANALYSIS
Hints
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Read the questions carefully.
Answer the specific questions asked.
Reread your answer at the end of your exam. Make sure you have
correctly done Hints1 and 2.
Think before you write.
Use graphs and diagrams where they aid your analysis. Be sure to
refer to your graphs/diagrams in your answer. Label axes and
important points on your diagrams.
Always relate your answers back to the models you have learned in
the class.
Essay form questions
1. Assume the economy is described by the following equations:
C = c0 + c1 (Y – T)
I = I0
But let’s add a wrinkle. Let’s say that taxes and government spending are
dependent on GDP. Taxes and government spending are given by:
G = g0 – g1 Y
T = t0 + t 1 Y
(a) Give an explanation for why G might be falling in Y and T might be rising
in Y.
Answer: If a portion of government spending is unemployment benefits and
welfare, then in the short-term as GDP rises, unemployment is lower and so
welfare payments and unemployment benefits will be lower. A portion of
taxes is income and company taxes. These taxes are higher when wages
and firm profits are higher, which will be when GDP is higher.
(b) Derive the new IS curve. (Although really this is just an aggregate
expenditure (AE) curve.)
Answer: Equilibrium in the goods market will require:
Y=C+I+G
Y = c0 + c1 (Y – T) + I0 + G
Then substituting our new terms in for G and T:
Y = c0 + c1 (Y – t0 – t1 Y) + I0 + g0 – g1 Y
Collecting terms we get
(1 – c1 + c1t1 + g1) Y = c0 – c1t0 + I0 + g0
or
Y = [1/(1 – c1 + c1t1 + g1)] (c0 – c1t0 + I0 + g0)
(c) What is the government expenditure multiplier in this case?
Answer: The multiplier on g0 in the above equation is
1/(1 – c1 + c1t1 + g1)
(d) Compare the multiplier to the standard multiplier. Give some intuition as
to why the multiplier is smaller or larger than in the standard case.
Answer: The multiplier in the simplest case when I, G and T do not depend
on income is:
1/(1 – c1) > 1/(1 – c1 + c1t1 + g1)
Since the denominator is larger, the multiplier will be smaller when G and T
vary with income.
An extra unit of income, when G and T do not vary, creates c1 extra units of
consumption demand, which is why we wind up with the multiplier. In the
case where G and T vary, an extra unit of income only creates (1 – t1) c1 units
of demand, as taxes consume some of the addition, and an extra unit of
income lowers government demand by g1. Less extra demand is generated
by an additional unit of income, so our multiplier is smaller.
(e) If an economy faces demand shocks (such as large random changes in
c0), are the shocks to the economy greater or smaller than in the standard
case? Explain.
Answer: Since the multiplier on government spending is smaller when G and
T vary with income, the multiplier on any consumption changes will also be
smaller. [If you check the IS equation, you should see that g0 and c0 enter
identically.] Since the multiplier is smaller, shocks to the economy will be
smaller than in the standard case. [When G and T vary with income like this,
they are sometimes called “automatic stabilizers”, since they reduce variability
in the economy.]
2. (a) Explain carefully using the basic AD-AS and IS-LM model how
equilibrating forces bring the economy back to the natural rate of output after
there is a shock to the economy.
Answer: Assume there is a shock to the economy, so that we move to point
A, where income is less and unemployment greater than the natural rate.
Since unemployment is greater than the natural rate, workers’ wage demands
through the wage-setting relation:
W = Pe F(u, z)
Is reduced as workers are willing to accept lower wages when unemployment
is higher. As wages fall, so prices fall through the firm price-setting relation.
As wages and prices fall, we move down the AD curve from Point A to Point
B. Unemployment falls, and output moves back to the natural rate.
As prices fall, the real supply of money increases. This shifts our LM curve
down/right, so that nominal interest rates drop. As we shift along the IS curve,
output moves back towards the natural rate.
The process stops when unemployment and output are back at their natural
rates, and wages stop falling.
In the opposite case, where the economy experiences a boom, output is
above and unemployment is below the natural rate. Now workers increase
wage demands through the wage-setting relation. Wages and prices rise, so
the AS curve shifts left/up, and we move back to equilibrium. Likewise the
rise in prices reduces the real supply of money, shifting the LM curve left,
raising interest rates, and moving the economy back to equilibrium.
(b) Assume labour unions refuse to allow a drop in nominal wages in
Australia. How might this fact lead to recessions turning into depressions?
Answer: In part (a), we saw that what began the process of moving the
economy back to equilibrium was the lower wages accepted by workers
because of the higher than natural rate of unemployment. If wages are not
reduced in the face of unemployment, firms will not reduce prices because
their costs (wages) do not change.
If prices do not fall when the economy is in a recession, there is no movement
back to the natural rate of output and unemployment in a recession. In this
case, the economy is now in a depression, because the economy can not
move out of a recession.
3. New stricter occupational health and safety rules drive up the mark-up that
firms charge over wages when firms set prices. Show the impact of new
workplace rules on the labour market and then on the economy as a whole.
Pay particular attention to the impact on the natural rate of unemployment.
Answer: Equilibrium in the labour market is given by two equations- the
wage-setting relation:
WS: W = Pe F(u, z)
Or if P = Pe
W/P = F(u, z)
And the price-setting relation:
PS: P = (1 + μ) W
Or
W/P = 1 / (1 + μ)
We can graph these two equations to derive the natural rate of
unemployment:
An increase in the firm’s mark-up will shift the PS curve down to PS’ and raise
the natural rate of unemployment from un to u’n. The real wage is reduced and
the natural rate of unemployment is increased.
For the economy as a whole, the increase in the mark-up has shifted the AS
curve left/up. Since the natural rate of unemployment has risen, the natural
rate of output will fall as well.
What about the effect on AD? We are not really certain about this. Higher
costs might mean lower profits for investors, so investment might drop as a
result. In this case, the AD curve would shift left as well. We might wind up in
a situation similar to the case of an oil shock in Chapter 7.
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A´
AD´
Yn´
4. Suppose the Phillips Curve is given by:
πt = πte + 0.18 – 3 ut
and assume that expectations are based purely on last year’s inflation:
πte = πt-1
(a) What is the natural rate of unemployment?
Answer: The natural rate of unemployment is the rate achieved when prices
are correctly predicted, so πt = πte:
0 = 0.18 – 3un
or un = 0.18/3 = 0.06
Suppose that the economy is initially at the natural rate of unemployment, but
a new government decides to lower unemployment to 4%. Let’s call this year
1.
(b) What is the inflation rate that is required to lower unemployment to 4% in
year 1?
Answer: Let’s say that last year’s inflation rate is π0 and so π e1 = π 0 then
the government needs to set π1 to be:
π1 = π e1 + 0.18 – 3 (0.04)
π1 = π0 + 0.06
So the inflation in year 1 has to be 6% higher than the inflation is year 0.
(c) What is the inflation that is required to keep unemployment at 4% in year
2, year 3, etc?
Answer: Expected inflation in year 2 will be equal to actual inflation in year 1,
so:
π e2 = π1 = π0 + 0.06
So inflation in year 2 will have to be:
π2 = π e2 + 0.18 – 3 (0.04) = π0 + 0.06 + 0.06 = π0 + 0.12
So inflation will have to be 12% higher in year 2 than in year 0.
We see that this process will keep repeating with expected inflation and actual
inflation rising by 6% each year. The inflation rate in year t will have to be:
π t = π0 + 0.06t
5. Given the medium-run model:
ut – ut-1 = -β (gYt – g*Y)
πt – πt-1 = - α (ut – un)
gYt = g*Y – φ(πt – πT)
(a) Explain the economic meaning of the terms g*Y, un and πT.
Answer: The terms g*Y, un and πT are the parameters of the model. g*Y is
the long-run rate of growth (or “natural rate of growth”) of real output, un is the
natural rate of unemployment and πT is the target rate of inflation set by the
reserve bank.
(b) In this model, what are the long-run levels to which gYt, ut and πt return?
Explain using the equations.
Answer: In the long-run, the reserve bank will set inflation equal to targeted
inflation, so the long-run level for πt is πT. If inflation is equal to targeted
inflation, then the dynamic AD equations tells us that gYt is equal to g*Y. Since
inflation is constant at πT then the Phillips Curve tells us that ut is equal to un,
so the long-run level for unemployment is the natural rate of unemployment.
(c) Explain what β, α and φ each represent.
Answer: The constants β tells us how much unemployment changes when
the growth of output is not equal to the natural rate of growth of output. The
constant α tells us how much inflation changes when unemployment is not at
the natural rate of unemployment. And the constant φ is a combination of
how the reserve bank changes interest rates in response to deviations of
inflation from its targeted rate and how responsive the rate of growth is to
changes in the nominal interest rate.
6. BHP has $100m in cash this quarter, and the CEO of BHP is wondering
what to do with the money. The interest rate/discount rate for investors is 5%.
BHP can get a return of 8% on investment projects already planned for the
next year.
(a) Using the concept of share value as the discounted stream of net future
profits, explain carefully and clearly whether BHP should return the money as
dividends to shareholders or whether it should keep the money to invest in the
company.
Answer: The concept of the share value of a firm says that the share value
of a firm (Vt) should obey:
Vt = (det+1 + Vet+1)/(1+r)
Where det+1 is expected dividends, Vet+1 is expected share value and r is the
discount rate.
The aim of the CEO should be to maximize the wealth of the shareholders. If
the CEO returns the $100m in cash to shareholders as dividends today, then
the wealth of the shareholders is
Vt + $100m
If the CEO retains the cash and invests it in the firm with an expected rate of
return of 8%, then the shareholders’ wealth is:
(det+1 + Vet+1 + (1+.08)$100m)/(1 + .05)
Substituting the value of Vt from our first equation, this reduces to:
Vt + (1+.08)$100m/(1 + .05) > Vt + $100m
So shareholder wealth is increased if BHP retains the $100m and invests it in
the company since the 8% return on the $100m invested within the company
exceeds the 5% discount rate on investments.
(b) How would your answer change if the interest rate/discount rate were
10%? Explain carefully.
Answer: We can use the same equations as in part (a). The shareholder
wealth if the $100m is returned in dividends is:
Vt + $100m
And the shareholder wealth if the $100m is invested within the firm is
(det+1 + Vet+1 + (1+.08)$100m)/(1 + .10)
In this case we have,
Vt + (1+.08)$100m/(1 + .10) < Vt + $100m
So the $100m is best returned to the shareholders since the 8% return on the
$100m invested within the company is less than the 10% discount rate on
investments.
7. The government raises taxes which the government plans to spend
updating Australia’s infrastructure- roads, bridges, ports and docks. The
government claims these new taxes are warranted because the improved
infrastructure will raise future growth in the economy.
(a) Using the expectations-augmented IS-LM model, what are the impacts of
these expected changes? Trace each change carefully through the model.
Answer: The government plans to raise taxes in the present, to increase G in
the present and to (hopefully) increase Y in the future. Let’s assume that the
government’s plans work, so that there is a future increase in Y.
In the expectations-augmented IS-LM model, consumption and investment
depend on present and future values of variables. Consumption is a function
of disposable income today and future wealth. Future wealth is a function of
future income and future taxes.
C(Y, T, W(Ye, Te))
In this case, present taxes rise which lowers C, but future wealth rises which
raises C, so the net effect on C is ambiguous.
Investment depends on the present real interest rate, future profits (which
depend on future income), future taxes and future real interest rates.
I(Profits(Ye, Te), r, re)
Future profits should rise if the government investment plans are a success,
so investment might rise.
(b) On a diagram, show the net impact of these changes.
Answer: From our answers in part (a), we are not certain which direction C
moves in, and we think I should rise. G is rising. The net result from
C+I+G
Is uncertain and will depend how each of the components shift.
r
LM
T
G
Ye
IS
Y
8. Consider two open economies- the lands of Nod and GDI- with a fixed
exchange rate between the two currencies.
(a) GDI puts a tariff (a tax) on imported goods from Nod. This tax raises the
price (and so lowers demand) for imports from Nod. What is the impact of the
tariff on the GDI economy? Explain carefully using diagrams where
appropriate.
Answer: The tariff on imported goods from Nod will raise the price and
reduce the quantity of imported goods from Nod. Since imports go down but
exports are unaffected (the exchange rate has not yet changed), net exports
will go up.
An increase in NX will shift the IS curve to the right to IS’, increasing output in
GDI. This increase in GDI income will partly increase demand for imports
from Nod, but the overall result will still be a fall in Nod imports.
In GDI, since we have a fixed exchange rate, interest rates must be kept
constant, so the LM curve will shift right along with the IS curve to LM’, as the
reserve bank moves to prevent the domestic interest rate from rising. Output
will rise in GDI, as will consumption.
LM
i
LM’
i*
IS
Y
Y’
IS’
Y
(b) What is the impact of the tariff on the Nod economy? Explain carefully
using diagrams where appropriate.
Answer: The tariff will have the reverse effect on the Nod economy. As Nod
exports fall due to the GDI tariff, NX will fall in Nod, shifting Nod IS curve to
the left to IS’. The Nod reserve bank will have to accommodate the shift in the
IS curve by shifting the LM curve to the left to LM’.
Nod output falls, as does Nod consumption.
LM’
i
LM
i*
IS’
Y’
Y
IS
Y
(c) How is your answer to (a) and (b) changed if Nod puts taxes on imports
from GDI in retaliation for the GDI tax?
Answer: If Nod puts a tariff on imported GDI goods into Nod, then exports
and imports for both countries will fall. The total amount of goods traded
between the countries will also fall. But NX might not fall in either country (if
exports and imports fall by the same amount). Assuming citizens in both
countries switch consumption from foreign to domestic goods, then the IS
curves might not shift, so output stays the same in both countries.