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Homework 7 Macroeconomi 1

Chapter 15

1. Two friends, Lucy and Adam, start working at the same time, right after graduating from
university. Lucy works as a computer programmer for an annual salary of $70,000; Adam as
a teacher for an annual salary of $45,000. Both friends expect their annual salary to increase
by 2% in real terms each year for the next 3 years. The real interest rate is 0% and the tax
rate on labor income is 30% for both friends. Lucy has no nonhuman wealth, while Adam
was just bequeathed $50,000 worth of bonds from an old aunt who passed away.
a. Calculate the human wealth and the total wealth of the two friends over the next three
years (assume there is uncertainty about the future beyond during these three years).
Lucy’s human wealth and total wealth amount to $149,960; Adam’s human wealth and
total wealth are $96,403 and $146,403, respectively.
b. If both friends wanted to maintain a constant consumption level over this period, what
would that consumption level be? Lucy’s permanent consumption level is $49,987;
Adam’s is $48,801.
c. How would an increase in taxation (to, for instance, 40%) affect the relative wealth
positions of Lucy and Adam? How would that affect their permanent consumption
levels? An increase in taxation would decrease the two friends’ human wealth and
therefore their consumption levels. Lucy’s total wealth and permanent consumption
would decline to $139,248 and $46,416, respectively. Adam’s total wealth and
permanent consumption would decline to $139,517 and $46,506, respectively.
3. Suppose that a private hospital is pondering its next investment the buying of costly medical
equipment for $1 million. The new equipment should bring in real net profits of $150,000
per year. The real interest rate is 8% this year and expected to be constant; the depreciation
rate is 10% for this kind of machinery.
a. Should the hospital make the investment? Compare the cost of the equipment and its
expected profits. No; the present value of expected profits is $833,333 below the actual cost
of the equipment.
b. Suppose that the rate of interest were to decrease permanently, due to an improvement of
the general conditions of the economy, to 5%. How would that affect the hospital’s
investment decision? The expected present value of future profits would rise to $1,000,000.
The investment would carry neither a net loss nor a net profit. The hospital may decide to
invest in the hope that future profits may be slightly higher than expected profits.
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4. Suppose that at age 22, you have just finished college and have been offered a job with a
starting salary of $40,000. Your salary will remain constant in real terms. However, you have
also been admitted to a professional school. The school can be completed in two years.
Upon graduation, you expect your starting salary to be 10% higher in real terms and to
remain constant in real terms thereafter. The tax rate on labor income is 40%.
a. If the real interest rate is zero and you expect to retire at age 60 (i.e., if you do not go to
professional school, you expect to work for 38 years total), what is the maximum you
should be willing to pay in tuition to attend this professional school?
$44,000(1-0.4)36-$40,000(1-0.4)38=$38400
b. What is your answer to part (a) if you expect to pay 30% in taxes?
$44,000(1-0.3)36-$40,000(1-0.3)38=$44,800

Chapter 16

2. Consider these two quotes concerning recent Federal Reserve policy On December 12, 2012
the Federal Reserve issued the following statement: “In particular, the Committee decided
to keep the target range for the federal funds rate at 0 to 1/4 percent and currently
anticipates that this exceptionally low range for the federal funds rate will be appropriate at
least as long as the unemployment rate remains above 6.5 percent.” On July 10, 2013, Ben
Bernanke, Chairman of the Federal Reserve said: “There will not be an automatic increase in
interest rate when unemployment hits 6.5%.”
a. Why do both quotes focus on what policy will be in the future, rather than just explain
what the Fed is doing in the present? Both quotes are clearly trying to influence the
expected future policy interest rate. One says that the rate will remain zero as long as
unemployment is high. The other indicates that even when unemployment falls to the
6.5% level, rates will not automatically rise.
b. Why do you think the Fed Chair made the second statement? A reasonable conjecture is
that the unemployment rate was getting close enough to 6.5% that the chair was
concerned that the expected future path of the policy rate would be at a higher level.
(As of June 2013, the unemployment rate was 7.5% and had rapidly fallen from a peak
of 10.0% in October 2009.)
c. On January 25, 2012, while the nominal policy interest rate was at the zero lower
bound, the Federal Reserve announced an inflation target of 2%. What was the goal of
this announcement? Here the Federal Reserve was trying to ensure that even at zero
nominal rates, expected inflation would be positive and expected real rates would be
negative.
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3. For each of the changes in expectations in parts (a) through (d), determine whether there is
a shift in the IS curve, the LM curve, both curves, or neither. In each case assume that no
other exogenou variable is changing.
a. a decrease in the expected future real interest rate. The IS curve shifts right.
b. an increase in the current real policy interest rate. The LM curve shifts up.
c. an increase in expected future taxes.
There are three effects.
First, an increase in expected future taxes tends to reduce expected future after-tax
income (for any given level of income), and therefore to reduce consumption. This
effect tends to shift the IS curve to the left.
Second, the increase in future taxes (a deficit reduction program) would require that
the central bank reduce the real policy rate so that output returns to potential. At the
lower real policy rate, there is more investment. More investment might, in the very
long run, increase the level of potential and actual output. This could increase wealth
(the expected present discounted value of future output) and thus shift the IS back,
even in the short run.
Third effect on the IS curve is ambiguous. Note that the model of the text has lump sum
taxes. If taxes are not lump sum, the tax increase may increase distortions in the
economy. These effects tend to reduce output (or the growth rate). So the size of any
increase in potential output could be affected by the mix of taxes chosen.
d. a decrease in expected future income. The IS curve shifts to the left.
5. A new president, who promised during the campaign that she would cut taxes, has just been
elected. People trust that she will keep her promise, but expect that the tax cuts will be
implemented only in the future. Determine the impact of the election on current output, the
current interest rate, and current private spending under each of the assumptions in parts
(a) through (c). In each case, indicate what you think will happen to Y=e, r=e, and T=e, and
then how these changes in expectations affect output today.
a. The Fed will not change its current real policy interest rate. The effect on current output
is fairly clear. The tax cut in the future leads to higher expected future income at the
same interest rate. Wealth and consumption rises today. The IS curve shifts right and
the LM curve remains unchanged. Current output rises. Here it is unclear whether the
Fed is expected to increase future interest rates to return output to its original level. If
this is the case, then the rightward shift in IS will be smaller and the increase in current
output will be smaller.
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b. The Fed will act to prevent any change in current and future output. This means that
the Fed will increase the interest rate in the future (shift the LM curve up) so that actual
output remains at the same level. The IS curve would still shift right but the LM curve
shifts up so the intersection is at the same level of income. The higher interest rate
reduces investment by the same amount that the decrease in expected future taxes
increases consumption.
c. The Fed will not change either the current real policy interest rate or the future real
policy interest rate. The contrast here is to part (a). If the Fed explicitly commits to no
change in current and future real interest rates, then the IS shifts right with the
decrease in expected future taxes. There is no leftward shift associated with a potential
increase in real interest rates to return output to its original level.
6. The Irish deficit reduction packages The Focus box “Can a Budget Deficit Reduction Lead to
an Output Expansion? Ireland in the 1980s” provides an example of fiscal consolidation.
Ireland had a large budget deficit in 1981 and 1982.
a. What does a deficit reduction imply for the medium run and the long run? What are the
advantages of reducing the deficit? A deficit reduction in the medium to long run
implies that, if output is to return to potential, the real interest rate must drop. Thus a
fiscal consolidation could lead to higher investment and an increase in the growth rate
of potential output.
b. The box discusses two deficit reduction programs. How did they differ? The discussion
in the text states that the first consolidation focused on tax increases and less on
government spending cuts. The second did the opposite.
c. The box presents evidence that the two deficit reduction programs had different effects
on household expectations. What is that evidence? The evidence presented was that in
the deficit reduction program that focused on spending cuts, household savings rate fell
(which means the consumption function shifted up). Hence although the IS shifted left
with the cut in G, it shifted right as consumer spending increased at the same level of
disposable income. One interpretation is that consumer expected higher future
disposable incomes and were willing to consume more today.
d. Although the data show strong output growth from 1987 to 1989, there is some
evidence of continued macroeconomic weakness in Ireland during the second fiscal
consolidation. What is that evidence? It is worrisome that the latter years of the
consolidation continue to show very high unemployment rates, in fact, much higher
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than earlier in the decade. This cautions against thinking all was well in Ireland during
the second fiscal consolidation.