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Solutions to End-of-Chapter Problems in Blanchard & Melino Textbook
Chapters 7+
Note of Jan. 09, 2003: There is no ‘Solution Manual’ for the textbook. The solutions appearing
below have been worked out by Prof. Jump and/or a TA and have not been fully verified; some
may contain errors. Additionally, the solutions have not been completed for all of the chapters in
the textbook; this is a work in progress and additional solutions will be added to this page as they
are completed on a chapter-by-chapter.
Solutions, Chapter 7
7-1
The “proof” follows directly from the fact that the expected rate of price inflation
between time periods t and t+1 is defined as
ðet = (Pet+1 - Pt ) / Pt .
7-2
The exact expression is rt = [(1 + it ) / (1 + ðet )] - 1 .
The approximation is rt . it - ðet .
Note that in both cases rt, it , and ðet are measured in decimal form.
(a) Exact is 4.95% ; approximate is 5.0%.
(b) Exact is 4.76%; approximate is 5.0%.
(c) Exact is 3.45%; approximate is 5.0%.
7-3
There is nothing to prevent the real rate of interest from being negative (though this
seems very unlikely to happen in the real world). A negative real rate would occur if the
expected rate of price inflation were greater than the nominal rate of interest. For
example, suppose ðet = 10% and it = 8%. Then rt = -2.0% (approximately). In this case
lenders are effectively paying borrowers for the privilege lending to them. Why would
anyone lend in that case? Because earning a -2.0% real return is preferable to holding
money and earning a -10% real return.
7-4
(a) This is just simple compounding. If ðem is the monthly expected rate of inflation, then
the annual rate is the value of ðea that solves the equation:
(1 + ðea ) = (1 + ðem )12 , where both rates are expressed in decimal form.
For ðem = 0.30 , ðea = 22.30 (or 2,230.0 %) .
(b) Exact is 4.72% ; approximate is 110.0%.
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7-5
(a) $300,000
(b) $285,940
(c) $173,550
7-6
(a) Will want to use real payments and real interest rates here. It will be difficult to
estimate the value of nominal income, say, 10- years from now without knowing what
will be the rate of price inflation over the next 10 years. But future values of income can
be expected to move in proportion to future rates of price inflation so that the future value
of real income may be estimated without having to know the rate of price inflation.
(b) The nominal value (price) of a house is equal to the present discounted value of the
future nominal rents it would generate. If the nominal rate of interest rises, the value of a
house declines. The choice between renting and buying a house depends upon one’s
expectations of the future value of nominal interest rates. If nominal rates are expected to
rise, it probably pays to rent and avoid the capital losses anticipated for home ownership.
7-7
(a) Using IS and LM schedules plotted on a graph with the axes labelled Y and r :
A decrease in ðe will cause the LM schedule to shift upwards to the left and result in
lower Y and higher r. [For a given value of r, a lower value of ðe will result in a decrease
in the nominal rate of interest – leading to an increase in the quantity of money
demanded. Since the supply of money has not changed, Y must fall and r must rise to
restore the demand for money to its original level.]
(b) Adding a contractionary monetary policy to a decrease in ðe will cause Y to fall by
more than Part (a) and r to rise by more than Part (a).
7-8
Left to the student as an exercise.
7-9
(a) Pa = $10,000 [1 + 1/(1.05) + 1/(1.05)2]
(b) Pi = Pa + $10,000 ;
Piii = $10,000 [1 + 1/(1.10) + 1/(1.05)2]
Pii = 2Pa ;
Piv = $10,000 [1 + 1/(1.10) + 1/(1.10)2]
Solutions, Chapter 8
8-1
Exercise left to student.
8-2
Certainly aggregate consumption would rise immediately as a result of the actions of
young households (e.g., students) who currently have low incomes but expect to have
high incomes in the future. Right now such households can’t borrow against future
earnings and are constrained to have consumption # current income. If borrowing is
suddenly permitted, the close link between C and YD for these households will weaken
2
and the marginal propensity to consume out of current disposable income will decrease.
8-3
The present discounted value of lifetime earnings exceeds $1million for recent university
graduates in Canada.
8-4
Here the present discounted value of profits is the sum of an infinite geometric series. To
answer the question you will have to know something about geometric series in general.
∞
Consider the sum S =
∑ B x . It turns out that S = F [ 1 − x ] , where F is the first term
1
t
t =a
in the summation and x is the common ratio. In the example the first term is F = Bxa , so
1
].
S = Bxa [
1−x
Now in the case of Problem 8-4, B = $10,000 , a = 0 , and x = (1 - 0.1) / (1+r); hence the
present discounted value of profits is
1 +r
1
PV = $10,000 [
] = $10,000 [
].
r + 0 .1
1 − [ 0 .9 / (1 + r )]
(a) r = 0.05; PV of profits = $70,000 > $50,000 cost ; buy the machine.
(b) r = 0.10; PV of profits = $55,000 > $50,000 cost ; buy the machine.
(c) r = 0.15; PV of profits = $46,000 < $50,000 cost ; do not buy the machine.
8-5
(a) Human wealth = (1-0.4 )$50,000 [1 +(1.05)/(1.0) +(1.05)2/(1.0)2] = $94,575
(b) Total wealth = human wealth + nonhuman wealth = $194,575.
(c) Since r = 0, this is easy. Annual consumption = total wealth ÷ 10 = $19,457.50 .
(d) Assuming she still wants the same annual consumption for each of the next 10 years,
current consumption will rise by $1,200. [Remember the tax rate is 40% so the bonus will
yields $12,000 in after-tax income.]
8-6
The (real) present discounted value of $20,000 to be received 30 years from now is
$20,000 / (1.04)30 = $6,166,37. The investor should sell the wine now for $7,000.
8-7
The nominal interest rate is i = 8.0 %, so the present discounted value is
$40,000 [1 +1/(1.08) +1/(1.08)2] .
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Solutions, Chapter 9
9-1
Let Fn denote the face value (or, cash payment at maturity) of a discount bond that will
mature in n years, and let Pn denote the current price of this bond. Then the yield to
maturity is the value of in that solves the following equation: Pn = Fn / (1+in)n .
(a) in = 11.08 %
(b) in = 5.41 %
(c) in = 3.57 %
9-2
(a) i2t . ½ (i1t + ie1t+1 ) = 7.5 %.
(b) (1+ i2t )2 = ( 1+ i1t )(1 + ie1t+1 ); i2t = 7.47 % .
9-3
(a) 4.0 %
9-4
The policy will cause the LM schedule to shift downwards to the right. The current rate
of interest will fall. The yield to maturity on an n-period bond is Rn t approx. equal to
(1/n)[it + ien t+1 + ..........+ ien t+n-1] . If the money supply increase had been anticipated, only
it will fall. Rn t will decline for all values of n but the effect will be smaller the larger is n.
Thus the yield curve will shift down more for shorter maturities than for longer maturities
and assume a more upward-sloping appearance.
9-5
(a) $1,047.62
9-6
Current price = initial dividend [1 / ( r - g )] , where r is the real rate of interest and g is
the annual rate of real dividend growth.
(a) $5,000
9-7
(b) 4.5 %
(c) 5.0 %
(b) $1,000.
(b) $1,428.57 .
(a) The interest rate will rise so stock prices will fall. Profits will also fall, reducing
dividends and further causing share prices to decline.
(b) Ambiguous. The interest rate falls but profits are also likely to fall.
(c) The interest rate falls so stock prices rise.
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(d) Profits will decline, reducing dividends and stock prices
Solutions, Chapter 10
10-1
(a) IS shifts left (down).
(b) IS shifts left, down.
(c) An increase in the current rate of interest is a movement along the IS and/or LM
schedules, but one of these schedules must have shifted for some unspecified reason to
cause the current interest rate to change.
(d) Same answer as Part (c).
(e) LM shifts right (up).
10-2
The critical difference between the statement in this question and the discussion in
section 10-3 of the text is that here, the central bank will act to keep expected future
interest rates from changing. Future taxes will be higher and expected future output will
be lower and both of these expectations cause the current IS schedule to shift to the left.
There is no ambiguity.
10-3
(a) Expected future taxes will be lower and expected future output higher – both effects
causing the current IS schedule to shift to the right. However, future interest rates are
expected to be higher and this causes the current IS schedule to shift to the left. The net
effect on the IS curve is ambiguous.
(b) Expected future taxes will be lower causing the current IS schedule to shift to the
right. To keep future Y constant, the central bank will have to reduce the future money
supply, which means the future interest rate will rise. This, in turn, will cause current I to
decline -- countering the expansionary effect of lowering current taxes. The net effect on
the IS curve in the current time period is ambiguous. What is not ambiguous is that by
preventing current Y from changing, the central bank ensures that current consumption
increases but is fully offset by a decline in current investment.
(c) Expected future taxes will be lower and expected future output higher – both effects
causing the current IS schedule to shift to the right. To keep the current interest rate from
rising, the central bank must take a expansionary policy and shift the LM curve to the
right. Current output unambiguously rises as both consumption and investment increase.
10-4
No. Rational expectations only requires that agents be consistent in their beliefs. For
example, suppose I believe that stock markets follow the phases of the moon – peaking at
full moon and bottoming out at new moon. If I make a prediction about the stock market
a year from now, it would be rational of me to base my prediction on what will be the
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phase of the moon a year from now. If I do, then my prediction is a “rational
expectation”, irrespective of whether my beliefs do or do not have merit. [That said, we
would expect rational agents to revise their beliefs if they systematically yielded incorrect
predictions, but that is a topic for future consideration.]
10-5
Exercise left to the student.
Solutions, Chapter 11
11-1
Exercise left to the student.
11-2
Tradeables are automobiles and computers.
11-3
(a) 1.0 (bushel per bottle)
11-4
The peak value (lowest exchange rate as defined in the text) of the Canadian dollar vis-avis currencies of G10 countries occurred in 1991. That would have been the best time to
travel around the world in terms of lowest cost as measured in Canadian dollars.
11-5
(a) 0.16 (Canadian good / French good)
(b) 1.2 (bushels per bottle)
(c) 1.5 (bushels per bottle)
(b) 0.10 (Canadian good / French good)
(c) A real appreciation of the Canadian dollar of 37.5% .
11-6
(a) $1.11
(b) $1.06
(c) 0.96363 Yen
(d) Since 1.01 > 0.96363, a Japanese resident should invest in Japan.
(e) Et = 0.01 ($cdn /Yen); The implied value of Eet+1 = 0.011, so the Canadian dollar is
expected to depreciate by 10 % relative to the Yen.
(f) i - i* = 5 % but (Eet+1 - Et ) / Et
= +10 %.
Solutions, Chapter 12
12-1
The “domestic demand for goods” is the quantity of all goods purchased by domestic
agents; that is, the sum of C+I+G. Note that the “domestic demand for goods” does not
distinguish between goods that are domestically-produced and those that are imported.
The “demand for domestic goods” is the quantity of all domestically-produced purchased
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either by domestic agents or by agents in the rest of world; that is, the sum of
C+I+G+X-åQ .
12-2
This is kind of roundabout. If a budget deficit occurs, government saving is negative and
total (aggregate) saving, S, is likely to decline. Recall that S-I must equal NX; so if S
declines with I unchanged, NX must also decline and NX is the balance of trade. Another
way of saying the same thing is that if the government runs a deficit, it must borrow to
finance it. If private agents neither save more nor invest less when this occurs, the
borrowed funds must come from the rest of world. As this borrowing from the rest of
world occurs, the balance on capital and financial account of the balance of payments
must move towards surplus. Since NX + Bal. on Capital Account = 0 , if the latter goes to
surplus, the former must go to deficit.
12-3
Large countries tend to be less reliant on foreign trade and, as a consequence, have large
multipliers – meaning that large countries can effectively counter recessions with
domestic monetary and fiscal policy without international co-ordination. In small counties
imports tend to be a large fraction of the “domestic demand for goods” so multipliers
have small values. This means that, say, an expansionary fiscal policy undertaken by a
small country will have a large import leakage and small impact on domestic output.
(The import leakage will benefit the small country’s trading partners.) To counter a
mutual recession, small countries should co-ordinate their monetary and fiscal policies to
gain the maximum effects.
12-4
Here the IS Schedule is
Y = C+I+G+X-åQ
= [400 + 0.5(Y-T)] + [700 - 4,000 i +0.2Y] + G + [100 + 0.1Y*+100å ] - å [0.1Y -50å]
= (0.5 + 0.2 - 0.1 å)Y [400- 0.5 T ] + [700 - 4,000 i ] + G + [100 + 0.1Y*+100å ] + 50 å2
=[
1
] {[400 -0.5 T ]+ [700 - 4,000 i ] + G + [100 + 0.1Y*+100å ] + 50
( 1 − 0 .7 + 0 .1ε )
å2}
Here the multiplier is [
1
] and has value 2.0 when å = 2.
( 1 − 0 .7 + 0 .1ε )
(a) The value of the terms in { } is 1,400 when i = 0.1; so equilibrium Y = 2,800.
(b) C = 400 + 0.5 (2,800 - 200) = 1,700
I = 700 - 4,000 (0.1) + 0.2 (2,800) = 860
NX = [ 100 + 0.1 (1,000) +100 (2)] - 2 [ 0.1 (2,800) - 50 (2)] = 400 - 360 = +40
7
Demand for domestic goods is Z = C+I+G+X-åQ = 2,800 .
(c) (i) The multiplier is 2.0, so an increase in G from 200 to 400 will cause Y to increase
by 400 to the level 3,200.
(ii) C = 400 + 0.5 (3,200 - 200) = 1,900
I = 700 - 4,000 (0.1) + 0.2 (3,200) = 940
NX = [ 100 + 0.1 (1,000) +100 (2)] - 2 [ 0.1 (3,200) - 50 (2)] = 400 - 440 = - 40
Demand for domestic goods is Z = C+I+G+X-åQ = 3,200 .
(iii) Net exports went from a surplus of + 40 to a deficit of - 40 as imports rose in
response to the increase in domestic production.
(d) Increase in Y* from 1,00 to 1,200 will cause X to increase by 20; the multiplier is 2.0
so Y will increase by 40 to the new level 2,840. Now C= 1,720; I=868; NX=+52 .
(iii) The 200 increase in Y* resulted in only a direct increase in the demand for
domestic goods of 20 via exports. This stimulated a multiplied increase of 40 in Y
and induced an increase in åQ of 8. The trade balance improved by 12 because
the original source of the domestic expansion was higher exports.
12-5
An appreciation will lower the prices paid by consumers for foreign goods but it will raise
the prices paid by the rest of world for domestic goods and lead to a decline in exports.
This will not only be disadvantageous to the firms that produce exported goods and their
employees but it will also be contractionary on the economy as a whole – causing GDP to
decline. Governments will normally want to avoid this.
12-6
(a) A depreciation of the exchange rate by itself will both improve the trade balance and
increase output. No fiscal policy is necessary.
(b) A fiscal contraction will by itself reduce output and improve the trade balance. No
exchange rate change is necessary.
12-7
This can be accomplished by an exchange rate depreciation coupled with a contractionary
fiscal policy – say, an increase in taxes. Exports will rise, consumption will decline, and
investment will be unchanged. As for imports, å rises and Q declines, so it is not certain
what happens to real imports åQ . It is possible that åQ might increase but, if so, the
increase must be smaller than the increase in X (because of the Marshall-Learner
condition, which we assume to be satisfied).
12-8
Assuming that I depends positively(+) on Y*, the effect will be to shift the ZZ schedule
8
upwards; i.e., increase the intercept. There will be no effect on the NX schedule.
12-9
The economy of a relatively small geographical area like Ontario is extremely open to
foreign trade. That is, the ratio of both exports and imports to GDP originating in Ontario
is very high. This means that the multiplier for fiscal actions taken by the government of
Ontario is quite small and may even be < 1.0 . (See solution to Q.12-3.)
Solutions, Chapter 13
13-1
Since the investor does not care about risk, she will be indifferent between a fixed and
floating exchange rate. Her expected rate of return from investing in a foreign bond is
(approximately) it* + (Eet+1 - Et) /Et . The investor does not care whether Et+1 is known
with certainty or not; she only cares about the value of Eet+1 .
13-2
We can answer this using either the exact or the approximate versions of interest rate
parity. With the exact version, Et = Eet+1 [(1+it*) /(1+tt)]. With the approximate version
Et = Eet+1 / (1+tt - it*) .
(a) Et = 0.2038 (exact); 0.2041 (approximate)
(b) Et = 0.20 (both)
(c) Et = 0.1963 (exact); 0.1961 (approximate).
13-3
There is no contradiction. Suppose that agents firmly believe that the future exchange
rate will be some specific value Eet+1 . Then interest rate parity implies that the current
exchange rate and the current rate of interest will be inversely related via (the
approximation) Et = Eet+1 / (1+tt - it*) . If we start with t t = it* , then Et = Eet+1 . Now if
the Canadian rate, it , rises, Et must decline in order to maintain interest rate parity in the
face of a fixed expectation about the value of the future exchange rate making Et < Eet+1 .
Now the exchange rate is expected to rise between time periods t and t+1, so the
Canadian dollar is expected to depreciate relative to the German currency (which is now
the Euro but was the Mark at the time our textbook was written).
13-4
The statement is “True” unless we can come up with a combination of policy actions that
will reduce the US trade deficit without simultaneously reducing the US government’s
budget deficit. I can think of only one such combination and it is rather contrived:
Pursue an expansionary monetary policy, coupled with a “balanced budget” fiscal
contraction (reduce both G and T by the same amounts), such that i increases but Y does
not change. The rise in i will lead to a depreciation of the US dollar, causing the trade
balance to improve while the budget deficit (G-T) remains unchanged. [Observe that this
requires that the foreign interest rate i* does not rise on a one-to-one basis in response to
9
higher i – a questionable result, explored in detail in Q. 13-9.]
13-5
Fiscal policy is less effective in an open economy for two reasons. First, the fact that
imports rise (fall) in response to increases (decreases) in Y creates “leakages” in the
circular flow of income and spending that causes the value of the multiplier to be smaller.
Second, fiscal policy actions are at least partially offset by movements in the exchange
rate. For example, an expansionary fiscal policy aimed at increasing Y will cause an
appreciation of the domestic currency, leading to lower NX and limiting the increase in Y.
Monetary policy, on the other hand, is more effective in an open economy. This is
because monetary policy actions cause reinforcing movements in the exchange rate. For
example, an expansionary monetary policy aimed at increasing Y will cause a
depreciation of the domestic currency, leading to higher NX and boosting the increase in
Y.
13-6 and 13-7 pertain to fixed exchange rates and will be answered at a later date.
13-8
(a) From interest rate parity Eet+1 = Et (1+tt - it*) = 0.8 (1 + 0.02 - 0.06) = 0.768
(b) The dollar is expected to appreciate by 4 %.
13-9
(a) If a = 0 , i* is independent of i; a change in the value of i has no effect on i*.
If a = 1, i* is always equal to i; a change in the value of i causes a 1:1 change in i*.
If a = 0.5, i* is partially dependent on i; a change in the value of i causes i* to change
by half the change in i.
(b) When i = 0.04 , i* = 0.05 and Et = Eet+1 / (1+tt - it*) = 10 /0.99 = 10.1010.
When i rises to 0.05, i* will increase to 0.055 and Et falls to 10.0525 – an appreciation
of the domestic currency of 0.5 %.
(c) True. In the extreme case a = 1, any change in i will cause a 1:1 change in i* and
there will be no change in the exchange rate so that monetary policy works as if the
economy was closed.
Addendum
The following “extra” problem is a numerical IS/LM exercise for an open economy.
Suppose P = P* = 1 so that å = E and that ðe = 0 so that r = i.
10
The behaviour of the components of aggregate demand are as follows:
C = 260 + 0.4 (Y-T) and T = 400
I = 0.2 Y - 1,000 i
G = 400
NX = 1,000 + 0.03 Y* - 0.4 Y - 1,500 (1 /E ) and Y* = 10,000 .
The LM schedule is given by
M = 0.10 Y - 600 i and M = 70 .
You are given the following additional information:
Interest rate parity holds between this economy and the rest of world. The rest-of-world
interest rate is i* = 0.10 and economic agents firmly expect the future exchange rate will
be Eet+1 = 1.5 (in units of domestic currency per unit of rest-of-world currency).
(a) Compute equilibrium values for Y, i, and E. Then compute equilibrium values for C,
I, and NX .
(b) Verify that your solution for E represents an equilibrium exchange rate by showing
that the sum of the Balance on Current Account and the Balance on Capital and Financial
Account equals 0. (Assume that the Balance on Investment Income = 0.)
Solutions
(a)
(b)
Y = 1,000
i = 0.05
E = 1.5789
C = 500
I = 150
NX = -50
Since there are no flows of international investment income here,
the Balance on Current Account just equals the Balance of Trade,
or NX = -50.
We know that the Balance on Capital & Financial Account must
equal -1 X Bal. on Current Account, or +50, but let’s verify it by
looking at the Difference between total saving and investment.
Personal Saving = Y - T - C = 100; Government Saving = 0. Total
Saving = 100 and S-I = -50. The difference between S and I
11
represents net purchases of foreign assets by domestic residents.
The value is -50 here, meaning that domestic residents sold 50
more in assets to the rest of world than they purchased. This
represents a net Capital Account inflow of +50 so the Bal. on
Capital & Financial Account is +50.
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