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Chapter 16: Suggested Answers to Textbook Questions
1.
(a) The value of the dollar has fallen relative to the mark and the value of the mark has risen relative
to the dollar. However, no conclusions can be made about the overall strengths of the currencies.
(b) It is more likely that the dollar/yen rate has gone up than down, although it is possible that it
could have declined.
(c) It is more likely that the mark/yen rate has gone down than up, although it is possible that it
could have increased.
Export Quantity
Import Quantity
(a)
10 m
.002 m
(b)
10 m
.002 m
(c)
10.5 m
.002 m
(d)
11 m
.0019 m
(e)
14 m
.0018 m
In Dollars:
Export Price
Import Price
Export Revenue
Import Spending
Trade Balance
$10
$50,000
$100 m
$100 m
0
$10
$55,000
$100 m
$110 m
$ −10 m
$10
$55,000
$105 m
$110 m
$ −5 m
$10
$55,000
$110 m
$104.5 m
$5.5 m
$10
$55,000
$140 m
$99 m
$41 m
In Euros:
Export Price
Import Price
Export Revenue
Import Spending
Trade Balance
20 euros
100,000 euros
200 m euros
200 m euros
0
18.18 euros
100,000 euros
181.8 m euros
200 m euros
−18.2 m euros
18.18 euros
100,000 euros
190.9 m euros
200 m euros
−9.1 m euros
18.18 euros
100,000 euros
200 m euros
190 m euros
10 m euros
18.18 euros
100,000 euros
254.5 m euros
180 m euros
74.5 m euros
2.
3.
(a) In parts (d) and (e) of question 2, the trade balance improves, whereas it worsens in (c) and
(b). This is a result of the fact that the Marshall-Lerner condition is satisfied in (d) and (e) but
not in (b) and (c).
(b) In case (e), import spending does not change. This is a result of the fact that import elasticity is
one.
(c) In case (d), export elasticity is one, and therefore export revenue in euros is unchanged.
(d) The initial trade balance would be −$50 million. The 10 percent devaluation will lead to the
same percentage change in quantities as in the above case, as the elasticities have not changed.
However, since the initial quantity of imports is larger, there will then be a larger absolute
change in imports, import revenue, and the trade balance.
4.
(a)
The devaluation will increase the domestic price of imports, and there will then be a movement
along the import demand curve from B to A. The effect on total import spending in the domestic
currency will be ambiguous. Export demand will shift outwards, thus leading to an increase in
export revenue.
(b) If import elasticity exceeds one, then total spending on imports will fall, as the percentage fall in
import quantity will exceed the percentage increase in the price of imports. Since total revenue
from exports unambiguously increases, the trade balance must improve.
5.
(a) Start from TB = X(E) − EM(E). Differentiate with respect to E:
dTB/dE = dX(E)/d(E) − M(E) − E dM(E)/dE
Divide by M(E) and note that dTB/dE = 0
0 = dX(E)/dE − 1 − (E/M(E))(dM(E)/dE)
Note that the last term is εm. When the trade balance is zero, X(E) = EM(E). Rearranging and
using this fact, we obtain:
1 = (dX(E)/dE) (E/X(E)) + εm and note that εx = (dX(E)/dE) (E/X(E))
Thus, the Marshall-Lerner condition is obtained.
(b) If we start from an initial trade deficit, then dTB/dE is not zero. The Marshall-Lerner condition
can then be shown to be too weak by following the same steps as in part (a).
(c) (i) Yes. This would imply that E TB* = 0 and thus TB* = 0.
(ii) No. dTB/dE = E dTB*/dE + TB*
Since TB = E TB*, this can be rewritten as dTB/dE = E dTB*/dE + TB/E
(iii) If TB < 0, dTB/dE < E dTB*/dE
(iv) If TB > 0, dTB/dE > E dTB*/dE
(v) If TB = 0, dTB/dE = E dTB*/dE
(d) (i) Using the answer to c (iii), its possible that the trade balance can improve in terms of
foreign currency while worsening in terms of domestic currency.
(ii) The contradiction can be reconciled by the fact that
d(E TB*)/dE = dTB*/dE + TB*
Therefore, although dTB/dE and dTB*/dE are of opposite signs, it will be the case that
dTB/dE and d(E TB*)/dE are the same sign. If the country is initially in a deficit, and a
devaluation restores balanced trade, then dTB/dE is negative, and TB* is negative, therefore,
although dTB*/dE will be positive, the overall effect d(E TB*)/dE will also be negative.
6.
(a) [εm εx(1 + σm+ σx) − εm εx(1− εm − εx)]/[( σm + εm)( σx + εx)] > 0 [σx(εm εx −σm(1 −εm)+ εx σm) +
(1 + σm) εm εx]/[( σm + εm)( σx + εx)] > 0
The denominator of the above expression is unambiguously positive. Therefore, the
Bickerdickie-Robinson-Metzler condition requires that
σx(εm εx − σm(1 − εm) + εx σm) + (1 + σm) εm εx > 0
This can be rearranged to get
εm(εx (1 + σm + σx) + σmσx) − σmσx(1 − εx) > 0
Taking the limit as σm σx goes to infinity will yield
[σmσx(−1 + εm + εx)]/[ σm σx] > 0
This simplifies easily to the Marshall-Lerner condition.
(b) This condition is less stringent than the Marshall-Lerner condition. If the Marshall-Lerner
condition is satisfied, then the above is always satisfied, whereas there may be situations where
the above is satisfied and the Marshall-Lerner condition is not.