Download Homework #4: Answers

Economics 0115
Homework #4: Answers
1.
Given the data on the production possibility frontiers for
the US and Japan in Table 1-1, do the following:
a. Construct a table showing the opportunity costs for
producing food and autos in each country. Which country has
the comparative advantage in producing food? In producing
autos? Explain.
Starting at F = 0, we note that a gain of 200 units of F
occurs for a 100 unit loss of A. That means that 1 unit of
F is gained when there is a loss of ½ unit of A. This
latter number is the opportunity cost of 1 more unit of F.
Similar reasoning is used to compute the other numbers in
Table 1-2.
b. Draw each country's production possibility frontier
(PPF) on a separate graph. Using autos on the vertical
axis, calculate the slopes of these two PPFs.
Slope(US) = (-500)/1000 = -1/2 A per unit of F
Slope(Japan) = (-800)/400 = -2 A per unit of F
2.
Assume that the terms of trade (TOT) are set at 1F = 1A.
a. Given the TOT, indicate what will happen to the
production of A and F in each country.
Japan is the low cost producer of A (1/2 F per unit of A
versus 2 F per unit of A for the US). The US is the low
cost producer of F (1/2 A per unit of F versus 2 A per unit
of F for Japan).
The US will specialize in the production of F by producing
at (1000 F, 0 A) and Japan will specialize in the
production of A by producing at (0 F, 800 A). This pattern
of specialization occurs because the US must give up 2 F to
obtain 1 A domestically but can obtain 1 A from Japan by
giving up 1 F. Likewise, Japan must give up 2 A for 1 F
domestically whereas it can obtain 1 F for 1 A from the US.
As long as it is cheaper for the US to obtain A from Japan
it will be willing to forego domestic production of A.
Similar logic applies to Japan.
See the graphs in part b.
b. Given the terms of trade, draw the consumption
possibility frontiers (CPF) for the US and Japan.
c. Before trade and specialization, if the US consumed 600
F, it could only consume 200 A. After specialization and
trade, how many units of A can be consumed if 600 F are
consumed? Explain.
After specialization the US has (1000 F, 0 A). If it wants
to consume 600 F then it can trade the remaining 400 F for
400 A (given that the TOT are 1 F for 1 A). Therefore its
position after specialization and trade is (600 F, 400 A),
a clear improvement over its initial position.
d. Given the combination of F and A in the US after trade
and specialization, what combination of F and A will be
consumed in Japan after trade and specialization? Explain.
Similar reasoning argues that Japan will specialize by
producing (0 F, 800 A) and then trading 400 A for 400 F
(again assuming the TOT are 1 A for 1 F). After
specialization and trade, Japan has (400 F, 400 A), a clear
improvement over its initial position of (200 F, 400 A).
e. What amounts of F and A do the US and Japan import and
export? Explain.
Japan exports 400 autos and imports 400 units of food. The
US exports 400 units of food and imports 400 autos. This is
a model of simple bilateral trade, a situation that does
not always occur in the real world (e.g. trade is
triangular or even rectangular-or more).
4.
Use the data in Table 2 to do the following:
a. If the world price of autos is $8, how many autos will
the US import? Graph and explain this situation.
Since domestic suppliers will only produce 100 autos when
the world price is $8, the US will import 800 more autos to
satisfy its consumers who wish to purchase 900 autos at a
price of $8.
b. Suppose the US government imposes a $2 tariff on autos.
Graph and explain this situation, being sure to note what
happens to:
(1) The price of autos
(2) The number of imports
(3) The domestic production of autos
(4) The revenue from the tariff and who collects it
(5) The welfare losses from the tariff
(1) The price of autos increases to $10.
(2) The number of imports decreases to 400.
(3) The domestic production of autos increases by 200.
(4) The revenue from the tariff is collected by the
government and can be calculated by multiplying $2
tariff by the number of imports 400. Revenue is
therefore $800.
(5) The welfare loss (WL) has two components. First,
since domestic producers supplying the 200 extra autos
(expanding output from 100 to 300) are less efficient
than foreign producers extra resources will be
attracted to the auto industry which could be used in
other parts of the economy. The WL1 = 1/2(200)$2 =
$200. Second, a higher price of autos (due to the
tariff) will cause domestic consumers to purchase 200
fewer autos than they would have with free trade.
Consumers lose the value of the gains from trade that
could have been achieved if 200 more foreign autos had
been imported. The WL2 is equal to 1/2(200)$2 = $200
also. Therefore the total welfare loss WL = $400.
c. Suppose the US government establishes a quota of 400
autos.
(3) The revenue generated by the quota is $2(400) =
$800. The import companies licensed by the government
to import autos capture the extra revenue generated by
the quota.
(3) The excess revenue is again $80. But the exporters
in Japan will capture it this time. This is one reason
why some countries may agree to a VER (their producers
can capture its benefits) where they may not agree to
a tariff or a quota.
5.
Answer the following questions on exchange rates:
a. If the exchange between the dollar and the mark is 2 DM per
dollar [e($) = 2 DM/$], what is the exchange rate in dollars
per mark? [e(DM) = ?]
e(DM) = $0.5/DM which is simply the inverse of the dollar
exchange rate.
b. If a camera sells for 250 DM, what is the dollar price of
the camera using the exchange rate from part a?
(250 DM)[e(DM)] = 250 DM ($0.5/DM) = $125
c. If a computer sells for $1000, what is the DM price of the
computer using the exchange rate from part a?
($1000)[e($)] = ($1000)(2 DM/$) = 2000 DM
6.
Using the data in Table 3, answer the following:
a. Compute the real exchange rate e*(Y) in the last column.
e*($) = [CPI(US)/CPI(J)]e($)
Year 1: e*($) = (100/100)100 ¥/$ = 100 ¥/$
Year 2: e*($) = (125/100)100 ¥/$ = 125 ¥/$
Year 3: e*($) = (125/100)80 ¥/$ = 100 ¥/$
b. What happens to e*($) when the price index in the US rises
but e($) remains unchanged?
e*($) rises and purchasing power parity (PPP) is
temporarily disrupted.
c. What happens to e*($) when the price index in the US rises
and e($) falls proportionately?
e*($) remains constant. This is a reflection of the idea
of purchasing power parity (PPP) which argues that
exchange rates adjust in the long run so the prices of
the same good in different countries is the same. This
should make sense insofar as inflation will cause the US
dollar to depreciate against other currencies such as the
Yen. This depreciation occurs because inflation causes
the demand for dollars (and dollar denominated assets) to
decrease. This causes e($) to decrease.
For example, suppose that an item costs $5 in the US but
500 ¥ in Japan. When the e($) = 100¥/$, the item costs
the same in both countries. But if the price level in the
US rises by 25% the item now costs $6.25 in the US but
still costs 500 ¥ in Japan (assuming the exchange rate
stays constant in the short-run). But the exchange rate
must change to maintain PPP. To see why, assume that the
exchange rate does not change. Then the item costs $6.25
in the US but $5 = ($0.01/¥)500¥ in Japan; conversely,
the item costs 500¥ in Japan but 625¥ = (100¥/$)$6.25 in
the US. Therefore the dollar per yen price must fall to
e($) = 80¥/$. At this exchange rate, the $6.25 and the
500¥ item will be the same price in both countries. That
is, ($6.25)80¥/$ = 500¥ or (500¥)$0.0125/¥ = $6.25.
7.
Suppose i(J) = interest rate in Japan = 4%/year and i(US) =
interest rate in US = 9%/year. Also suppose that e($) = 100¥/$
today but is expected to be 95¥/$ in one year (the dollar is
expected to depreciate against the yen). If a firm in the US
has $1 million to lend:
a. How much will this firm receive in dollars in one year if
it lends this money to an American firm?
In one year, this firm will be repaid $1,090,000 =
$1M(1.09).
b. Suppose that this firm lends $1 million to a
(assume that it converts $1 million into yen to
much will this firm receive in yen in one year?
the exchange rate is 95¥/$ in one year, what is
return on this firm's loan?
firm in Japan
do so). How
Assuming that
the dollar
$1M(100¥/$) = 100M-¥. This amount will be loaned to a
Japanese firm. In one year, the amount to be repaid in
yen will be 104M-¥. Assuming this amount is then
converted into dollars at e(¥) = $0.010526/¥ (e($) =
95¥/$) the total dollar repayment on the loan is
$1,094,704.
c. Where should the firm make its loan? Explain.
It should loan the money to the Japanese firm whenever
the dollar exchange rate is expected to fall. This result
occurs because the appreciation of the Yen is added to
the interest on the loan to give the firm a higher rate
of return on its money.
8.
Suppose that the money markets for the US and Japan have
reached equilibrium at e($) = 80 ¥/$. Using this information,
do the following:
a. Using two supply-demand graphs, illustrate this situation
and briefly explain your graphs.
The yen price of the dollar is 80¥/$ and is the equilibrium
price in the dollar market. The dollar price of the yen is
$0.0125/¥ and is the equilibrium price in the yen market.
c. Begin with the equilibrium established in part a. Then
assume that the supply of dollars increases. Illustrate this
situation for both countries and explain your results. Be sure
to explain what is occurring at the original exchange rate
(increased imports or exports for the US and vice versa for
Japan) and how the markets adjust.
As noted in lecture, the supply of dollars is equivalent to
the demand for yen. The demand for yen expresses a desire on
the part of the Americans to purchase Japanese goods. The
supply of dollars ultimately represents the demand for
Japanese exports/US imports). An increase in the supply of
dollars therefore represents an increase demand for yen and
consequently increased Japanese exports/US imports. This
occurs because the excess supply of dollars at e($) = 80¥/$
causes e($) (the yen price of the dollar) to fall and e(Y) to
rise. In other words, the dollar depreciates and the yen
appreciates in value when supply of dollars increases.