Consider two countries, say the United States and Japan. Both countries produce tradables and nontradables. Suppose that at some point in time the production technology in the United States is described by and Q US US aLs; with a=0.4 US,US LT QaLS; with a = 0.3 US where Q and Q denote, respectively, output of tradables and nontradables in the U.S., a and a denote, respectively, labor productivity in the traded and the nontradable sector, and LUS and LUS denote, respectively, the amount of labor employed in the tradable and nontradable sectors in the United States. The total supply of labor in the United States is equal to 1, so that 1 = LUS+L. At the same point in time, production possibilities in Japan are given by and Q+= 0.21 Q=0.31%, where the superscript J denotes Japan. The total supply of labor in Japan is also equal to 1. Assume that in each country wages in the traded sector equal wages in the nontradable sector. Suppose that the price index in the United States, which we denote by pls, is given by = PUS where PS and PS denote, respectively, the dollar prices of tradables and nontradables in the United States. Similarly, the price index in Japan is given by where Japanese prices are expressed in yen. 1. Sp Calculate the dollar/yen real exchange rate, defined as e, where S denotes the dollar-yen nominal exchange rate (dollar-price of one yen).
Consider two countries, say the United States and Japan. Both countries produce tradables and nontradables. Suppose that at some point in time the production technology in the United States is described by and Q US US aLs; with a=0.4 US,US LT QaLS; with a = 0.3 US where Q and Q denote, respectively, output of tradables and nontradables in the U.S., a and a denote, respectively, labor productivity in the traded and the nontradable sector, and LUS and LUS denote, respectively, the amount of labor employed in the tradable and nontradable sectors in the United States. The total supply of labor in the United States is equal to 1, so that 1 = LUS+L. At the same point in time, production possibilities in Japan are given by and Q+= 0.21 Q=0.31%, where the superscript J denotes Japan. The total supply of labor in Japan is also equal to 1. Assume that in each country wages in the traded sector equal wages in the nontradable sector. Suppose that the price index in the United States, which we denote by pls, is given by = PUS where PS and PS denote, respectively, the dollar prices of tradables and nontradables in the United States. Similarly, the price index in Japan is given by where Japanese prices are expressed in yen. 1. Sp Calculate the dollar/yen real exchange rate, defined as e, where S denotes the dollar-yen nominal exchange rate (dollar-price of one yen).
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.9P
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Transcribed Image Text:Consider two countries, say the United States and Japan. Both countries produce tradables and
nontradables. Suppose that at some point in time the production technology in the United States
is described by
US US,
US
Q7 = a L; with a = 0.4
and
QKS = aSLKS; with aks = 0.3
„US
where QUS and QUS denote, respectively, output of tradables and nontradables in the U.S., as
and aks denote, respectively, labor productivity in the traded and the nontradable sector, and
LUS and LS denote, respectively, the amount of labor employed in the tradable and nontradable
sectors in the United States. The total supply of labor in the United States is equal to 1, so that
1 = L4S + L. At the same point in time, production possibilities in Japan are given by
%3D
Qf = 0.21
and
Qk = 0.3Lk,
where the superscript J denotes Japan. The total supply of labor in Japan is also equal to 1.
Assume that in each country wages in the traded sector equal wages in the nontradable sector.
Suppose that the price index in the United States, which we denote by pUS, is given by
pUS =
where PS and PS denote, respectively, the dollar prices of tradables and nontradables in the
United States. Similarly, the price index in Japan is given by
p' = PP
where Japanese prices are expressed in yen.
Act
sp
Go
1..
Calculate the dollar/yen real exchange rate, defined as e = rs, where S denotes
the dollar-yen nominal exchange rate (dollar-price of one yen).
Transcribed Image Text:Suppose that the U.S. labor productivity in the traded sector, a, grows at a 5
percent rate per year, whereas labor productivity in the nontraded sector, as, grows at 2
percent per year. Assume that labor productivities in Japan are constant over time. Calculate
the growth rate of the real exchange rate.
3.
Now assume that the price index in the United States is given by
Similarly, the price index in Japan is given by
p' = (P)* (PX)*.
%3D
Calculate the dollar/yen real exchange rate e assuming the other conditions unchanged.
Consider the same situation in question 3. Suppose that the U.S. Iabor productivity
in the traded sector, as, grows at a 5 percent rate per year, whereas labor productivity in
the nontraded sector, as, grows at 2 percent per year. Assume that labor productivities in
Japan are constant over time. Calculate the growth rate of the real exchange rate.
2.
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