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Global Economy II – Spring 2016/17
Miguel Lebre de Freitas
Sharmin Sazedj
Problem set 3 – The Real Exchange Rate
Keywords: The Law of One Price. Purchasing power theory, Tradables and non-tradables;
Real exchange Rate; equilibrium Real Exchange Rate; The Balassa Samuelson effect; PPP
cmparisons of purchasing power.
Exercises
3.1.
(FT Ch03, ex.1 ) Suppose that two countries, Brazil and Mexico, produce
bananas. Brazil uses the real, Mexico uses the peso. In Mexico, bananas sell for 10
pesos per pound of bananas. The exchange rate is 0.5 reals per peso, Ereals/pesos =0. 5.
The peso–dollar exchange rate is Epesos/$ =10.
a) If LOOP holds, what is the price of bananas in Brazil? What is the price in the
United States?
b) Suppose the price of bananas in Brazil is 5.5 reals per pound. At the same
time, the price of bananas in the United States is $1. 00 per pound. Based on
this information, where does LOOP hold?
c) How will banana traders respond to the previous situation? In which markets
will traders buy bananas? Where will they sell them? What will happen to the
prices of bananas in Mexico, Brazil, and the United States?
3.2.
(FT Ch03, ex.2) For each of the following goods and services, indicate whether
you expect LOOP to hold. Explain briefly why you believe each good or services
satisfies the assumptions necessary for LOOP to hold.
d) Wheat
e) Childcare
f) Automobiles
g) Milk
h) MP3 players
i) Attorney services
3.3.
Consider a world with a single homogeneous good, which can either be
produced domestically or abroad under conditions of perfect competition. Initially,
the world price of this good is 100 USD and the price of the USD in terms of
domestic currency (pesos) is 2.
a) Suppose the price of the good in the domestic economy was initially 190
pesos. In the absence of trade costs, what do you think it would happen?
b) In the real life, do you believe the adjustment described in a) would be
instantaneous? Why?
c) Suppose now that transport and other trade costs amounted to 20% of the price
of the good. In this case, how would the non-arbitrage condition hold for
exports and for imports? Find out the implied band for the real exchange rate.
3.4.
Consider a small open economy producing a tradable good (T) and a nontradable (N) good. The corresponding production functions are YT = aLT and
YN = LN , with a = 1 . Define w as the nominal wage rate, PT as the price of T, PN
as the price of N and θ as the real exchange rate. The weight of each good in the
consumer price index is 50%. The foreign price of the tradable good is PT* = 1 and
the nominal exchange rate in this economy is e = 100 .
a) Assuming that firms maximize profits under perfect competition, find out the
equilibrium wage rate in this economy in units of domestic currency, as well
as the prices of the two goods and the consumer price index.
b) Now assume that the foreign economy is similar to the home economy,
except in that 4 . What would be the wage rate there, in units of foreign
currency?
c) Find out the equilibrium real exchange rate between the two economies?
Would absolute PPP hold in this case? Why? d) On the basis of your findings, how much would be the purchasing power of
workers at home relative to that of workers abroad? Explain the exchange rate
measure used in this international comparison.
3.5.
Consider a small open economy producing a tradable good (T) and a nontradable (N) good. The corresponding production functions are YT = aLT and
YN = bL N . Assume that the foreign prices of these goods are PT* = PN* = 1 and that
the nominal exchange rate is e = 1 . Finally, assume the weight of each good in the
consumer price index is 50%. Define w as the nominal wage rate, PT as the price of
T , PN as the price of N and θ as the real exchange rate.
1. Assume first that a = b = 1
a) Find out the labor demand equations in the two sectors.
b) Compute the equilibrium for the wage rate, the price level and the real exchange
rate.
2. Consider an increase in the productivity of the tradable good from a = 1 to a = 4 .
c) Describe the implications of such a shift on PT , PN , w and the equilibrium real
exchange rate, assuming that the nominal exchange rate was fixed.
d) If instead the central bank’ goal was to keep the inflation rate equal to zero, what
should happen to prices and to the nominal exchange rate?
e) What should happen to the real exchange rate if the productivity shock was instead
on parameter b?
3.6.
Consider a small open economy producing a tradable good (T) and a nontradable (N) good. The corresponding production functions are YT = aLT and
YN = LN . Assume that the foreign prices of these goods are PT* = PN* = 1 and that the
nominal exchange rate is e = 100 . Finally, assume the weight of each good in the
consumer price index is 50%. Define w as the nominal wage rate, PT as the price of
T , PN as the price of N and θ as the real exchange rate.
1. Assume first that a = 4 .
a) Find out the labor demand equations in the two sectors.
b) Compute the equilibrium wage rate, the corresponding price level and the
real exchange rate.
c) Now suppose that the nominal exchange rate depreciated to e = 400 . What
would happen to the price level and to the real exchange rate? Was PPP a
good theory in that case? In absolute terms or in relative terms?
2. Departing again from e = 100 , examine the impact of a fall in the productivity of
the tradable good from a = 4 to a = 1
d) Describe the implications of such a shift on PT , PN , and the equilibrium real
exchange rate, assuming that the nominal exchange rate was fixed.
e) If non-tradable good prices were sticky, how could the central bank easy the
adjustment process setting the nominal exchange rate?
3.7.
Consider a small open economy producing a tradable good (T) and a nontradable (N) good. The corresponding production functions are YT = aL1T 2 and
YN = LN . In this economy, there are 100 workers, and prices are flexible, so full
employment is always met. Assume that the foreign prices of these goods are
PT* = PN* = 1 and that the nominal exchange rate is e = 1 . Finally, assume the weight
of each good in the consumer price index is 50%. Define w as the nominal wage
rate, PT as the price of T , PN as the price of N and θ as the real exchange rate.
a) Find out the labor demand equations in the two sectors.
b) Find out the expressions for the wage rate, the price level and the real exchange rate,
as a function of the unknown parameters a and LT .
c) Assume that the steady state in this economy is characterized by a = 1 and LT = 64.
Find out what the long run equilibrium real exchange rate will be.
d) Now, consider a temporary departure form the steady state, implying a – also
temporary- reallocation of 60 workers away from the tradable good sector to the
non-tradable good sector. What would happen to the real exchange rate in this case?
e) Distinguish the phenomenon described in this exercise from the Balassa-Samuelson
effect.