Download Problem 1. Assume that the price level is set as a weighted average

Problem 1.
Assume that the price level is set as a weighted average of prices of goods in the tradable
sector (T) and non-tradable sector (NT):
where α is between 0 and 1. Suppose
that purchasing power parity holds, but for tradable goods only. To simplify the analysis,
normalize the foreign prices to 1 P* = 1. Assuming ceteris paribus, what is the impact on the
nominal and real exchange rate of the following events:
− total expenditures are constant & the overall price level P is constant, but domestic
residents decide to spend more of their income on non-tradables
− foreign residents move their demand to their country’s non-tradable goods.
Problem 2
Suppose that the world consists of two economies: Home and Foreign (marked with *).
Assume that the price level is given by
(both in Home and in Foreign), where α
=α*=0,5. The rate of growth of prices in a given sector is equal to the difference between the
rate of growth of nominal wages ω and growth rate of labor productivity πi = ω − ai , i=T, N
(analogously for Foreign).
a) Write down the formula for Home and Foreign inflation, using the formula for the
average price level (hint: use logs)
b) Suppose that nominal wages at Home grow by 10 %, and in Foreign country by 5%.
At Home, the labour productivity growth in the T sector is 7% and in N sector: 4%. In
Foreign, the labour productivity in the T sector grows by 3% and in N sector by 1%.
Calculate the average level of inflation in the country and abroad. If relative PPP holds
how will the nominal exchange rate change?
c) Assume now that PPP holds in the T sector only. What will be the change in the real
exchange rate, resulting from the growth rates given in b)? What is the impact of
changes in productivity in the tradable sector and non-tradable sector in Home and in
Foreign on real exchange rate?
Problem 3
Assume that the real demand for money (L ) is given by: L = Yα exp(-βi),
a) Using a money market equilibrium condition write down the formula for inflation at
Home and in Foreign country. Hint: use logs and calculate the derivative with respect
to time
b) Using purchasing power parity condition (assume it holds everywhere) and the
equations derived above, write down a formula for the rate of growth of the nominal
exchange rate.
c) Suppose Home wants to fix its nominal exchange rate with respect to Foreign. The
growth rate of domestic real GDP is 4 % per year, and foreign real GDP growth is 3%.
The central banks in both countries will not change interest rates, and the expected
increase in money supply in Foreign is 2%. If α = 0.4; β = 0.6 , calculate the required
rate of growth of Home’s money supply.
Problem 4
Using the monetary approach, explain how will the nominal PLN/USD exchange rate
change as a result of the following:
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•
•
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An increase in money supply in Poland and US equal to 10%
An increase in money supply: in Poland it is equal to 5% and in US - equal to 10%
An increase in expected inflation in US equal to 2%
An increase in US output
Problem 5
Compare the long run consequences of a permanent increase in money supply with a
temporary increase in money supply and with an increase in the rate of growth of money
supply.