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Economics 215 Intermediate Macroeconomics
Homework 4
Assigned: Thursday, May 5, 2005
Due: Thursday, May 11, 2005
1.
Fundamental Exchange Rate. Assume that the exchange rate of the Japanese yen
for the US dollar 10 years in the future can be defined as the long run fundamental
exchange rate: et+T = eLR. Further, assume we can estimate the market’s
assessment of future interest rates over the next 10 years by looking at the interest
rate on 10 year bonds. Define 1+i10 as the interest rate on a 10 year bond.
1  i 
10
t
10
 1  it 1  it 1 1  it  2 1  it 3  ..... 1  it 9 
The following table contains information on the interest rate for 10 year bonds for
Japan (the domestic economy) and the US (the foreign economy) as well as the
spot Yen-Dollar exchange for the period 1998 to 2004. Assume that uncovered
interest parity holds. Calculate the markets expectation of the long-term
fundamental level of the exchange rate, eLR.
10 Year Bond Rate
Japan
USA
i10
1998
1.97
1999
1.645
2000
1.64
2001
1.365
2002
0.9
2003
1.36
2004
1.435
i10
Yen-Dollar Rate
e
4.65
115.2
6.28
102.08
5.24
114.9
5.09
131.47
4.03
119.37
4.27
106.97
4.23
103.78
2. Investment. A firm has a Cobb-Douglas production function.
Q L
Yt  Kt Qt Lt  MPKt 1  1  t 1 t 1
2
Kt 1
The real interest rate is 5% (r = .05) and the depreciation rate of capital is 7.5%
(d=.05).
a. Calculate the average productivity of capital when the firm is at its optimal capital
stock. Calculate the capital-labor ratio when technology next period is equal to Q
= 1.
b. Calculate the optimal capital stock when Qt+1 = 1 and Lt+1 = 4. Calculate the
output level at the optimal capital stock. If the current capital stock is equal to Kt
=100, how much investment will you need to set next period’s capital stock equal
to the optimal level if Kt+1 = (1-d)Kt. + It.
c. Now assume that the technology level goes up by 1%, so Qt+1 = 1.01. Calculate
the optimal capital stock at the new technology level. Calculate the new level of
output at the new technology level. What is the percentage increase in the optimal
capital stock compared to the answer in b. How much investment will you need to
do to set next period’s capital stock equal to the optimal level? How much of an
increase in investment, in percentage terms, will a 1% increase in technology lead
to?
3. Sustainable Current Account. The Bureau of Census and Statistics
(http://www.info.gov.hk/censtatd/eng/hkstat/index.html) has information on the
net international investment position of Hong Kong’s GDP. For 2003, calculate
the NIIP to GDP ratio. Obtain the end of year, international investment position,
NIIPt here (http://www.info.gov.hk/censtatd/eng/hkstat/fas/bop/iip1_index.html)
Find the GDP level for 2003 here
(http://www.info.gov.hk/censtatd/eng/hkstat/fas/nat_account/gdp/gdp2_index.htm
) . Assume the real interest rate is 4% (r = .04). Calculate the sustainable trade
deficit to GDP ratio for HK if the growth rate of GDP is 6% (gY = .06) and if (gY
= .02).
4. Third Generation Crisis Business Cycle Model.of Exchange Rates, (Geometry).
In an open economy, consumption is a linear function of disposable income,
Ct  100  .5  (Y  T ) ;
investment is a linear function of output, the government bond interest rate, it,
and a risk premium paid by corporate borrowers, rpt:
It  35  .1 Yt  100  it  rpt  ;
the treasury runs a balanced budget,
Gt = Tt = 50;
net exports are a linear function of income and the exchange rate
NX t  50  20  (et  1)  .2Yt ;
and demand is the sum of absorption
Yt = Ct + It+ Gt+ NXt.
The central bank sets a fixed exchange rate,
et = eFIX = 1.
Foreign exchange market conditions are given by the linear equation
it = it$ + eLR – et + rpt
a. Let it$ = .1, eLR = 1, and rp = 0. Solve for equilibrium output, interest rate,
consumption, investment and net exports.
b. Assume that rp = 0. Let forex markets believe that the exchange rate loses
credibility and the fundamental exchange rate changes to eLR = 1.2.. Solve
for equilibrium output, interest rate, consumption, investment and net exports
if the central bank maintains a fixed exchange rate et = eFIX = 1. Solve for
equilibrium output, interest rate, consumption, investment and net exports if
the central bank devalues the currency et = 1.2.
c. Assume that domestic firms have a great deal of foreign currency debt, so a
devaluation reduces their credit worthiness and increases the risk premium.
rpt = 1.5∙(et – 1)
Let forex markets believe that the exchange rate loses credibility and the
fundamental exchange rate changes to eLR = 1.2.. Solve for equilibrium
output, interest rate, consumption, investment and net exports if the central
bank maintains a fixed exchange rate et = eFIX = 1. Solve for equilibrium
output, interest rate, consumption, investment and net exports if the central
bank devalues the currency et = 1.2.