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Homework 3
Intermediate Macroeconomics
Economics 215
Assigned: Thursday, May 6th, 2004
Due: Friday, May 14th, 2004
1. Foreign Real Estate. You consider buying an apartment in London. The
apartment will earn a rental income of ₤10,000 next year. The current HK$
interest rate is 5%. The spot exchange rate is HK$13.23 per British pound and the
1-year forward rate is 12. The price of real estate in London is expected to remain
constant, so capital gains are zero. The depreciation rate of the rental property is
5%. In each period, the sum of tax and other costs is 2% of the value of the
apartment. Calculate the price level of the apartment in HK$ using covered
interest parity.
2. Predicting Exchange Rates The current exchange rate with Singapore is S =
4.44925 (i.e. HK$ per Sing$). Table 3 includes the yield curve for Singapore
government securities and HK Exchange Fund bills. Assume that uncovered
interest parity and the expectations theory of the term structure holds true for HK
and Singapore. Calculate the markets expectation of the exchange rate in 1 year
(T = 1) and 2,5,7, and 10 year (T = 2,5,7,10).
Table 3 – Yield Curves for Hong Kong & Singapore
T
1 Year
2 Year
5 Year
7 Year
10 Year
Nominal Intereest Rate
HK
Singapore
0.70%
1.31%
0.87%
1.71%
1.48%
3.00%
1.84%
3.73%
2.05%
4.31%
StET
3. Tax Wedge and Deadweight Loss. Assume that a firm has a quadratic
production function in capital.
GDP  5K  K 2
This implies that the faces a linear marginal product of capital schedule.
MPK  5  2K
Assume that the price of goods is always equal to the price of capital (i.e. pK = 1) and
the depreciation rate is 10% (i.e. δ = .10). The real interest rate is equal to 10% (i.e. r
= .1) so the real cost of capital is r+δ.
a. Calculate, the profit maximizing level of capital when the tax wedge is zero
and the level of output that could be produced with that amount of capital.
Calculate the level of profit (Hint: The profit is the level of output minus
costs. Costs are equal to the product of the cost of capital and the capital used,
Profit = GDP – (r+δ) ․K* ).
b. Assume that government imposes a tax on capital with each firm having to
pay taxes equal to a fraction of their capital stock, TaxesτK. Calculate the
real cost of capital when the tax wedge is equal to 10% (i.e. τ=.1). What is
the profit maximizing level of capital and output? What is the after-tax profit
level (Profit = GDP – {r+δ+τ} ․K* ) and how much tax is collected?
c. Calculate the social cost of the tax distortion which is the loss in profits that
does not go to the government in taxes. Social cost is the profits from part a.
minus the profits and tax revenues in part b. Draw a graph of these losses.
4. Compare output per capita in East Asia. Sometimes we would like to compare
levels of GDP across countries. However, GDP is measured in national currencies.
To compare, we have to convert into the same units. There are two methods,
exchange rate conversion and PPP conversion. Exchange rate conversion simply
multiplies by the nominal exchange rates, the number of foreign currency units
per domestic currency units. This calculates the number of foreign currency units
necessary to buy the domestic currency necessary to buy domestic GDP. The
price of domestic currency relative to foreign currency. PPP conversion
PF
, the price of foreign goods relative to the price of
P
domestic goods. PPP conversion divides spending on domestic goods by the price
level of domestic goods, then re-multiplies by the price of foreign goods. This
gives the cost of domestic goods produced if their prices were the same as in the
foreign country.
multiplies by XP 
Table 2 gives some data for a number of East Asian economies in 2000 on GDP
per capita measured in domestic currency, nominal exchange rates (# of domestic
currency units per US$) and prices of goods in the US relative to domestic prices.
Treating the US as the foreign economy, calculate GDP per capita for each
economy in US dollars using exchange rate conversion and PPP conversion.
Exchange Rates
Hong Kong
China
Japan
Macau
Singapore
Philippines
Indonesia
GDP per Capita
(US$ per
in Domestic Currecy
LCU)
192,776
6,423
3,920,922
132,230
45,193
35,433
4,732,761
0.128
0.121
0.009
0.125
0.580
0.023
0.022
Foreign Prices relative
to Domestic Prices
XP
0.150
0.522
0.006
0.203
0.724
0.091
0.130
GDP per Capita in US Dollars
Exchange
PPP
Rate Conversion
Conversion
5. Technology and the Current Account. Assume that a countries savings level is
fixed and equal to S = 100. In every period, the countries capital depreciates
100% (i.e. δ = 1). In this economy, the real price of capital is constant and equal
to pK = 1. Further, the technology of this economy is described with a
Cobb-Douglas production function.
12
GDP  24 K  MPKt 1 
Kt 1
Therefore, the real cost of capital is rck = 1+r where r is the real interest rate. The
level of investment today is next period’s capital stock, Kt+1 = It.
a. Calculate the level of investment when the real interest rate is 10% (r = .10).
What is the current account (Hint: The current account is S - I)?
b. Calculate the autarky interest rate.
c. Technology increases so that next period’s marginal product of capital is
12.5
GDP  25 K  MPKt 1 
Kt 1
.
What is the current account after the increase of technology? Draw a graph
of the effect of the increase in technology on the current account.