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Homework #3
Economics 215
Intermediate Macroeconomics
Assigned: Tuesday, April 29th 2003
Due: Tuesday, May 6th 2003
1. Sustainable Deficits. You are employed by New Zealand’s Finance Minister to
analyze his country’s finances. The current GDP in New Zealand is NZ$101
billion while the government has a current outstanding debt level of NZ$31
billion. New Zealand has a current level of current government expenditures equal
to NZ$16 billion. The Finance Minister would like to maintain a constant ratio of
debt to GDP across time and he would like to know how much taxes he needs to
collect to do so. He suggests three scenarios in terms of interest rates and growth
rates. For each scenario, calculate the sustainable deficit to GDP ratio which
would keep the debt to GDP ratio constant across time. Calculate the current
deficit which would allow us to currently meet this target deficit to GDP ratio
given current GDP. For each scenario, calculate the government revenues which
we must raise to meet this deficit level.
In New Zealand the Debt-to-GDP ratio is 31101 . If we can say our debt grows over
time according to D  (1  i ) D  ( PG  PT )  Dt  (1  i ) Dt 1  ( PG  PT )t
t
t 1
t
PYt
PYt
PYt

(1  i ) Dt 1 ( PG  PT )t
(1  i)

 dt 
dt 1  pt
PY
1  g PYt 1
PYt
1  g PY
(1  i )
1.05 31
]d  [1 
] 101
PY
1 g
1  g PY
1.05
( PG  PT )  [1 
]  31
1  g PY
1.05
PT  16  [1 
]  31
1  g PY
Where D is debt, (PG-PT) is the operating deficit, d is the debt to GDP ratio and p is
the sustainable deficit to GDP ratio.
Table 1 – New Zealand Deficit Scenarios
p  [1 
Scenario
A
B
C
GDP
Sustainable
Interest
Growth
Deficit to GDP
Rate
Rate
Ratio
Deficit
0.05
0.1 0.013951 1.409091
0.05
0.07 0.005737 0.579439
0.05
0.04 -0.002951 -0.298077
Taxes
14.59091
15.42056
16.29808
2. Comparing GDP Levels. You want to compare the per capita GDP of Hong
Kong with some of its Asian neighbors. Table 2 reports the 1998 level of GDP
measured in local currency units (called LCU’s) for a number of Asian economies
as well as their 1998 population levels. Calculate the per capita GDP of each
economy measured in local currency. Now, translate this into HK dollars. Table 2
also reports the nominal (Z) and real exchange rate (E = Z P
) of each
PUS
currency with the USA dollar. Use the nominal and real exchange rate with the
US to calculate the ratio of the price level in the US to the price level in each
US
country (XPUS = P
). Now, use each country’s nominal exchange rate with
P
the US (the # of US$ per LCU) as well as HK’s exchange rate with the US (the #
of US$ per HK$) to calculate the number of HK$ necessary to buy 1 local
currency unit for each country. Calculate the ratio of HK prices to prices in each
HK
country (XPHK = P
). Use ZHK and XPHK, to transform the PC_GDP from
P
local currency units to Hong Kong dollars using the exchange rate method and the
PPP method.
To calculate PC_GDP, divide GDP by the population level. The ratio of US prices to
domestic price is equal to Z/E. The exchange rate for HK$ per LCU is (# of HK$ per
US$) / (# of LCU per US$). The ratio of the price in Hong Kong to P is (PUS/P)/
(PUS/PHK ). To convert PC_GDP in HK$ using the exchange rate method multiply
PC_GDP in local currency by the # of HK$ per LCE. To convert PC_GDP using the
PPP method, multiply by P HK .
P
Table 2 – Currency Conversion
Z
GDP
(in millions)
Z
Population (US$ per
E
PC_GDP
(in millions) LCU)
(in LCU)
PUS
PC_GDP
P HK
(HK$ per
P
P
Method
(in HK$)
PPP
Method
Hong Kong
1,289,129
7
0.128
0.858
192775.606
1
1
192775.6062
192775.606
China
7,955,300
1,239
0.121
0.231
6422.819
0.52206644 0.9437092
3.48897233
6061.273314
22409.0386
Japan
495,250,800
126
0.009
1.448 3920922.409
0.00640716 0.0724957
0.0428191
284250.0471
167890.381
Macau
60,197
0
0.125
0.613
132229.542
0.20321209 0.9734111
1.3580673
128713.7013
179576.617
Singapore
142,968
3
0.580
0.801
45192.888
0.72400916 4.5317098
4.83855637
204801.0533
218668.337
Philippines
2,662,408
75
0.023
0.249
35433.275
0.09086358 0.1767844
0.60724168
6264.050015
21516.5617
963,961,051
204
0.022
0.171 4732761.069
0.13032213 0.1738367
0.87094335
822727.4423
4121966.78
Indonesia
0.14963326
LCU)
Exchange Rate
3. Predicting Future Exchange Rates The current exchange rate with Singapore is
S = 4.44925 (i.e. HK$ per Sing$). Table 3 includes the yield curve for Singapore
government securities and HK Exchange Fund bills. Assume that uncovered
interest parity holds true for HK and Singapore. Calculate the markets expectation
of the exchange rate in 3 months (T = .25), 1 year (T = 1) and 2,5,7, and 10 year
(T = 2,5,7,10).
We can calculate the market’s expectation using the yield curve
 1  itHK

,T 
  St

 1  itSNG
,T  

T
S t T
Table 3 – Yield Curves for Hong Kong & Singapore
Nominal Intereest Rate
T
HK
Singapore
3 Months
0.63%
1.18%
1 Year
0.70%
1.31%
2 Year
0.87%
1.71%
5 Year
1.48%
3.00%
7 Year
1.84%
3.73%
10 Year
2.05%
4.31%
St T
4.443191
4.422461
4.376149
4.130102
3.912402
3.574024
T
0.25
1
2
5
7
10