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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