# ECON300, Spring 2012 Intermediate Macroeconomics Professor: Hui He. Homework 1 Suggested Answer (Total points: 100)

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1 ECON300, Spring 2012 Intermediate Macroeconomics Professor: Hui He Homework 1 Suggested Answer (Total points: 100) Understanding the growth rate and how to measure it Problem no. 1 on page 35. (10 points) ANSWER: Calculating Growth Rates Data: Year Real Per Capita GNP 1950 \$11, \$13, \$18, \$22, \$28, \$30, \$31, \$32, \$33, \$34, \$35, \$35, \$35, \$35, \$36, \$37,773 (a) Actual Percentage Growth Rates, (3 points) Year Real Per Capita GNP %Growth 1995 \$30, \$31, \$32, \$33, \$34, \$35, \$35, \$35, \$35, \$36, \$37,

2 (b) Approximate Percentage Growth Rates, (4 points) Year Real Per Capita GNP %Growth 1995 \$30, \$31, \$32, \$33, \$34, \$35, \$35, \$35, \$35, \$36, \$37, The approximation is extremely close. The approximation works well for small percentage changes. (c) Actual Percentage Growth Rates for Decades, (3 points) Year Real Per Capita GNP %Growth 1950 \$11, \$13, \$18, \$22, \$28, \$35, Approximate Percentage Growth Rates Year Real Per Capita GNP %Growth 1950 \$11, \$13, \$18, \$22, \$28, \$35, The approximation is still relatively close, but the approximation errors are larger because the growth rates are larger. Note that the approximation formula actually calculates the continuously compounded growth rate. Measurement of GDP Problem no. 2, 3 on page 63. (15 points + 15 points) ANSWER: 2. Coal producer, steel producer, and consumers. (15 points) (a) (i) Product approach: Coal producer produces 15 million tons of coal at \$5/ton, which adds\$75 million to GDP. The steel producer produces \$10 million tons of 2

4 investment (\$15,000) plus net exports (\$60,000). GDP is therefore equal to \$190,000. (5points) (c) Income approach: Firm A pays \$50,000 in wages. Firm B pays \$20,000 in wages. Total wages are therefore \$70,000. Firm A produces \$150,000 worth of wheat and pays \$50,000 in wages. Firm A s profits are \$100,000. Firm B produces \$100,000 worth of bread. Firm B pays \$20,000 in wages and pays \$60,000 to Firm A for wheat. Firm B s profits are \$100,000 \$20,000 \$60,000 = \$20,000. Total profit income in the economy equals \$100,000 + \$20, 000 = \$120,000. Total wage income (\$70,000) plus profit income (\$120,000) equals \$190,000. GDP is therefore \$190,000. (5points) Nominal GDP vs. Real GDP Problem no. 4, 5 on page 64. (10 points + 10 points) ANSWER: 4. Price and quantity data are given as the following. Year 1 Good Quantity Price Computers 20 \$1,000 Bread 10,000 \$1.00 Year 2 Good Quantity Price Computers 25 \$1,500 Bread 12,000 \$1.10 (a) Year 1 nominal GDP 20 \$1,000 10,000 \$1.00 \$30, 000. Year 2 nominal GDP 25 \$1,500 12,000 \$1.10 \$50,700. (2 points) (b) With year 1 as the base year, we need to value both years production at year 1 prices. In the base year, year 1, real GDP equals nominal GDP equals \$30,000. In year 2, we need to value year 2 s output at year 1 prices. Year 2 real GDP 25 \$1,000 12,000 \$1.00 \$37,000. The percentage change in real GDP equals (\$37,000 \$30,000)/\$30,000 = 23.33%. We next calculate chain-weighted real GDP. At year 1 prices, the ratio of year 2 real GDP to year 1 real GDP equals g1 = (\$37,000/\$30,000) = We must next compute real GDP using year 2 prices. Year 2 GDP valued at year 2 prices equals year 2 nominal GDP = \$50,700. Year 1 GDP valued at year 2 prices equals (20 \$1, ,000 \$1.10) = \$41,000. The ratio of year 2 GDP at year 2 prices to year 1 GDP at year 2 prices equals g2 = (\$50,700/\$41,000) = The chain-weighted ratio of real GDP in the two years therefore is equal to gc gg The percentage change chain-weightd real GDP from year 1 to year 2 is therefore approximately 23.5%. 4

5 If we (arbitrarily) designate year 1 as the base year, then year 1 chain-weighted GDP equals nominal GDP equals \$30,000. Year 2 chain-weighted real GDP is equal to ( \$30,000) = \$37, (4 points) (c) To calculate the implicit GDP deflator, we divide nominal GDP by real GDP, and then multiply by 100 to express as an index number. With year 1 as the base year, base year nominal GDP equals base year real GDP, so the base year implicit GDP deflator is 100. For the year 2, the implicit GDP deflator is (\$50,700/\$37,000) 100 = The percentage change in the deflator is equal to 37.0%. With chain weighting, and the base year set at year 1, the year 1 GDP deflator equals (\$30,000/\$30,000) 100 = 100. The chain-weighted deflator for year 2 is now equal to (\$50,700/\$37,048.75) 100 = The percentage change in the chainweighted deflator equals 36.85%. (2 points) (d) We next consider the possibility that year 2 computers are twice as productive as year 1 computers. As one possibility, let us define a computer as a year 1 computer. In this case, the 25 computers produced in year 2 are the equivalent of 50 year 1 computers. Each year 1 computer now sells for \$750 in year 2. We now revise the original data as: Year 1 Good Quantity Price Year 1 Computers 20 \$1,000 Bread 10,000 \$1.00 Year 2 Good Quantity Price Year 1 Computers 50 \$750 Bread 12,000 \$1.10 First, note that the change in the definition of a computer does not affect the calculations of nominal GDP. We next compute real GDP with year 1 as the base year. Year 2 real GDP, in year 1 prices is now 50 \$1,000 12,000 \$1.00 \$62,000. The percentage change in real GDP is equal to (\$62,000 \$30,000)/\$30,000 = 106.7%. We next revise the calculation of chain-weighted real GDP. From above, g 1 equals (\$62,000/\$30,000) = The value of year 1 GDP at year 2 prices equals \$26,000. Therefore, g 2 equals (\$50,700/\$26,000) = 195. The percentage change chainweighted real GDP from year 1 to year 2 is therefore %. If we (arbitrarily) designate year 1 as the base year, then year 1 chain-weighted GDP equals nominal GDP equals \$30,000. Year 2 chain-weighted real GDP is equal to ( \$30,000) = \$60,225. The chain-weighted deflator for year 1 is automatically 100. The chain-weighted deflator for year 2 equals (\$50,700/\$\$60,225) 100 = The percentage rate of change of the chain-weighted deflator equals 15.8%. When there is no quality change, the difference between using year 1 as the base year and using chain weighting is relatively small. Factoring in the increased performance of year 2 computers, the production of computers rises dramatically while its relative price falls. Compared with earlier practices, chain weighting provides a smaller estimate of the increase in production and a smaller estimate of the reduction in prices. This difference is due to the fact that the relative price of the good that increases 5

6 most in quantity (computers) is much higher in year 1. Therefore, the use of historical prices puts more weight on the increase in quality-adjusted computer output. (2 points) 5. Price and quantity data are given as the following: Year 1 Good Quantity (million. Price (per lb.) lbs.) Broccoli 500 \$0.50 Cauliflower 300 \$0.80 Year 2 Good Quantity (million. lbs.) Price (per lb.) Broccoli 400 \$0.60 Cauliflower 350 \$0.85 (a) Year 1 nominal GDP = Year 1 real GDP 500m. \$ m. \$0.80 \$490m. Year 2 nominal GDP 400m. \$ m. \$0.85 \$537.5m. Year 2 real GDP 400m. \$ m. \$0.80 \$480m. Year 1 GDP deflator equals 100. Year 2 GDP deflator equals (\$537.5/\$480) 100 = 112. The percentage change in the deflator equals 12%. (5 points) (b) Year 1 production (market basket) at year 1 prices equals year 1 nominal GDP= \$490m. The value of the market basket at year 2 prices is equal to 500m. \$ m. \$0.85 \$555m. Year 1 CPI equals 100. Year 2 CPI equals (\$555/\$490) 100 = The percentage change in the CPI equals 13.3%. This calculation shows that CPI has upward bias compared to GDP deflator. (5 points) Macro identities Problem no. 9 and 11 on page 65. (10 points + 10 points) ANSWER: 9. S p 1 = CA + D p d (a) (6 points) By definition: S Y C Y NFP TR INT T C Next, recall that Y C I G NX. Substitute into the equation above and subtract I to obtain: 6

7 p S I C I G NX NFP INT T C I ( NX NFP) ( G INT TR T ) CA D (b) (4 points) Private saving, which is not used to finance domestic investment, is either lent to the domestic government to finance its deficit (D), or is lent to foreigners (CA). 11. Macro identities ( 10 points) Assume the following: (a) (b) (c) (d) (e) D 10 INT 5 T 40 G 30 C 80 NFP 10 CA 5 S 20 d p Y S C S D C D G TR INT T TR D G INT T S GNP C G GNP S C G GDP GNP NFP g Government Surplus S D 10 (f) CA NX NFP NX CA NFP (g) GDP C I G NX I GDP C G NX

8 Labor Market Measurement Problem no. 12 on page 65 (5 points) 12. Unemployment rate (a) Unemployment rate = # of unemployed (2.5 m) / labor force = 5% labor force = 50 million. Participation rate = labor force / working age population = 50 m / 100 m = 50%. (b) Labor force = 50 million. (c) # of employed = labor force - # of unemployed (2.5 m) = m = 47.5 million. Make your hands dirty by working with the data Problem no. 1, 3 on page 36, problem no. 3 on page 66. (each 5 points) ANSWER: The graph is below (5 points) Real GDP vs. GNP: base year= billion of US \$ year GNP GDP There is no much difference between GDP and GNP, which shows the net factor payments only account for a tiny part of the GNP. The graph is below. (5 points) 8

9 Inflation Rate and the Growth Rate of M2: year CPI M2 We see these two data sequences commove, although the correlation is not that high. It shows that inflation IS a monetary phenomenon, increase in money supply will induce the inflation. The Figure 1.13 uses M0 as the measure of the money supply. The graph is below. (5 points) K: total capital stock Kpn: private nonresidential capital Kpr: private residential capital Kg: government capital Cd: Consumer durable goods They all increase over time. K=Kpr+Kpn+Kg. 9

10 The composition of the capital stock million of 2000 US dollars K Kpn Kpr Kg Cd year 10

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