#### GeometricMean

Arkansas State, QM 2113
Excerpt: ... QM 2113 Business Statistics Study Note: Geometric Mean The geometric mean is used to calculate average growth rates of time series variables such as financial investments, sales trends, inventories, and population size. Example: Annual sales of National Distributors (ND) is presented in the following table. Determine the average annual growth rate of ND's sales. Year 1990 1991 1992 1993 1994 1995 1996 1997 Sales \$ 7,500,000 6,450,000 8,500,000 5,145,000 4,750,000 5,406,000 6,090,000 8,615,143 t 0 1 2 3 4 5 6 7 Ratios 0.8600 1.3178 0.6053 0.9232 1.1381 1.1265 1.4146 First Method Step 1: Calculate the period-to-period ratios. rt = r1 = 2 x x x r =x G=n x x 1 0 2 1 t for t=1, 2 , 3, ., n. 6,450,000 = 0.8600 7,500,000 8,500,000 = 13178 . 6,450,000 t -1 = = Step 2: Calculate the geometric mean of the ratios. r r r r 1 2 3 n = ( r1r 2r 3r n) 1 n G = 7 ( 0.8600) ( 13178) ( 0.6053) ( 0.9232) ( 11381) ( 11265) ( 14146) . . . . = 7 1148686 . = 102 . Step 3: The average growth rate is G - 1. R = G - ...

#### 808_hw1

Sveriges lantbruksuniversitet, ECON 808
Excerpt: ... of GDP data for international comparisons. If your chosen country is not available on the PWT, I suggest chosing a country that is. If you prefer, you can track down your own data. The web address for the PWT data set is http:/datacentre.chass.utoronto.ca/pwt/index.html a) I would like to see the following things (the printouts and graphs should be clearly labeled): ECON 808, Fall 2004 1. A printout from your computer program showing annual time series on (a) Capital per worker (b) Real GDP per worker (c) The growth rates for capital per worker and real GDP per worker (d) The Solow residual (growth rate of TFP) 2. A graph (also from your computer program) showing the time series of (a) The growth rate of capital per worker (b) The growth rate of real GDP per worker (c) The Solow residual 3. For the entire time frame of available data: (a) The average annual growth rate in capital per worker (b) The average annual growth rate in real GDP per worker (c) The average annual growth rate in TFP 3 (d) The perce ...

#### 09ExogenousGrowth3

Allan Hancock College, ECON 2102
Excerpt: ... -time exogenous permanent increase in s or z, or fall in n results in one-off permanent increase in perworker income (standard of living). There needs to be perpetual shifts in z (technological advancement) to deliver perpetual growth in per-worker income. c.f. Malthus? Growth Accounting Solow (1957, ReStats). From the Solow-Swan model we know if Y is to grow over time there must be growth in inputs e.g. (K,N), or TFP, z . Assume economy-wide production function: Growth Accounting Typically = 0.36. We then have: Given statistically measured data: we can back out TFP measure as: a.k.a. Solow residual Table 6.1 Average Annual Growth Rates in the Solow Residual 26 Figure 6.23 Natural Log of the Solow Residual, 19482001 27 Figure 6.24 Percentage Deviations from Trend in Real GDP (black line)and the Solow Residual (colored line), 19482001 28 Growth Accounting A growth accounting exercise. How much do z, K, N contribute to growth in Y? Step 1: Compute Solow residuals Step 2: Compute average ann ...

#### QUIZ 3

Punjab Engineering College, PHI 407
Excerpt: ... _ _ _ _ _ _ Part II- Exercises [55 Points] 1) We noted that the growth rate of per capita GDP in the United States between 1870 and 1929 was slightly lower than 2.0%, while the growth rate between 1950 and 2004 was slightly higher. Using the following table, calculate the actual average annual growth rates during these two periods. 2) Consider the following production function Y = A1 K 1 3 L2 3 + A , does it exhibit increasing, constant or decreasing returns to scale in K and L? Assume that A = 0 , what is the growth rate of Y in terms of the gr ...

#### questions04

UVA, LC 202
Excerpt: ... Lecture 4 January 29, 2008 1. Dr. Evil's original ransom amount was \$1 million. The price index (P) was about 25 in 1969 but increased to near 100 by 1997. If Dr. Evil adjusted the ransom amount appropriately, he'd: A. Increase it to \$4 million B. Increase it to \$4 billion C. Increase it to. \$100 billion! D. Decrease it to \$250,000 2. Looking at GDP, the recession of 2001 seems to have started: A. in early 2000 B. in mid 2000 C. in late 2000 D. in early 2001 E. in mid 2001 3. The average annual growth rate of U.S. real GDP for the past fifty years was: A. 3.3 B. 2% C. approximately zero. D. \$14 trillion. E. 2% ...

#### 318hw5key

Sonoma, ECON 318
Excerpt: ... ulate the average annual growth rate of gdp, assume annual compounding. The growth formula assuming annual compounding is, Yt = Y0(1 + g)t To find g, the average annual growth rate assuming annual compounding take the log of GDP and regress against time. LogYt = LogY0 + Log(1 + g)t, where Y0 is GDP at time zero and g is the average annual growth rate. SUMMARY OUTPUT Nominal Growth Rate Compounded Annually Regression Statistics Multiple R 0.994717 R Square 0.989462 Adjusted R Square 0.989198 Standard Error 0.043069 Observations 42 Standard Error 0.013532 0.000548 t Stat 198.3931 61.28393 P-value 1.7E-61 3.6E-41 Lower 95% Upper 95% 2.657384 0.032493 2.712083 0.034709 Intercept X Variable 1 Coefficients 2.684734 0.033601 Based on the summary output, LogYt = Log(2.684734) + Log(0.033601)t Taking the anti-log gives Yt = 483.8754(1.080441)t The average annual growth rate of nominal GDP is 8% per year assuming annual compounding. (4) Based on your data, calculate the average annual growth rate of gdp, assume ...

#### case-study

Pacific Lutheran, ECON 330
Excerpt: ... Economics 330 Energy and Natural Resource Economics Case Study #1 Neoclassical Scarcity vs. Limits to Growth In this case study, you will compare some of the predictions of the neoclassical model of scarcity to the neomalthusian Limits to Growth mode ...

#### HW5

S.F. State, ECON 560
Excerpt: ... ne to the graph, right-mouse click on the graph and choose Add Trendline. Choose the linear trend, and from the options choose Display equation on chart. Excel will add a linear trend (linear regression line) to the chart and will display the estimated regression coefficients. b. Based on the above graph, approximately, what is the average annual growth rate of productivity in the U.S. during the years 1948 2004? c. Some economists argue that the number of workers is not a good measure of labor input because the hours worked may change during the business cycle. Repeat part a using the aggregate hours as the labor input. Show the equation you used to obtain the time series of TFP. d. Based on the above graph, approximately, what is the average annual growth rate of productivity in the U.S. during the years 1948 2004? Compare this with part b is there a big difference in the estimated growth rate of productivity when you use different measures of labor input? 2. (5 points). The next gra ...

#### GrowthRates

UCSD, GENERAL ED MMW 1,2; E
Excerpt: ... How to Calculate Average Annual Growth Rates for Geometric Growth Suppose P=0.4 in year t=0 =0.7 in year t=10 % change in price from year 0 to 10 is 100 (0.7-0.4/0.4) = 75% How to calculate average annual growth when growth is geometric compounding. 75%/10 years = 7.5% not very accurate P(0) (1 +avg annual growth rate)^10 = P(10) A Useful Approximation Z=WxY Growth rate of Z is approx growth rate of W plus the growth rate of Y Works for more than two additional growth rates If Z = X/Y Growth rate of Z = grwth rate of X/ grwth rate of Y ...

#### 30

Wisconsin, ECON 102
Excerpt: ... Econ 102 Lecture 1/30/2008 1:18:00 PM Growth Rate Calculation Recall growth rate formula : GDP1991 GDP1990 x100 o GDP1990 Suppose growth rate is constant at rate 4% per year since 1990. In 2008 it doubles! The Power of Growth: Rule of 70 Economists use rule of 70 to compute how many years it takes for a GDP to double o 70/g number of years after which GDP doubles Going back to our example from the previous slide: 70/4=17.5 years (about right!) Ex of Power of growtho Between 1950-2004 average annual growth rate was: In Argentina less than 1% In Japan about 4.5% In US about 2.2% o These growth rates imply: Income in Japan doubles every 15 year, 30years in US and 70 in Argentina o In the long run it makes a huge difference Business Cycle Fluctuations Business cycles- fluctuations in real GDP around its long-term growth trend Phases of the business cycle o Expansion- a period of real GDP increasing faster than usual o Contraction- a period of real GDP increasing slower than usual o Recession- a fall ...

#### questions04

UVA, LC 202
Excerpt: ... Lecture4January29,2008 1.Dr.Evil'soriginalransomamountwas\$1million. Thepriceindex(P)wasabout25in1969butincreasedtonear100by1997. IfDr.Eviladjustedtheransomamountappropriately,he'd: A.Increaseitto\$4million B.Increaseitto\$4billion C.Increaseitto.\$1 ...

#### 00mid3b

Drake, ECON 001
Excerpt: ... est tenth of a percentage point. Average annual growth rate of Average annual growth rate of Average annual growth rate of real GDP per hour of work capital per hour of work technology 1.69% 0.93% % (7) [Money: 12 pts] Use the following financial data for the U.S. in December 1998 to compute quantities listed below. [Hint: Some of the data are extraneous and not needed for these computations.] Currency Bank reserves Travelers checks, demand deposits, and other checkable deposits Consumer credit Federal debt held by the public Savings deposits, small time deposits, money-market mutual funds, and other deposits on which check writing is limited or not allowed a. Compute the monetary base. b. Compute "M1." c. Compute "M2." d. Assume banks hold zero excess reserves. Compute the money multiplier for M1 to the nearest tenth. \$ billion \$ billion \$ billion \$459 billion \$45 billion \$635 billion \$1300 billion \$3722 billion \$3308 billion Principles of Macroeconomics (Econ 001) Drake University, Fall 2000 Mi ...

#### 00mid3a

Drake, ECON 001
Excerpt: ... ndredth of a percentage point. Average annual growth rate of Average annual growth rate of Average annual growth rate due real GDP per worker capital per worker to technology 8.59% 6.03% % (7) [Money: 12 pts] Use the following financial data for the U.S. in December 1999 to compute quantities listed below. [Hint: Some of the data are extraneous and not needed for these computations.] Travelers checks, demand deposits, and other checkable deposits Currency Federal debt held by the public Bank reserves Consumer credit Savings deposits, small time deposits, money-market mutual funds, and other deposits on which check writing is limited or not allowed a. Compute the monetary base. b. Compute "M1." c. Compute "M2." d. Assume banks hold zero excess reserves. Compute the money multiplier for "M1" to at least the nearest tenth. \$ billion \$ billion \$ billion \$622 billion \$517 billion \$3633 billion \$42 billion \$1387 billion \$3538 billion Principles of Macroeconomics (Econ 001) Drake University, Fall 2000 Midterm ...

#### 98mid3b

Drake, ECON 001
Excerpt: ... (1/3), as it is in the United States. Compute your answer to the nearest tenth of a percentage point. Average annual growth rate of real GDP per hour of work Average annual growth rate of capital per hour of work Average annual growth rate of technology 6.33% 7.89% % (8) [Money: 8 pts] Use the following financial data for the U.S. in May 1998 to compute quantities listed below. [Hint: Some of the data are extraneous and not needed for these computations.] Currency Personal income Travelers checks, demand deposits, and other checkable deposits Bank reserves Trade deficit Savings deposits, small time deposits, money-market mutual funds, and other deposits on which check writing is limited or not allowed a. Compute the monetary base. b. Compute "M1." c. Compute "M2." d. Assume banks hold zero excess reserves. Compute the money multiplier for M2 to the nearest tenth. (9) [Money multiplier: 6 pts] Suppose the required reserve ratio were 0.05 and the Federal Reserve increased bank reserves by \$5 billion. a. ...

#### 00mid3a

Drake, ECON 001
Excerpt: ... earest hundredth of a percentage point. Average annual growth rate of Average annual growth rate of Average annual growth rate due real GDP per worker capital per worker to technology 8.59% 6.03% % (7) [Money: 12 pts] Use the following financial data for the U.S. in December 1999 to compute quantities listed below. [Hint: Some of the data are extraneous and not needed for these computations.] Travelers checks, demand deposits, and other checkable deposits Currency Federal debt held by the public Bank reserves Consumer credit Savings deposits, small time deposits, money-market mutual funds, and other deposits on which check writing is limited or not allowed a. Compute the monetary base. b. Compute "M1." c. Compute "M2." d. Assume banks hold zero excess reserves. Compute the money multiplier for M1 to at least the nearest tenth. (8) [Money multiplier: 6 pts] Suppose the required reserve ratio were 0.10 and the Federal Reserve increased bank reserves by \$10 billion. a. If everyone held money in the form ...

#### 00mid3b

Drake, ECON 001
Excerpt: ... percentage point. Average annual growth rate of Average annual growth rate of Average annual growth rate of real GDP per hour of work capital per hour of work technology 1.69% 0.93% % (7) [Money: 12 pts] Use the following financial data for the U.S. in December 1998 to compute quantities listed below. [Hint: Some of the data are extraneous and not needed for these computations.] Currency Bank reserves Travelers checks, demand deposits, and other checkable deposits Consumer credit Federal debt held by the public Savings deposits, small time deposits, money-market mutual funds, and other deposits on which check writing is limited or not allowed a. Compute the monetary base. b. Compute "M1." c. Compute "M2." d. Assume banks hold zero excess reserves. Compute the money multiplier for M1 to the nearest tenth. \$ billion \$ billion \$ billion \$459 billion \$45 billion \$635 billion \$1300 billion \$3722 billion \$3308 billion (8) [Money multiplier: 6 pts] Suppose the required reserve ratio were 0.05 and the Federal ...

#### 98mid3a

Drake, ECON 001
Excerpt: ... onal income is about (1/3), as it is in the United States. Compute your answer to the nearest tenth of a percentage point. Average annual growth rate of real GDP per hour of work Average annual growth rate of capital per hour of work Average annual growth rate of technology 3.43% 6.99% % (8) [Money: 8 pts] Use the following financial data for the U.S. in September 1998 to compute quantities listed below. [Hint: Some of the data are extraneous and not needed for these computations.] Currency Personal income Bank reserves Trade deficit Savings deposits, small time deposits, money-market mutual funds, and other deposits on which check writing is limited or not allowed Travelers checks, demand deposits, and other checkable deposits a. Compute the monetary base. b. Compute "M1." c. Compute "M2." d. Assume banks hold zero excess reserves. Compute the money multiplier for M1 to the nearest tenth. \$ billion \$ billion \$ billion \$449 billion \$7086 billion \$45 billion \$17 billion \$3226 billion \$622 billion (9) [ ...

#### 01mid3b

Drake, ECON 001
Excerpt: ... sidual") over this period. Assume that the share of capital income plus depreciation in national income is about (1/3), as it is in the United States. Compute your answer to the nearest hundredth of a percentage point. Average annual growth rate of Average annual growth rate of Average annual growth rate due real GDP per worker capital per worker to technology 6.33% 7.89% % (7) [Money: 12 pts] Use the following financial data for the U.S. in July 2001 to compute quantities listed below. [Hint: Some of the data are extraneous and not needed for these computations.] Travelers checks, demand deposits, and other checkable deposits Currency Federal debt held by the public Bank reserves Consumer credit Savings deposits, small time deposits, money-market mutual funds, and other deposits on which check writing is limited or not allowed a. Compute the monetary base. b. Compute "M1." c. Compute "M2." d. Assume banks hold zero excess reserves. Compute the money multiplier for M1 to at least the nearest tenth. ...

#### 4_1_Tues_Feb_3_04

Penn State, FOR 466
Excerpt: ... oint Basic Growth and Yield Concepts Yield (Ya) refers to the volume of usable wood fiber per unit area at a given age, a. Growth (Ya) refers to the change in the yield over some period of time. The Annual Increment ()Ya ) is just the annual growth of the stand per unit of area at a given age. It is the difference between the yield at age a and the yield a year earlier, at age a-1. )Ya = Ya - Ya-1 The Periodic Annual Increment (PAIa1, a2) is the average annual increment per unit area over some period longer than one year. The PAI for ages a1 to a2 is: PAI a1 , a2 = Ya2 Ya1 a2 a1 Growth and Yield Concepts (continued.) The Mean Annual Increment (MAIa) is the average annual growth rate per unit area up to age a. It is calculated by dividing the yield at age a by the age: MAI a = Ya a The age where MAI is maximized is known as the Culmination of Mean Annual Increment or (CMAI) Managing on this rotation will maximize the average volume production of a given area over time. - For this ...

#### 060919stuck

Chester, ECO 338
Excerpt: ... he Harare-based African Forum and Network on Debt and Development, a non-governmental organisation. "Health delivery services are in shambles, transport systems are in bad shape and Africans are still begging for food from donor agencies," he told IPS. "Africa is getting poorer. Countries like the DRC (Democratic Republic of Congo) and Somalia are sinking further into poverty. It's the same with oil-producing Angola. We are not seeing efforts by Angola to escape from the least developed countries category soon." Between 2001 and 2004, LDC states Angola, Chad and Equatorial Guinea - all oil producers - together with Mozambique and Sierra Leone, met or exceeded an average annual growth rate of seven percent, says UNCTAD. However, Angola failed to make substantial progress in providing access to safe drinking water and in reducing child mortality. According to Valodia, African LDCs are stifled by a variety of factors, both internal and external. "There are issues directly under the control of LDCs. These are l ...

#### Sol1

Oakland University, FIN 361
Excerpt: ... this). 1 216.6 61 - 1 *100 = 3.77% 21.5 or [LN (216.6) - LN (21.5)] *100 = 3.79% 61 3) Consider the following data for GDP in the United States. Date 1947 Q1 2007 Q1 2008 Q1 Nominal GDP (Billions) 237 13,552 14,196 a) Calculate the average annual growth of GDP from 1947 to 2007. 1 13,552 60 - 1 *100 = 6.69% or 237 [LN (13,552 ) - LN (237 )] *100 = 6.74% 60 b) Using your answer from 2b, calculate average real annual growth. Subtract the average inflation rate from the average annual growth rate to get average real growth: i.e. 6.69% - 3.77% = 2.92% Alternatively, you could do the following (this is not quite right.we have a price for 2008 when what we really need is a price for 2007. However, it will be close enough). Note that I used the May value for 2008 the April value would work as well. 216.6 Real GDP in 1947 (in 2008 dollars): 237 = 2,387.6 21.5 216.6 Real GDP in 2007 (in 2008 dollars.almost): 13,552 = 13,552 216.6 1 13,552 60 - 1 * 100 = 2.8% 2, ...

#### KW_Macro_Ch_08_End_of_Chapter_Problems

Rutgers, ECONOMICS 103
Excerpt: ... a per capita 1960 1970 1980 1990 2000 \$7,395 9,227 10,556 7,237 10,995 \$832 1,275 1,204 1,183 1,349 \$1,571 2,777 4,830 9,959 15,881 \$12,414 16,488 21,337 26,470 33,308 2. The accompanying table shows the average annual growth rate in real GDP per capita for Argentina, Ghana, and South Korea using data from the Penn World Table, Version 6.1, for the past few decades. a. For each decade and for each country, use the Rule of 70 to calculate how long it would take for that country's real GDP per capita to double. b. Suppose that the average annual growth rate that each country achieved over the period 19902000 continues indefinitely into the future. Starting from 2000, use the Rule of 70 to calculate, where possible, the year in which a country will have doubled its real GDP per capita. Average annual growth rate of real GDP per capita Argentina Ghana South Korea Years 19601970 19701980 19801990 19902000 2.24% 1.35 -3.70 4.27 4.36% -0.57 -0.18 1.33 5.86% 5.69 7.51 4.7 ...

#### EC115_Problem set9_Solutions

East Los Angeles College, EC 115
Excerpt: ... (since I can invest 5000 at 10% for 5 years, after 5 years I get y = 5000(1 + 0.1)5 = 5000(1.61) = 8052.55, the present value is simply (8052.55)/(1.61) = 5000 the initial amount) We can see that PV1 < PV2. This implies that the first investment opportunity is worse for me and thus, I will take the second. The internal interest rate IIR is given by: 7000 IIR = 5000 1/ 5 1 = 1.0696 1 = 0.0696. The IIR is 6.9% that is lower than the market interest rate 10%. The IIR measures the average annual growth rate of my investment. Starting with 5000, I will need an annual growth rate of 6.9% to reach 7000 after 5 years. 3. Suppose that a given country starts with a GDP level of 1000. (a) Assume that the GDP is growing at an annual rate of 3%. What is the value of the GDP after 10 years? (b) Given a growth rate of 3%, how many years it will take for the GDP to double? (c) You know that in 5 years from now the GDP is going to be 1500, what is the average annual growth rate? Solution ...

#### HO005

Richmond, PS 240
Excerpt: ... Table 1: India vs. China: Two Paths, Same Goal? India Size Population Total (1995, millions) world rank (out of 192 countries) average annual growth rate (1980-90, %) average annual growth rate (1990-95, %) Economy GDP (1995, \$ billions) world rank GNP by PPP (1995, \$billions) world rank average annual growth rate (1965-80, %) average annual growth rate (1980-90, %) average annual growth rate (1990-95, %) 929 2 2.1 1.8 324 15 1,301 5 3.6 5.8 4.6 1,200 1 1.5 1.1 698 7 3,505 2 6.9 10.2 12.8 China Wealth and Welfare Wealth GNP per capita (1989, \$) GNP per capita (1995, \$) world rank (1995) PPP estimate of GNP per capita (1995, \$) Equity Ratio of top 20% to bottom 20% percentage share of income1 Welfare Life expectancy at birth (1995, years) world rank Adult literacy rate (1995, %) world rank Infant mortality rate (1995, per 1,000 live births) world rank Human development index rank (1991) world rank 340 340 171 1,400 5.0 330 620 148 2,920 8.6 62 138 52 159 68 149 0.436 134 69 90 81 118 34 94 0.609 111 Selec ...