Homework 1 Questions | Macroeconomic Theory | ECON 3204, Assignments of Introduction to Macroeconomics

Download Homework 1 Questions | Macroeconomic Theory | ECON 3204 and more Assignments Introduction to Macroeconomics in PDF only on Docsity! 1This is 100 times the change divided by the earlier value. Dr. Ashley ECON 3204 – Homework # 1 Due: see Calendar 1. I want you to convince yourself numerically that the exponential growth rates of the individual factors in a product add up to the exponential growth rate of the product, but that the same is not true of ordinary (fractional) growth rates. Fill in the blank areas of these tables and answer the questions below it. x y z x*y*z t-1 50 60 70 t 60 75 100 change fractional growth rate1 ln(x) ln(y) ln(z) ln(x*y*z) t-1 t 100*change in logarithm = exponential growth rate a. For x, y, z, and the product, how close is the fractional growth rate to the exponential growth rate? b. How close is the sum of the individual exponential growth rates to the exponential growth rate of the product? c. How close is the sum of the individual fractional growth rates to the fractional growth rate of the product? 2. Suppose that the money supply, Mt, grows exponentially with a constant annual (exponential) growth rate of .06, or 6%, where t is in years. {You could think of this as “trend line Mt” since, while Mt for a real country would not have a constant growth rate every year, one might well find that the trend in Mt has an approximately constant growth rate over a period of some years.} a. State the mathematical formula for Mt. {Hint: your answer will involve Mo.} b. By what factor does Mt increase each year? {Hint: it is not 1.06.} c. Use your answer for part a to show that a graph of ln(Mt) versus t would be a straight line. Show your work! What would the intercept and slope of this line be? {Hint: one of your answers will involve Mo, the other will be a number.} 3. Suppose that the aggregate production function is adequately modeled as a Cobb-Douglas function β = .3, the capital input grows at a 4% rate, and the labor input grows at a 6% rate. (These are, of course, exponential growth rates.) a. If real output grows at an 8% rate, what is the growth rate in multifactor productivity? b. If multifactor productivity grows at a 1% rate, how fast will real output grow? c. If multifactor productivity grows at a 1% rate, at what rate is labor productivity growing? 4. The Malthusian view: Population grows exponentially (he calls it “geometrically’) whereas the food supply grows arithmetically (i.e., with a linear time trend): therefore mass starvation is inevitable. a. As a warm-up exercise, skim the following comments on Malthus: http://www.blupete.com/Literature/Biographies/Philosophy/Malthus.htm http://en.wikipedia.org/wiki/Thomas_Malthus b. Now read Chapters 1 and 2 in Malthus’ 1798 book; it is reproduced on the Web at: http://www.econlib.org/library/Malthus/malPop.html c. Malthus states that (at the time) the population of the United States was doubling every 25 years. What (exponential) growth rate does this imply for the 18th century U.S.? {Hint: .} Also, you might find it handy to know that ln(2) = .693147. (Doubling every 25 years doesn’t require a very large population growth rate, does it?)