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Econ 101b: Fall 2003: Problem Set 1 (Chapters 1 & 2)

Problem Set 1: Econ 101b: Fall 2003 (Chapters 1 & 2)

Due at the start of section on September 2

1. Explain whether or not and why the following items are included in the calculation of GDP:

1. Declines in business inventories
2. The fees earned by real estate agents on selling existing homes
3. Social Security checks written by the government
4. Purchase of a new aircraft carrier by the Department of Defense
5. Rent that you pay to your landlord
6. Purchases of American-made trucks by foreign residents

2. Do you calculate real GDP by dividing nominal GDP by the price level or by subtracting the price level from nominal GDP?

3. Do you calculate the real interest rate by dividing the nominal interest rate by the price level or by subtracting the inflation rate from the nominal interest rate?

4. Are your answers to 2 and 3 the same? Since both sets of calculation aim to transform a real into a nominal quantity, shouldn't they be calculated in a parallel fashion?

5. In 1979 the (short-term) nominal interest rate on three-month Treasury bills averaged 10.0%, and the GDP deflator rose from 50.88 to 55.22. What was the annual rate of inflation in 1979? What was the real interest rate in 1979?

6. Were real interest rates higher in 1979, or in 1998 (when the (short-term) nominal interest rate on three-month Treasury bills was 4.8%, and the inflation rate was 2.6%? Which interest rate concept--the nominal interest rate or the real interest rate--should lenders and borrowers care more about? Why?

7. Suppose that the appliance store buys a refrigerator from the manufacturer on December 15, 2003 for $600, and that you then buy that refrigerator on January 15, 2004 for $750. a. What is the contribution to GDP in 2003? b. How is the refrigerator accounted for in the NIPA in 2003? c. What is the contribution to GDP in 2004? d. How is the refrigerator accounted for in the NIPA in 2004?

8. What do economists mean when they say that it is time to "build a model" of a situation or a problem?

9. In what sense can a line on a graph "be" an equation?

10. What are the principal flaws in using GDP per worker as a measure of material welfare? Given these flaws, why do we use it anyway?

11. Suppose a quantity is growing at a steady proportional rate of 3% per year. How long will it take to double? Quadruple? Grow 1024-fold?

12. Suppose we have a quantity x(t) that varies over time following the equation: dx(t)/dt = -(0.08)x -0.32. Without integrating the equation, tell me what the long-run steady-state value of x is going to be. Suppose that the value of x at time t=0, x(0), equals 6. Without integrating the equation, tell me how long it will take x to close half the distance between its initial value of 6 and its steady-state value. How long will it take to close 3/4 of the distance? 7/8 of the distance? 15/16 of the distance?

13. Now you are allowed to integrate dx(t)/dt = -(0.08)x -0.32. Give me first the indefinite integral, and then the definite integral for the initial condition x(0) = 6. Give me the definite integral for the initial condition x(0)=8.

14. Suppose we have a quantity y = x^a, and suppose that x is growing at a constant proportional rate of 6% per year. How fast is y growing if a=0.25? If a=0.5? If a=1? If a=2?

15. Suppose we have a quantity z = (x/y)^b. Suppose x is growing at 6% per year and that b=1/3. How fast is z growing if y is growing at 0% per year? If y is growing at 2% per year? If y is growing at 6% per year? And if y is growing at 12% per year?

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Econ 101b: Fall 2003: Answers to Problem Set 1.

Posted by DeLong at August 24, 2003 10:40 AM | TrackBack