## Economics 101b Fall 2005 Problem Set 1: Basics

A simple problem set to fix some concepts and give some confidence. Due at lecture on Friday September 9:

- A. Explain whether or not, why, and how the following items are included in the calculation of GDP:
a. Increases in business inventories.

b. Fees earned by real estate agents on selling existing homes.

c. Social Security checks written by the government.

d. Building of a new dam by the Army Corps of Engineers.

e. Interest that your parents pay on the mortgage they have on their house.

f. Purchases of foreign-made trucks by American residents

- B. Calculating real magnitudes:
a. When you calculate real GDP, do you do so by dividing nominal GDP by the price level or by subtracting the price level from nominal GDP?

b. When you calculate the real interest rate, do you do so by dividing the nominal interest rate by the price level or by subtracting the inflation rate from the nominal interest rate?

c. Are your answers to (a) and (b) the same? Why or why not?

- C. Suppose that the appliance store buys a refrigerator from the manufacturer on December 15, 2005 for $600, and that you then buy that refrigerator on January 15, 2006 for $1000:
a. What is the contribution to GDP in 2005?

b. How is the refrigerator accounted for in the NIPA in 2005?

c. What is the contribution to GDP in 2006?

d. How is the refrigerator accounted for in the NIPA in 2004?

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

E. Why do DeLong and Olney think that the interest rate and the level of the stock market are importnant macroeconomic variables?

F. 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?

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

H. What, roughly, was the highest level the U.S. unemployment rate reached in

a. the 20th century?

b. the past fifty years?

c. the past twenty years?I. Do you think there is a connection between your answer to the qeustion above and the fact that Federal Reserve Chair Alan Greenspan received a five-minute standing ovation at the end of the first of many events marking his retirement last wekend?

J. Suppose we have a quantity x(t) that varies over time following the equation: dx(t)/dt = -(0.06)x + 0.36.

a.

Withoutintegrating the equation, tell me what the long-run steady-state value of x--that is, the limit of x as t approaches in infinity--is going to be.

b. Suppose that the value of x at time t=0, x(0), equals 12. Once again,withoutintegrating the equation, tell me how long it will take x to close half the distance between its initial value of 12 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?

- K. Now you are allowed to integrate dx(t)/dt = -(0.06)x + 0.36.
a. Write down and solve the indefinite integral.

b. Write down and solve the definite integral for the initial condition x(0) = 12.

c. Write down and solve the definite integral for the initial condition x(0)=6.

L. Suppose we have a quantity z = (x/y)

b . Suppose x is growing at 4% per year and that b=1/4. 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 4% per year?M. What is the difference between the nominal interest rate and the real interest rate? Why do DeLong and Olney think that the real interest rate is more important?

N. What (briefly!) does Robert Heilbroner think of Karl Marx?

O. What (briefly!) does Robert Heilbroner think of John Maynard Keynes?