## Problem Set 1: National Income Accounting: Economics 101b: U.C. Berkeley: Spring 2008

**Due at start of lecture, Feb 1 2007:**

**Economics 101b Problem Set 1**

Spring 2008, U.C. Berkeley

Brad DeLong

Marc Gersen

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

- Increases in business inventories.
- Fees earned by real estate agents on selling existing homes.
- Social Security checks written by the government.
- Building of a new dam by the Army Corps of Engineers.
- Interest that your parents pay on the mortgage they have on their house.
- Purchases of foreign-made trucks by American residents

Calculating real magnitudes:

- 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?
- 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?
- Are your answers to the two parts the same? Why or why not?

Suppose that the appliance store buys a refrigerator from the manufacturer on December 15, 2007 for $600, and that you then buy that refrigerator on February 15, 2008 for $1000:

- What is the contribution to GDP in 2008?
- How is the refrigerator accounted for in the NIPA in 2008?
- What is the contribution to GDP in 2007
- How is the refrigerator accounted for in the NIPA in 2007?

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

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?

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

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

*Without*integrating 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.- Suppose that the value of x at time t=0, x(0), equals 12. Once again, without integrating 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?

Now you are allowed to integrate dx(t)/dt = -(0.06)x + 0.36.

- Write down and solve the indefinite integral.
- Write down and solve the definite integral for the initial condition x(0) = 12.
- Write down and solve the definite integral for the initial condition x(0)=6.

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?

Which do you think is a more important macroeconomic variable, real GDP per capita or the unemployment rate? Why?