# 5. Measuring Changes in Prices - Sample Problems

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3. Measuring Inflation with Price Indexes

1. The following figures are the nominal GDP, real GDP (in billions of 1996 dollars), and GDP deflator for the United States for the years 1989 to 1994.

 Year Nominal GDP GDP Deflator Real GDP 1989 ? 83.6 6,569 1990 ? 86.8 6,683 1991 5,986 ? 6,669 1992 6,319 ? 6,891 1993 6,642 94.2 ? 1994 7,054 96.1 ?

1. Fill in the missing figures.

Answer: If you know two values you can always calculate the third (or you can look up the missing numbers on the Bureau of Economic Analysis web site, http://www.bea.doc.gov):

GDP Deflator = (Nominal GDP / Real GDP) x 100
Nominal GDP = Real GDP x (GDP Deflator / 100)
Real GDP = Nominal GDP / (GDP Deflator / 100)

1989 Nominal GDP = 5,492
1990 Nominal GDP = 5,801
1991 GDP Deflator = 89.8
1992 GDP Deflator = 91.7
1993 Real GDP = 7,051
1994 Real GDP = 7,340

2. During what year(s) was the economy contracting?

Answer: The change in real GDP indicates whether the economy is growing or contracting. The economy grows if real GDP increases. The economy contracts if real GDP declines. The economy contracted in 1991, which was the last recession the U.S. has gone through. Actually the recession lasted from a peak in the business cycle in July 1990 until the trough (bottom point) in March 1991. Note that the base year for calculating real GDP is 1996 and the 1996 GDP deflator = 100.

For a summary of U.S. business cycles expansions and contractions refer to the National Bureau of Economic Research (http://www.nber.org) or The Conference Board (http://www.tcb-indicators.org)

3. During what year(s) was there inflation (i.e., the average level of prices increased)?

Answer: The GDP deflator is a price index. An increase in the value of the GDP deflator represents inflation. A decrease in the GDP deflator indicates deflation, a decline in the average level of prices. The U.S. economy was experiencing inflation every year from 1990 to 1994. We don't know about 1989 since we don't know what the GDP deflator for 1988 was, but it is safe to say the U.S. has experienced inflation every year since 1939.

2. Consider a simple economy in which only three items are in the consumer price index (CPI): food, housing, and entertainment (fun). Assume in the base period, say 1987, the household consumed the following quantities at the then prevailing prices:

 Quantity Price per unit Expenditure Food 5 \$ 14 \$ 70 Housing 3 \$ 10 \$ 30 Fun 4 \$ 5 \$ 20 Total expenditure \$ 120

1. Define the consumer price index

 CPI = sum of [(current prices) x (fixed market basket quantities)]   * 100 sum of [(base year prices) x (fixed market basket quantities)]

2. Assume that the market basket of goods that define the CPI is as given in the table. Calculate the CPI for 1994 if the prices prevailing in 1994 are as follows: food \$30 per unit; housing, \$20 per unit; and fun, \$6 per unit.

 1994 CPI (1987 = 100) = [(5*30 + 3*20 + 4*6) / (5*14 + 3*10 + 4*5)] * 100 = (234 / 120) * 100 = 195

3. What was the total inflation rate over this 7 year period (1987 to 1994)?

 Inflation = (Price Index Year 2 - Price Index Year 1) * 100 Price Index Year 1 = [(195 - 100)/ 100] * 100 = 95 %

Note - to calculate the average annual inflation rate over this period you would have to use the annual compound interest rate formula:

(1 + avg. annual interest rate)no. years = (Price Index Year 2 / Price Index Year 1)
(1 + avg. annual interest rate)7 = 1.95
1 + avg. annual interest rate = 1.10
average annual interest rate = 0.10, or 10%

4. The consumer price index and GDP deflator are both measures of an average price level. How are they different, and when might you prefer one of these measures over the other?

Answer: The CPI measures the increase in the cost of a particular market basket of consumer goods and services purchased y private households while the GDP deflator measures the increase in the cost of all final goods and services, including those purchased by firms and government. The type and quantity of goods and services included in the CPI market basket do not change from year to year while the type and quantities of goods and services covered by the GDP deflator change every year. The CPI includes imported goods and services purchased by households while the GDP deflator does not.

The CPI would be preferred if you were evaluating the cost of living of a typical household. The GDP deflator would be preferred if you were evaluating entire economies.