  Monday  December 16, 2019
 AmosWEB means Economics with a Touch of Whimsy! ENDPOINT FORMULA: A simple technique for calculating the coefficient of elasticity that estimates the elasticity for discrete changes in two variables, A and B. The distinguishing characteristic of this formula is that percentage changes are calculated based on the initial values of each variable. This is much simpler than the midpoint formula, which is based on the percentage change from an average of the initial and ending values. The primary problem with the endpoint formula is that different elasticity values are obtained for price increases than for price decreases of the same segment of the demand curve.                              PRICE INDEX:

A measure of the average of a group of prices calculated as a ratio to prices in a given time period (that is, a base year). A price index is primarily used to compare relative prices, or changes in the group prices over time. Such an index is a handy indicator of overall price trends. Two common price indexes that surface in the study of macroeconomics are the Consumer Price Index (CPI) and the GDP price deflator. Both are used to indicate the macroeconomy's average price level and to estimate the inflation rate. The Dow Jones Industrial Average (the Dow), Standard & Poor's 500, and the NASDAQ are well-known indexes of stock market prices.
A price index provides a means of tracking the prices of a group of goods, services, commodities, or other items. For the study of macroeconomics, the most important prices are those for the final goods and services that comprise gross domestic product. This average price level of aggregate production is measured by two alternative price indexes--Consumer Price Index (CPI) and GDP price deflator.

### Two Features

Price indexes share two common features:

• An Average: First, a price index is an average of many prices. But it is not a simple, arithmetic mean type of average. A price index is weighted, or adjusted, by the quantities of the goods. As an index of consumer prices, the CPI is calculated using the quantities of goods purchased by consumers. As an index of stock prices, the Dow is calculated using the quantities of stocks issued by corporations.

• A Base Period: Second, a price index is measured relative to a given period, or base year. The value of the price index in the base year is typically assigned a value of 100 (or some comparable unitary designation like 1 or 1000). The year or period in question is then compared to this base year. Suppose, for example, that the base year is 2002, which carries a price index value of 100. The price index for 2003 might then be something like 105, making it 5 percent higher than the base year.

### Deriving a Price Index

To see how a price index is computed, consider the derivation of a hypothetical measure of consumer prices--the Amblers Price Index (API).
• Total Expenditures: The first step is to determine "total expenditures." Total expenditures effectively weight consumer prices with the quantities purchased. Suppose that 500 pairs of jogging shoes (the quantity weight) are purchased for \$100 each. If so, the total "shoe expenditure" is \$50,000. Now suppose that amblers also purchase 10,000 hot fudge sundaes (the quantity weight) for \$2 a piece. If so, the total "hot fudge sundae expenditure" is \$20,000. If these are the only two goods purchased by amblers that make up the Amblers Price Index calculation, then total expenditures are \$70,000.

• Different Periods: An index is based on total expenditures for different time periods. For macroeconomic price indexes (CPI, GDP price deflator) the time periods are months or years. For stock price indexes (the Dow, NASDAQ), the time periods are days, or even minutes. The key is to use the same quantity weights when calculating total expenditures for the different time periods. For the Amblers Price Index, the quantities purchased by amblers in a given base year are the weights used.

Suppose that the \$70,000 expenditure for 500 pairs of shoes and 10,000 hot fudge sundaes is for 2000, designated as the base year for this API calculation. The trick is to calculate total expenditures for subsequent years, using the same quantities purchased in 2000 as the weights, but with prices for other years. Suppose that the 2001 price of hot fudge sundaes is \$2.50 and the 2001 price of jogging shoes is \$110. Total expenditures in 2001 (assuming amblers purchase the same quantities as they did in 2000) is then \$80,000. This includes \$55,000 for jogging shoes (500 pairs at \$110 each) and \$25,000 for hot fudge sundaes (10,000 sundaes at \$2.50 each).

• Relative Comparison: The last step is to compare expenditures in one period with those in another. In this case, the task is to divide 2001 expenditures by 2000 expenditures, then multiplying by 100 to provide a nice, easy to use number. The API in this example is 114.29 (= \$80,000/\$70,000 x 100).

Note what happens if the API is computed for 2000. That is, calculating 2000 total expenditures on shoes and sundaes using 2000 prices, which is \$70,000, then dividing by the \$70,000 value of 2000 base year total expenditures. Hopefully, this is somewhat obvious that the 2000 API is equal to 100 (= \$70,000/\$70,000 x 100). This is really just another way of saying that the API, like other price indexes, sets the value of the index equal to 100 for the base year.

### What Does It Mean

The specific interpretation of an API of 114.29 is that amblers spend 14.29 percent more on 500 pairs of jogging shoes and 10,000 hot fudge sundaes in 2001 than they did in 2000, \$80,000 versus \$70,000. The more general interpretation is that ambler prices increased by 14.29 percent from 2000 to 2001. Because the quantities are identical for both 2000 and 2001, the ONLY reason total expenditures are greater in 2001 than 2000 is that prices are, on average, higher.

Given comparable API values for 2002, 2003, etc., makes it possible to calculate other price changes. A 2002 API of 119.92, indicates ambler prices increased by 19.92 percent from 2000 to 2002. Moreover, the change in ambler prices from 2001 to 2002 can be obtained by calculating the percentage change in API values between these two years. The result is 4.92 percent (= [119.92 - 114.29]/114.29 x 100). This, by the way, is the basic method used to calculate the inflation rate.

There is an important qualification when interpreting this API and other comparable price indexes. The key assumption is that amblers purchased the same quantities of shoes and sundaes in 2001 and 2002 as they purchased in 2000. This is not necessarily the case. In fact, people generally DO not buy the same quantities of goods year after year. While an assumption of fixed quantities is needed to isolate price changes, this creates a built-in source of error. When quantities change from the base year, the index effectively measures price changes for goods that ARE not purchased. For this reason such "fixed-weight" price indexes must be used and interpreted carefully.

 <= PRICE FLOOR PRICE LEVEL => Recommended Citation:

PRICE INDEX, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2019. [Accessed: December 16, 2019].

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