Prices+-&nbsp;What+is+the+CPI?+How+would+you+calculate+the+inflation+rate++(annual+and+not+annual)?+What+are+some+problems+with+the+CPI?

=**What is the CPI?**= The Consumer Price Index (CPI) is a form of measurement in economics which examines the average change in prices over time for a market basket of goods and services. It is released monthly and is calculated by the Bureau of Labor Statistics [1]. The CPI is a primary indicator of changes in inflation for a particular market. Additionally, it is used to calculate cost of living adjustments (COLAs) for government programs. Lastly, it serves as the basis for COLAs for numerous private labor agreements [3]. As a result, another name for the CPI is the cost-of-living index [2].

Eight categories are considered in the CPI calculations with approximately 200 goods and services total incorporated into the market basket. The categories and examples from each category are as follows:


 * 1. Food and Beverage** Ex. Breakfast cereal, milk, coffee, chicken, wine, service meals and snacks
 * 2. Housing** Ex. Rent of primary residence, owners' equivalent rent, fuel oil, bedroom furniture
 * 3. Apparel** Ex. Men's shirts and sweaters, women's dresses, jewelry
 * 4. Transportation** Ex. New vehicles, airline fares, gasoline, motor vehicle insurance
 * 5.** Medical Care Ex. Prescription drugs and medical supplies, physicians' services, eyeglasses and eye care, hospital services
 * 6. Recreation** Ex. Televisions, pets and pet products, sports equipment, admissions
 * 7. Education and Communication** Ex. College tuition, postage, telephone services, computer software and accessories
 * 8. Other Goods and Services** Ex. Tobacco and smoking products, haircuts and other personal services, funeral expenses [4]

=How to Calculate Inflation Rate= There are two ways to calculate inflation rate, annually and non-annually.

Annually
Calculating the annual inflation rate is done by using the following formula:

Inflation Rate = [(FV/PV)^(1/n)] - 1

FV stands for Future Value and is expressed by the equation PV(1+i)^n PV stands for Present Value and is expressed by the equation FV/[(1+i)^n] n stands for Time Period in Years

Non-Annually
Calculating the non-annual inflation rate is done by using the following formula:

Inflation Rate = [(CPI NewYear – CPI OldYear)/CPI OldYear ] * 100 [5]

For example, if the CPI for Jan. 2006 was 198.3 and the CPI for Jan. 2005 was 190.7, the inflation rate from 2005 to 2006 is:

Inflation Rate = [(198.3-190.7)/190.7] * 100 Inflation Rate = (7.6/190.7) * 100 Inflation Rate = 3.99%

Past monthly CPI numbers which allow someone to find the inflation rate between any two periods of time can be found [|here] [6].

=Problems with the CPI= Although the Consumer Price Index is the most widely cited inflation indicator [3], there are three main problems associated with the CPI.

Substitution Bias
While the prices of goods and services change on a yearly basis, all of the products don't necessarily change by the same amount. The number of specific items that consumers purchase changes depending upon the relative prices of items in the fixed basket. Because the market basket is fixed, the CPI does not reflect consumer's preference for items that increase in price little from one year to the next. The CPI does not account for consumers substituting the purchase of low priced items for higher priced items [7].

Introduction of New Items
New items enter into the basket of goods and services purchased by the typical consumer on a consistent basis; however, the CPI is unable to reflect this. If consumers regularly start to purchase a certain product, then that must be reflected in the cost of living. Unfortunately, due to the fact that the CPI only features a fixed basket of goods, the introduction of a new product cannot be incorporated into the index. Thus, the new product cannot be included in the calculation of the CPI so that time periods can be accurately compared to one another [7].

Quality Changes
Changes in quality of goods and services are not reflected well in the CPI. When one of the items used in the fixed basket of goods used in the calculation of the CPI experiences a change in quality, the value and desirability of the item changes as well. This change is unable to be reflected in the CPI from one period to the following period. In an attempt to counter this problem, the Bureau of Labor Statistics adjusts the price of goods in the calculations, but it still remains a cause for concern for the CPI [7].

=Example Problems= 1) Which of the following categories is NOT used in the computation of the Consumer Price Index: a. Food and Beverage b. Transportation c. Medical Care d. Taxes e. Recreation

2) What is the formula used to calculate the non-annual inflation rate? a. [(CPI OldYear – CPI NewYear)/CPI NewYear ] * 100 b. [(CPI NewYear – CPI OldYear)/CPI NewYear ] * 100 c. [(CPI NewYear – CPI OldYear)/CPI OldYear ] * 100 d. [(CPI OldYear – CPI NewYear)/CPI OldYear ] * 100

3) The CPI for March 2007 was 205.4 while the CPI in March 2006 was 199.8. Using these numbers, calculate the non-annual inflation between March 2006 and March 2007. a. -3.7% b. 2.8% c. 4.2% d. 3.7%

4) Given that the inflation rate from Feb. 2006 to Feb. 2007 is 2.42%, and the CPI for Feb. 2007 is 203.5, what was the CPI for Feb. 2006? a. 201.3 b. 196.4 c. 200.8 d. 199.9 e. 198.7

5) Given that the annual inflation rate for health care is 7.21%, and the CPI for health care in 1984 is 75.3, calculate how much $2000 in 2007 was worth in 1984 with regards to health care services. a. $356.04 b. $384.54 c. $403.29 d. $521.34

=Example Answers= The other four are all examples of categories that are used in the calculation of the CPI. In addition to those four, Housing, Apparel, Education and Communication, and Other Goods and Services are used.
 * 1) d. Taxes.**

This formula is used to find the inflation rate given two years worth of CPI numbers.
 * 2) c. [(CPI NewYear – CPI OldYear)/CPI OldYear ] * 100**

[(205.4-199.8)/199.8] * 100 = 2.8%
 * 3) b. 2.8%**

[(203.5-x)/x] * 100 = 2.42% (203.5-x)/x = .0242 203.5-x = .0242x 203.5 = .0242x + x 203.5 = x(.0242 + 1) 203.5 = 1.0242x x = 198.7
 * 4) e. 198.7**

2000/(1.0721^23) = 403.29
 * 5) c. $403.29**

=Sources= [1] minneapolisfed.org/research/data/us/calc [2] investorwords.com/1062/Consumer_Price_Index.html [3] biz.yahoo.com/c/terms/cpi.html [4] csgnetwork.com/cpicalc.html [5] qrc.depaul.edu/cyorke/Class%20Notes/CPI_Inflation_Rates.htm [6] inflationdata.com/inflation/Consumer_Price_Index/HistoricalCPI.aspx [7] sparknotes.com/economics/macro/measuring1/section2.rhtml

Written by Eric Maroun