The consumer price index or CPI is a more direct measure than per capita GDP of the standard of living in a country. It is based on the overall cost of a fixed basket of goods and services bought by a typical consumer, relative to price of the same basket in some base year. By including a broad range of thousands of goods and services with the fixed basket, the CPI can obtain an accurate estimate of the cost of living. It is important to remember that the CPI is not a dollar value like GDP, but instead an index number or a percentage change from the base year.

### Constructing the CPI

Each month, the Bureau of Labor Statistics publishes an updated CPI. While in practice this is a rather daunting task that requires the consideration of thousands of items and prices, in theory computing the CPI is simple.

The CPI is computed through a four-step process.

- The fixed basket of goods and services is defined. This requires figuring out where the typical consumer spends his or her money. The Bureau of Labor Statistics surveys consumers to gather this information.
- The prices for every item in the fixed basket are found. Since the same basket of goods and services is used across a number of time periods to determine changes in the CPI, the price for every item in the fixed basket must be found for every point in time.
- The cost of the fixed basket of goods and services must be calculated for each time period. Like computing GDP, the cost of the fixed basket of goods and services is found by multiplying the quantity of each item times its price.
- A base year is chosen and the index is computed. The price of the fixed basket of goods and services for each comparison year is then divided by the price of the fixed basket of goods in the base year. The result is multiplied by 100 to give the relative level of the cost of living between the base year and the comparison years.

For example, let's compute the CPI for Country B. In this simplified example, consumers in Country B only purchase bananas and backrubs (lucky fools). The first step is to fix the basket of goods. The typical consumer in Country B purchases 5 bananas and 2 backrubs in a given period of time, so our fixed basket is 5 bananas and 2 backrubs. The second step is to find the prices of these items for each time period. This data is reported in the table, above. The third step is to compute the basket's cost for each time period. In time period 1 the fixed basket costs (5 X $1) + (2 X $6) = $17. In time period 2 the fixed basket costs (5 X $2) + (2 X $7) = $24. In time period 3 the fixed basket costs (5 X $3) + (2 X $8) = $31. The fourth step is to choose a base year and to compute the CPI. Since any year can serve as the base year, let's choose time period 1. The CPI for time period 1 is ($17 / $17) X 100 = 100. The CPI for time period 2 is ($24 / $17) X 100 = 141. The CPI for time period 3 is ($31 / $17) X 100 = 182. Since the price of the goods and services that comprise the fixed basket increased from time period 1 to time period 3, the CPI also increased. This shows that the cost of living increased across this time period.

### Changes in the CPI over time

As we have just seen, the CPI changes over time as the prices associated with the items in the fixed basket of goods change. In the example just explored, the CPI of Country B increased from 100 to 141 to 182 from time period 1 to time period 3. The percent change in the price level from the base year to the comparison year is calculated by subtracting 100 from the CPI. In this example, the percent change in the price level from the base period (time period 1) to time period 2 is 141 - 100 = 41%. The percent change in the price level from time period 1 to time period 3 is 182 - 100 = 82%. In this way, changes in the cost of living can be calculated across time.

### Problems with the CPI

While the CPI is a convenient way to compute the cost of living and the relative price level across time, because it is based on a fixed basket of goods, it does not provide a completely accurate estimate of the cost of living. Three problems with the CPI deserve mention: the substitution bias, the introduction of new items, and quality changes. Let's examine each of these in detail.

#### Substitution Bias

The first problem with the CPI is the substitution bias. As the prices of goods and services change from one year to the next, they do not all 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. But since the basket is fixed, the CPI does not reflect consumer's preference for items that increase in price little from one year to the next. For example, if the price of backrubs in Country B jumped to $20 in time period 4 while the cost of bananas remained fixed at $3, consumer would likely purchase more bananas and fewer backrubs. This intuitive phenomenon of consumers substituting purchase of low priced items for higher priced items is not accounted for by the CPI.

#### Introduction of New Items

The second problem with the CPI is the introduction of new items. As time goes
on, new items enter into the basket of goods and services purchased by the
typical consumer. For example, if in time period 4 consumers in Country B began
to purchase books, this would need to be included in an accurate estimate of the
cost of living. But since the CPI uses only a *fixed* basket of goods, the
introduction of a new product cannot be reflected. Instead, the new items,
books, are left out of the calculation in order to keep time period 4 comparable
with the earlier time periods.

#### Quality Changes

The third problem with the CPI is that changes in the quality of goods and services are not well handled. When an item in the fixed basket of goods used to compute the CPI increases or decreases in quality, the value and desirability of the item changes. For example, if backrubs in time period 4 suddenly became much more satisfying than in earlier time periods, but the price of backrubs did not change, then the cost of living would remain the same while the standard of living would increase. This change would not be reflected in the CPI from one year to the next. While the Bureau of Labor Statistics attempts to correct this problem by adjusting the price of goods in the calculations, in reality this remains a major problem for the CPI.