Fixed market basket price indexes
It may seem that index numbers are little more than a plot to disguise simple statements in complex language. Why say, “The Consumer Price Index (1982–84 = 100) stood at 238.7 in July 2015,” instead of “Consumer prices rose 138.7% between the 1982–84 average and July 2015”? In fact, the term “index number” usually means more than a measure of change relative to a base. It also tells us the kind of variable whose change we measure. That variable is a weighted average of several quantities, with fixed weights. Let’s illustrate the idea by a simple price index.
EXAMPLE 2 The mountain man price index
Bill Smith lives in a cabin in the mountains and strives for self-sufficiency. He buys only salt, kerosene, and the services of a professional welder. Here are Bill’s purchases in 1990, the base period. His cost, in the last column, is the price per unit multiplied by the number of units he purchased.
| Good or service | 1990 quantity | 1990 price | 1990 cost |
|---|---|---|---|
| Salt | 100 pounds | $0.50/pound | $50.00 |
| Kerosene | 50 gallons | 0.80/gallon | 40.00 |
| Welding | 10 hours | 13.00/hour | 130.00 |
| Total cost = | $220.00 |
The total cost of Bill’s collection of goods and services in 1990 was $220. To find the “Mountain Man Price Index” for 2015, we use 2015 prices to calculate the 2015 cost of this same collection of goods and services. Here is the calculation:
370
| Good or service | 1990 quantity | 2015 price | 2015 cost |
| Salt | 100 pounds | $0.65/pound | $65.00 |
| Kerosene | 50 gallons | 1.50/gallon | 75.00 |
| Welding | 10 hours | 23.00/hour | 230.00 |
| Total cost = | $370.00 |
The same goods and services that cost $220 in 1990 cost $370 in 2015. So the Mountain Man Price Index (1990 = 100) for 2015 is
The point of Example 2 is that we follow the cost of the same collection of goods and services over time. It may be that Bill refused to hire the welder in 2015 because he could not afford him. No matter—the index number uses the 1990 quantities, ignoring any changes in Bill’s purchases between 1990 and 2015. We call the collection of goods and services whose total cost we follow a market basket. The index number is then a fixed market basket price index.
Fixed market basket price index
A fixed market basket price index is an index number for the total cost of a fixed collection of goods and services.
The basic idea of a fixed market basket price index is that the weight given to each component (salt, kerosene, welding) remains fixed over time. The CPI is, in essence, a fixed market basket price index, with several hundred items that represent all consumer purchases. Holding the market basket fixed allows a legitimate comparison of prices because we compare the prices of exactly the same items at each time. As we will see, it also poses severe problems for the CPI.