## Price Indexes

How do we actually measure inflation and deflation (that is, changes in the price level)? Price-level change is measured as the percentage rate of change in the level of prices. But how do we find a price level?

Economists measure the price level with a price index. A price index is a number whose movement reflects movement in the average level of prices. If a price index rises 10%, it means the average level of prices has risen 10%.

There are four steps one must take in computing a price index:

- Select the kinds and quantities of goods and services to be included in the index. A list of these goods and services, and the quantities of each, is the “market basket” for the index.
- Determine what it would cost to buy the goods and services in the market basket in some period that is the base period for the index. A base period is a time period against which costs of the market basket in other periods will be compared in computing a price index. Most often, the base period for an index is a single year. If, for example, a price index had a base period of 1990, costs of the basket in other periods would be compared to the cost of the basket in 1990. We will encounter one index, however, whose base period stretches over three years.
- Compute the cost of the market basket in the current period.
- Compute the price index. It equals the current cost divided by the base-period cost of the market basket.

*Price index = Current cost of basket / Base-period cost of basket*

(While published price indexes are typically reported with this number multiplied by 100, our work with indexes will be simplified by omitting this step.)

Suppose that we want to compute a price index for movie fans, and a survey of movie watchers tells us that a typical fan rents 4 movies on DVD and sees 3 movies in theaters each month. At the theater, this viewer consumes a medium-sized soft drink and a medium-sized box of popcorn. Our market basket thus might include 4 DVD rentals, 3 movie admissions, 3 medium soft drinks, and 3 medium servings of popcorn.

Our next step in computing the movie price index is to determine the cost of the market basket. Suppose we surveyed movie theaters and DVD-rental stores in 2007 to determine the average prices of these items, finding the values given in Table 5.1 “Pricing a Market Basket.” At those prices, the total monthly cost of our movie market basket in 2007 was $48. Now suppose that in 2008 the prices of movie admissions and DVD rentals rise, soft-drink prices at movies fall, and popcorn prices remain unchanged. The combined effect of these changes pushes the 2008 cost of the basket to $50.88.

**Table 5.1 Pricing a Market Basket**

Item | Quantity in Basket | 2007 Price | Cost in 2007 Basket | 2008 Price | Cost in 2008 Basket |
---|---|---|---|---|---|

DVD rental | 4 | $2.25 | $9.00 | $2.97 | $11.88 |

Movie admission | 3 | 7.75 | 23.25 | 8.00 | 24.00 |

Popcorn | 3 | 2.25 | 6.75 | 2.25 | 6.75 |

Soft drink | 3 | 3.00 | 9.00 | 2.75 | 8.25 |

Total cost of basket | 2007 |
$48.00 | 2008 |
$50.88 |

To compute a price index, we need to define a market basket and determine its price. The table gives the composition of the movie market basket and prices for 2007 and 2008. The cost of the entire basket rises from $48 in 2007 to $50.88 in 2008.

Using the data in Table 5.1 “Pricing a Market Basket”, we could compute price indexes for each year. Recall that a price index is the ratio of the current cost of the basket to the base-period cost. We can select any year we wish as the base year; take 2007. The 2008 movie price index (MPI) is thus

The value of any price index in the base period is always 1. In the case of our movie price index, the 2007 index would be the current (2007) cost of the basket, $48, divided by the base-period cost, which is the same thing: $48/$48 = 1.