## The Price of a Basket of Goods

To calculate the **price level**, economists begin with the concept of a **basket of goods and services**, consisting of the different items individuals, businesses, or organizations typically buy. The next step is to look at how the prices of those items change over time. In thinking about how to combine individual prices into an overall price level, many people find that their first impulse is to calculate the average of the prices. Such a calculation, however, could easily be misleading because some products matter more than others.

Changes in the prices of goods for which people spend a larger share of their incomes will matter more than changes in the prices of goods for which people spend a smaller share of their incomes. For example, an increase of 10% in the rental rate on housing matters more to most people than whether the price of carrots rises by 10%. To construct an overall measure of the price level, economists compute a weighted average of the prices of the items in the basket, where the weights are based on the actual quantities of goods and services people buy. The following Work It Out feature walks you through the steps of calculating the annual rate of inflation based on a few products.

### Calculating an Annual Rate of Inflation

Consider the simple basket of goods with only three items, represented in this table. Say that in any given month, a university student spends money on 20 hamburgers, one bottle of aspirin, and five movies. Prices for these items over four years are given in the table through each time period (Pd). Prices of some goods in the basket may rise while others fall. In this example, the price of aspirin does not change over the four years, while movies increase in price and hamburgers bounce up and down. Each year, the cost of buying the given basket of goods at the prices prevailing at that time is shown.

**A University Student’s Basket of Goods**

Items | Hamburger | Aspirin | Movies | Total | Inflation Rate |
---|---|---|---|---|---|

Qty | 20 | 1 bottle | 5 | – | – |

(Pd 1) Price | $3.00 | $10.00 | $6.00 | – | – |

(Pd 1) Amount Spent | $60.00 | $10.00 | $30.00 | $100.00 | – |

(Pd 2) Price | $3.20 | $10.00 | $6.50 | – | – |

(Pd 2) Amount Spent | $64.00 | $10.00 | $32.50 | $106.50 | 6.5% |

(Pd 3) Price | $3.10 | $10.00 | $7.00 | – | – |

(Pd 3) Amount Spent | $62.00 | $10.00 | $35.00 | $107.00 | 0.5% |

(Pd 4) Price | $3.50 | $10.00 | $7.50 | – | – |

(Pd 4) Amount Spent | $70.00 | $10.00 | $37.50 | $117.50 | 9.8% |

To calculate the annual rate of inflation in this example:

Step 1. Find the **percentage change** in the cost of purchasing the overall basket of goods between the time periods. The general equation for percentage changes between two years, whether in the context of inflation or in any other calculation, is:

\(\begin{array}{rcl}\cfrac{(\text{Level in new year – Level in previous year})}{\text{Level in previous year}}& \text{=}& \text{Percentage change}\end{array}\)

Step 2. From period 1 to period 2, the total cost of purchasing the basket of goods in this table rises from $100 to $106.50. Therefore, the percentage change over this time—the inflation rate—is:

\(\begin{array}{rclll}\cfrac{(\text{106.50 – 100})}{\text{100.0}}& \text{=}& \text{0.065}& \text{=}& \text{6.5%}\end{array}\)

Step 3. From period 2 to period 3, the overall change in the cost of purchasing the basket rises from $106.50 to $107. Thus, the inflation rate over this time, again calculated by the percentage change, is approximately:

\(\begin{array}{rclll}\cfrac{(\text{107 – 106.50})}{\text{106.50}}& \text{=}& \text{0.0047}& \text{=}& \text{0.47%}\end{array}\)

Step 4. From period 3 to period 4, the overall cost rises from $107 to $117.50. The inflation rate is thus:

\(\begin{array}{rclll}\cfrac{(\text{117.50 – 107})}{\text{107}}& \text{=}& \text{0.098}& \text{=}& \text{9.8%}\end{array}\)

This calculation of the change in the total cost of purchasing a basket of goods takes into account how much is spent on each good. Hamburgers are the lowest-priced good in this example, and aspirin is the highest-priced. If an individual buys a greater quantity of a low-price good, then it makes sense that changes in the price of that good should have a larger impact on the buying power of that person’s money. The larger impact of hamburgers shows up in the “amount spent” row, where, in all time periods, hamburgers are the largest item within the amount spent row.