1. What is a price index?
A price index is number which gives us the price level or (roughly) the average level of prices.

2. How do we calculate a price index?
In order to calculate a price index, we must compare the nominal value of a certain group of goods to the real value of that same group of goods. Put another way: we compare the cost of buying a certain group of goods in one year (or time period) to their cost in another year (or time period). An example follows below:

To calculate a (yearly) price index for consumers, we must:
a) select a base year, which allows us to compare prices between years
b) select quantity-weights, which gives varying levels of importance to the different commodities that a consumer buys (e.g. the price of toothpaste shouldn't play as big a role in changing the CPI as a change in the price of gas)
c) obtain data on expenditures (preferably with prices and quantities separate)

Suppose consumers buy only 4 different goods, at the prices and quantities listed below. Before calculating our price index, we need to select a base year and quantity-weights. We'll choose 1990 as the base year and the quantities purchased in 1990 as quantity-weights.

The formula for calculating a price index in year i (where year i may be 1993, 1992, 1991 or 1990) is:

Q = Quantity (weights) for shirts (Q_S), meat (Q_M), gas (Q_G), and months of rent (Q_R)
P_Si = price of shirts in year i (where year i can be 1990, 1991, 1992 or 1993)
[P_Mi = price of shirts in year i; P_Gi = price of gas in year i; P_Ri = Rent/month in year i]
P_SB = price of shirts in (base year) 1990
[P_MB = price of shirts in 1990; P_GB = price of gas in 1990; P_RB = Rent/month in 1990]

To calculate the price index for 1993, we just plug the 1993 prices, base year (1990) prices and 1990 quantity-weights (from our table) into the formula above:

Similarly, we can calculate price indexes for the other years:

Price Index (1992) = 114.98

Price Index (1991) = 106.74

Price Index (1990) = 100.00

3. How do we interpret our results?
The best way to interpret these resulting price indexes is by restating what we were trying to measure. Remember, to calculate a price index, we wanted to compare the cost of a group of goods in one year to the cost of those same goods in the base year. Our interpretation follows from this:

Goods that would have cost consumers $100 in 1990, cost $112.15 in 1993 (or $114.98 in 1992, or $106.74 in 1991). Our consumer price index increased between each year, except 1992-1993, which implies inflation. In the last two years, we see deflation.