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
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 (QS), meat (QM), gas (QG), and months of rent (QR)
PSi = price of shirts in year i (where year i can be 1990, 1991, 1992 or 1993)
[PMi = price of shirts in year i; PGi = price of gas in year i; PRi = Rent/month in year i]
PSB = price of shirts in (base year) 1990
[PMB = price of shirts in 1990; PGB = price of gas in 1990; PRB = 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
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.