University of Louisville

Department of Economics

Economics 202

**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.