Price Indexes
A Simple Example
The concept of a price index can be better seen with the aid of the simple example below. In this simple world we are concerned only with changes in the cost of entertainment. We begin by picking a base year, the year which we will use as the basis for our computations. For that year a survey is conducted in which we determine the types of entertainment that people participate in and their level of consumption. In this example, the base year is 1987, the year in which a survey revealed that the average household purchased four theater tickets, two concert and basketball tickets, five basketball tickets, went out to dinner eight times and escaped to a hotel twice.
ENTERTAINMENT PRICE INDEX
Price |
Quantity |
|||
1987 |
1997 |
1987 |
1997 |
|
| Theatre Ticket | 10 |
25 |
4 |
3 |
| Concert Ticket | 3.5 |
10 |
2 |
1 |
| Basketball Ticket | 4 |
7 |
5 |
6 |
| Football Ticket | 5 |
10 |
2 |
3 |
| Dinner | 8 |
18 |
8 |
6 |
| Hotel Room | 30 |
75 |
2 |
2 |
ACTUAL 1987 EXPENSES = 10*4 +3.5*2 +4*5 +5*2 +8*8 +30*2 = 201
The level of expenditures on the entertainment basket in 1987 was $201. But what happens to the level of expenditures on entertainment by 1997? The expenditures on entertainment in 1997 are $415. The problem is that the difference [$415-$201] can be attributed to changes in the prices [the price of dinner rose from $8 to $18] and the entertainment mix changed [in 1997 we went to dinner 6 times instead of 8 times].
ACTUAL 1997 EXPENSES = 25*3 +10*1 +7*6 +10*3 +18*6 +75*2=415
To isolate the price changes we can calculate the value of our 1987 entertainment mix at 1997 prices.
HYPOTHETICAL 1997 EXPENSES ( 1987 PURCHASES/ 1997 PRICES )
= 25*4 +10*2 +7*5+ 10*2+ 18*8+ 75*2 = 469
With the hypothetical expenses in 1997 we can now create an index of prices in 1997, what we will call an Entertainment Price Index (EPI). The index is the ratio of the hypothetical to the base year expenditures multiplied by 100. In this example the EPI in 1997 is 233
EPI = 100*(469/201) = 233
Once we have the EPI, we can then make some statements about price level changes. With an EPI of 233, we can say the following:
(1) WHAT COST $100 IN 1987 COST $233 IN 1993
(2) PRICES MORE THAN DOUBLED
(3) PRICES WENT UP 133% (233-100)
(4) A 1987 DOLLAR IS WORTH $.43 (100/233)
And what about inflation?
Once you have the price index, inflation is easy. The inflation rate is simply defined as the percentage change in the price index. This rate is either specified as a monthly rate or as an annual rate. In the simple example above, if the EPI was 210 at the end of 1995 and 233 at the end of 1996, then the inflation rate for 1996 would be:
(233-201)/201 = 32/201 = .1592 = 15.92%
A few unresolved issues