CPI can be used to compare money values over time
The following questions and answers illustrate the uses that can be made of the CPI.
Question: What would $200 in 1988 be worth in September quarter 1998?
Response: This question is best interpreted as asking ‘How much would need to be spent in September quarter 1998 to purchase what could be purchased in 1988 for $200?’ As no specific commodity is mentioned, what is required is a measure comparing the general level of prices in September quarter 1998 with the general level of prices in calendar 1988. The All groups CPI would be an appropriate choice.
Because CPI index numbers are not published for calendar years, two steps are required to answer this question. One, derive an index for calendar 1988. Two, multiply the initial dollar amount by the ratio of the index for September quarter 1998 to the index for 1988.
The index for calendar 1988 is obtained as the simple arithmetic average of the quarterly indexes for March (87.0), June (88.5), September (90.2) and December (92.0) 1988 — giving 89.4 rounded to one decimal place. The index for September quarter 1998 is 121.3.
The answer is then given by:
$200 x 121.3 / 89.4 = $271.
For specific items, need to use indexes representative of those items
Question: Household Expenditure Survey data shows that average weekly expenditure per household on the purchase of motor vehicles increased from $19.49 in 1988–89 to $26.61 in 1993–94 (i.e. an increase of 36.5%). Does this mean that households, on average, purchased 36.5% more motor vehicles in 1993–94 than they did in 1988–89?
Response: This is an example of one of the most valuable uses that can be made of price indexes. Often the only viable method of collecting and presenting information about economic activity is in the form of expenditure or income in monetary units (e.g. dollars). While monetary aggregates are useful in their own right, economists and other analysts are frequently concerned with questions related to volumes—for example, whether more goods and services have been produced in one period compared to another period. Comparison of monetary aggregates alone are not sufficient for this purpose as dollar values can change from one period to another due to either changes in quantities or changes in prices (most often a combination).
To illustrate this, consider a simple example of expenditure on oranges in two periods. The expenditure in any period is given by the product of the quantity and the price. Suppose that in the first period 10 oranges were purchased at a price of $1.00 each and in the second period 15 oranges were purchased at a price of $1.50 each. Expenditure in period one would be $10.00 and in period two $22.50. Expenditure has increased by 125%, yet the volume (number of oranges) has only increased by 50% with the difference being accounted for by a price increase of 50%. In this example all the price and quantity data are known, so volumes can be compared directly. Similarly, if prices and expenditures are known, quantities can be derived.
But what if the actual prices and quantities are not known? If expenditures are known and a price index for oranges is available, the index numbers for the two periods can be used as if they were prices to adjust the expenditure for one period to remove the effect of price change. If the price index for oranges was equal to 100.0 in the first period, the index for the second period would equal 150.0. Dividing expenditure in the second period by the index number for the second period and multiplying by the index number for the first period, results in a value that equals the expenditure that would have been observed in the second period had the prices remained as they were in the first period. This can easily be demonstrated by reference to the oranges example:
$22.50 / 150.0 x 100.0 = $15.00 = 15 x $1.00.
So, without ever knowing the actual volumes (quantities) in the two periods, the adjusted second period expenditure ($15.00), can be compared with the expenditure in the first period ($10.00) to derive a measure of the proportional change in volumes—$15/$10 = 1.50, which equals the ratio obtained directly from the comparison of the known volumes.
Turning to the question on expenditure on motor vehicles recorded in the HES in 1988–89 and 1993–94. As the HES data relates to the average expenditure of Australian households, the ideal price index would be one that covers the retail prices of motor vehicles for Australia as a whole. The price index which comes closest to meeting this ideal is the index for the Motor vehicles expenditure class of the CPI for the weighted average of the eight capital cities. The Motor vehicles index number for 1988–89 is 95.8 and for 1993–94 it is 113.6. Using these index numbers, recorded expenditure in 1993–94 ($26.61) can be adjusted to 1988–89 prices as follows:
$26.61 / 113.6 x 95.8 = $22.44.
The adjusted 1993–94 expenditure of $22.44 can then be compared to the expenditure recorded in 1988–89 ($19.49) to deliver an estimate of the change in volumes. This indicates a volume increase of 15.1%.
Forecasting impact of price changes on the CPI
Question: What would be the impact of a 10% increase in petrol prices on the All groups CPI in the December quarter 1998?
Response: Two pieces of information are required to answer this question; the All groups index number for September quarter 1998 (121.3), and the September quarter 1998 points contribution for Automotive fuel (4.78).
An increase in petrol prices of 10% would increase Automotive fuel points contribution by 4.78 x 0.1 = 0.48 index points which would result in an All groups index number of 121.8, an increase of 0.4%.
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