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Index Numbers, Ratios and Price Index

In 1990, a price index based on 1980 = 100 had a value of z. During 1990, it was rebased at 1990 = 100, and in 1998 the new index stood at 112.

If the total price movement between 1980 and 1998 was an increase of 40%, was was the value of z in 1990, that is, before rebasing?

The answer given was,

Using ratios, 1.12 x (z/100) = 1.40, giving z = 125.

The bits of this I do not understand are,

1. Why did 40% get changed to 1.40, why not 0.40? Where does the one come from?
2. Why is the left had side of the equation 1.12 x (z/100) and not 1.12 + (z/100).
3. Can you recomend any books so I can learn about this type of question and how the underlying algebra works.

I would be very grateful for any assistance. Thank you for your time.

Solution Preview

Index number is a specialized average designed to measure the change in the level of an activity or item, either with respect to time or geographic location or some other characteristic. It is described either as a ratio or a percentage.

For example, when we say that consumer price index for 1998 is 175 compared to 1991, it means that consumer prices have risen by 75% over these seven years.

Price index means the ratio of price ...

Solution Summary

Index Numbers, Ratios and Price Index are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.