Which of the following statements is/are correct? 1. A price index captures the change in the average price of a constant basket of commodities. 2. If the price index takes values 100, 110 and 121 in three consecutive years respectively, then the inflation rates in the 2nd and 3rd years are 10% and 21% respectively. Select the correct answer using the code given below.
- (a)1 only
- (b)2 only
- (c)Both 1 and 2
- (d)Neither 1 nor 2
Correct — A, 1 only. Statement 1 is the textbook definition of a price index: you fix a basket of commodities, cost that same basket in the base year and again in the current year, and express the second as a percentage of the first. Holding the basket constant is the whole point, because it guarantees that any movement in the index is a price movement and not a change in what people bought. Statement 2 fails on the arithmetic of the third year. Inflation is always measured against the immediately preceding year, not against the base. From 100 to 110 the rise is 10 out of 100, which is 10 per cent, so the second year is right. From 110 to 121 the rise is 11 out of 110, which is again 10 per cent, not 21 per cent. The 21 in the statement is the cumulative rise over the base year, and mistaking cumulative change for the annual rate is precisely the error the examiner has planted. The series 100, 110, 121 is 10 per cent compounded twice.
- (b)2 only — Keeps the faulty arithmetic and throws away the correct definition. The third-year inflation is 11/110, which is 10 per cent, not 21 per cent.
- (c)Both 1 and 2 — Statement 1 is right but statement 2 is not, so the pair cannot both stand. Do the division 121 minus 110, over 110, before choosing this.
- (d)Neither 1 nor 2 — Rejects a definition that is correct. A constant basket is exactly what a price index uses — that is what distinguishes it from the GDP deflator, whose weights move with output.
A price index compares the weighted average price of a fixed basket of goods between a base year and the current year, with the base year set at 100. If a representative household buys 90 kg of rice and 5 pieces of cloth, you cost that same bundle in both years and take the ratio. Inflation is then not the level of the index but the rate at which it changes, computed year on year as the increase divided by the previous year's value.
This is one of the few CDS economics items that is decided by a division you can do in your head, so it rewards slowing down for ten seconds. The number 121 is chosen with care: it is 110 increased by 10 per cent, and it is also 21 per cent above 100, so the wrong reading is sitting right there in the figure. Watch for the same trap phrased with an index of 100, 120 and 144, or 100, 105 and 110.25. It is also worth pairing this item with the GDP deflator question a page earlier in the same paper, because the two are testing opposite halves of one contrast — the constant basket that statement 1 correctly attributes to a price index is the very feature that the deflator does not have.
- A price index costs a fixed basket in the base year and the current year and expresses the second as a percentage of the first.
- The base year of an index is conventionally set at 100.
- Inflation in any year is the rise in the index over the previous year, divided by the previous year's value.
- An index series of 100, 110, 121 is 10 per cent inflation in each of the two years, compounded.
- The CPI's weights are constant; the GDP deflator's weights change with the production level of each good.
Ten per cent compounded twice on 100 gives 121 — recognising that number for what it is settles the question.
- Measuring the third year's inflation against the base year instead of the previous year.
- Reading an index level as an inflation rate — an index of 121 is not 21 per cent inflation in that year.
- Rejecting statement 1 by confusing a price index with the GDP deflator, whose basket does change.
Asked as a two-statement code item that pairs a definition with a small arithmetic trap, so one statement is checked by recall and the other by division.
The current price index (base 1960) is nearly 330. This means that
- (a) all items cost 3.3 times more than what they did in 1960
- (b) the prices of certain selected items have gone up to 3.3 times
- (c) weighted mean of prices of certain items has increased 3.3 times
- (d) gold price has gone up 3.3 times
Answer(c) weighted mean of prices of certain items has increased 3.3 times
The same definition, tested by asking what an index number means rather than what an index is. That item turns on the words 'weighted mean' and 'certain items' — a basket, not every good in the economy — which is exactly the claim statement 1 makes here.
- practice — not a real PYQ
A price index moves 100, 120 and 144 over three consecutive years. The inflation rate in the third year is
- (a)20 per cent
- (b)24 per cent
- (c)44 per cent
- (d)144 per cent
Answer(a) 20 per cent — (144 − 120)/120 = 24/120 = 20 per cent; 44 per cent is the cumulative rise over the base year.
- practice — not a real PYQ
In constructing a consumer price index, the basket of commodities is held constant in order to
- (a)keep the computation simple
- (b)ensure that changes in the index reflect price changes alone
- (c)allow imports to be excluded
- (d)make the index comparable across countries
Answer(b) ensure that changes in the index reflect price changes alone — a fixed basket removes the effect of changing quantities.