ACCA MA · Guided practice (Show me how)
Chapter 20: Index Numbers
Index numbers - one item, then a whole basket
An index number shows the rate of change of a variable from one specified time to another. The base year is always 100.
Part (a). The price of coffee was $2.40 in 2006, $2.50 in 2007 and $2.60 in 2008. Sales of tea were 8,200 packets in 2008, 9,000 packets in 2009 and 9,400 packets in 2010.
Parts (b) and (c). Below are the quantities and unit prices for a typical shopping basket in each of 2008, 2009 and 2010.
| 2008 quantity | 2008 price p.u. | 2009 quantity | 2009 price p.u. | 2010 quantity | 2010 price p.u. | |
|---|---|---|---|---|---|---|
| Coffee | 20 | $4.00 | 15 | $4.50 | 15 | $4.80 |
| Sugar | 15 | $0.60 | 18 | $0.70 | 20 | $1.00 |
| Bread | 30 | $0.80 | 35 | $1.00 | 40 | $1.10 |
Calculate price index numbers for 2009 and 2010, with 2008 as the base year, using (b) the Laspeyre method and (c) the Paasche method. Work to one decimal place.
The Laspeyre price index uses BASE period quantities; the Paasche price index uses CURRENT period quantities.
(a) Simple index numbers
Calculate the coffee price index for 2007 and 2008 with 2006 as the base year, and the tea quantity index for 2009 and 2010 with 2008 as the base year.
(b) Laspeyre price index
Calculate the Laspeyre price index for 2009 and for 2010, with 2008 as the base year.
(c) Paasche price index
Calculate the Paasche price index for 2009 and for 2010, with 2008 as the base year.
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