QUAT6221 LU2
QUAT6221 LU2 – Index Numbers
Chapter 14 – Index Numbers: Measuring Business Activity
Single price index / price relative
= percentage change in price from a base period to another time period for a single item
p1
price relative= x 100 %
p0
Since the price relative for X in 2021 was 116.90, this means that the price of X increased by
16.90% between 2020 and 2021.
Composite price index
= percentage change in the average price of a basket of g/s from one year to the current
year. It is calculated using two methods – Laspeyres and Paasche.
Laspeyres approach – holds qtys constant at base period levels
- assume this approach if not specified
Laspeyres ( weighted aggregates ) price index=
∑ (p 1 x q 0) x 100 %
∑ ( p 0 x q 0)
For this basket of goods, the base period value is R4011.00 and the current period value is
R5001.00. This means that in 2020, R4011.00 was spent on the basket of three goods, while
in 2021, R5001.00 was spent on the same basket of three goods. Overall, the average price
of this basket has increased by 24.68% from 2020 to 2021, while holding quantities
consumed constant at 2020 (base period) levels.
Paasche approach – holds qtys constant at current period levels
Paasche ( weighted aggregates ) price index=
∑ (p 1 x q 1) x 100 %
∑ ( p 0 x q 1)
For this basket of goods that is based on the quantity of items consumed in 2021 (i.e., the
current period), the base period value is R4326.50 and the current period value is R5301.50.
This means that in 2020, R4326.50 was spent on the basket of three goods, while in 2021,
R5301.50 was spent on the same basket of three goods. Overall, the average price of this
basket has increased by 22.53% from 2020 to 2021, while holding quantities consumed
constant at 2021 (current period) levels.
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QUAT6221 LU2 – Index Numbers
Chapter 14 – Index Numbers: Measuring Business Activity
Single price index / price relative
= percentage change in price from a base period to another time period for a single item
p1
price relative= x 100 %
p0
Since the price relative for X in 2021 was 116.90, this means that the price of X increased by
16.90% between 2020 and 2021.
Composite price index
= percentage change in the average price of a basket of g/s from one year to the current
year. It is calculated using two methods – Laspeyres and Paasche.
Laspeyres approach – holds qtys constant at base period levels
- assume this approach if not specified
Laspeyres ( weighted aggregates ) price index=
∑ (p 1 x q 0) x 100 %
∑ ( p 0 x q 0)
For this basket of goods, the base period value is R4011.00 and the current period value is
R5001.00. This means that in 2020, R4011.00 was spent on the basket of three goods, while
in 2021, R5001.00 was spent on the same basket of three goods. Overall, the average price
of this basket has increased by 24.68% from 2020 to 2021, while holding quantities
consumed constant at 2020 (base period) levels.
Paasche approach – holds qtys constant at current period levels
Paasche ( weighted aggregates ) price index=
∑ (p 1 x q 1) x 100 %
∑ ( p 0 x q 1)
For this basket of goods that is based on the quantity of items consumed in 2021 (i.e., the
current period), the base period value is R4326.50 and the current period value is R5301.50.
This means that in 2020, R4326.50 was spent on the basket of three goods, while in 2021,
R5301.50 was spent on the same basket of three goods. Overall, the average price of this
basket has increased by 22.53% from 2020 to 2021, while holding quantities consumed
constant at 2021 (current period) levels.
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