Name: Understanding the Consumer Price Index (CPI)
Uploaded: 2019-07-19
Duration: 5 min 26 s
Description: Learn about index numbers, their significance in economics, and how they help us compare data over time in this engaging and informative video.

Question

Commodity	Base Year price P₀	Base year Quantity Q₀	Current year price P₁	Current year Quantity Q₁
A	$4$	$5$	$2$	$10$
B	$6$	$10$	$5$	$12$
C	$5$	$15$	$4$	$20$
D	$3$	$10$	$2$	$15$

Calculate the price index using Laspeyre's, and Paasche's formula.

Interchange the current period values with the base period values. Calculate the price index using Laspeyre's, and Paasche's formula. What difference do you observe from the earlier illustration?

Accepted Answer

Commodity Base Year price P₀ Base year Quantity Q₀ Current year price P₁ Current year Quantity Q₁

A $4$ $5$ $2$ $10$

B $6$ $10$ $5$ $12$

C $5$ $15$ $4$ $20$

D $3$ $10$ $2$ $15$

Price index using Laspeyre's formula,

$P_{01} = \frac{2 \times 5 + 5 \times 10 + 4 \times 15 + 2 \times 10}{4 \times 5 + 6 \times 10 + 5 \times 15 + 3 \times 10} \times 100 = 75.67$

Price index using Paasche's formula,

$P_{01} = \frac{2 \times 10 + 5 \times 12 + 4 \times 20 + 2 \times 15}{4 \times 10 + 6 \times 12 + 5 \times 20 + 3 \times 15} \times 100 = 73.93$

Now, current period values and base period values are interchanged.

Commodity Base year price Po Base year quantity Q0 Current year price P1 Current year quantity Q1

A $2$ $10$ $4$ $5$

B $5$ $12$ $6$ $10$

C $4$ $20$ $5$ $15$

D $2$ $15$ $3$ $10$

Price index using Laspeyre's formula, $P_{01} = \frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times 100$

$P_{01} = \frac{4 \times 10 + 6 \times 12 + 5 \times 20 + 3 \times 15}{2 \times 10 + 5 \times 12 + 4 \times 20 + 2 \times 15} \times 100 = 135.3$

Price index using Paasche's formula, $P_{01} = \frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}} \times 100$

$P_{01} = \frac{4 \times 5 + 6 \times 10 + 5 \times 15 + 3 \times 10}{2 \times 5 + 5 \times 10 + 4 \times 15 + 2 \times 10} \times 100 = 132.1$

A big difference is seen in both values as previous values are above $100 %$ and current values are below $100 %$ .

Important Questions on Index Numbers

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