Question

The following table reports prices and usage quantities for two items in 1989 and 2001

	Quantity		Unit Price
Item	1989	2001	1989	2001
A	1500	1800	7.5	7.75
B	2	1	630	1500

1. Compute price relatives for each item in 2001using 1989 as the base period
2. Compute an unweighted aggregate price index for the two items in 2001using 1989 as the base period
3. Compute a weighted aggregate price index for the two items using the Laspeyre’s method.
4. Compute a weighted aggregate price index for the two items using the paasche method.

Answer 1

We have the following information

Item	Quantity		Unit Price
	1989	2001	1989	2001
A	1,500.00	1,800.00	7.50	7.75
B	2.00	1.00	630.00	1,500.00

Part 1) Price Relatives are calculated by using the following formula

Price Relative = (P₁/P₀) × 100; where P₁ is current year price (year 2001) and P₀ is base year price (year 1989).

Item	Unit Price		Price Relatives
	1989	2001
A	7.50	7.75	103.33
B	630.00	1,500.00	238.10

Part 2) Unweighted aggregate price index is calculated by using the following formula

Unweighted aggregate price index = (ƩP₁/ƩP₀) × 100

Item	Unit Price
	1989	2001
A	7.50	7.75
B	630.00	1,500.00
Total	ƩP0 = 637.50	ƩP1 = 1,507.75

Unweighted aggregate price index = (ƩP₁/ƩP₀) × 100

Unweighted aggregate price index = (1,507.75/637.50) × 100

Unweighted aggregate price index = 236.51

Part 3) Laspeyre’s weighted aggregate price index is calculated by using the following formula

Laspeyre’s weighted aggregate price index = (ƩQ₁P₀/ƩQ₀P₀) × 100; Where Q₀ is base year quantity (year 1989) and Q₁ is current year quantity (year 2001).

Item	Quantity		Unit Price		Q1P0	Q0P0
	1989	2001	1989	2001
A	1,500.00	1,800.00	7.50	7.75	13,500.00	11,250.00
B	2.00	1.00	630.00	1,500.00	630.00	1,260.00
					ƩQ1P0 = 14,130.00	ƩQ0P0 = 12,510.00

Laspeyre’s weighted aggregate price index = (ƩQ₁P₀/ƩQ₀P₀) × 100

Laspeyre’s weighted aggregate price index = (14,130.00/12,510.00) × 100

Laspeyre’s weighted aggregate price index = 112.95

Part 4) Paashce’s weighted aggregate price index is calculated by using the following formula

Paashce’s weighted aggregate price index = (ƩQ₁P₁/ƩQ₀P₁) × 100

Item	Quantity		Unit Price		Q1P1	Q0P1
	1989	2001	1989	2001
A	1,500.00	1,800.00	7.50	7.75	13,950.00	11,625.00
B	2.00	1.00	630.00	1,500.00	1,500.00	3,000.00
					ƩQ1P1 = 15,450.00	ƩQ0P1 = 14,625.00

Paashce’s weighted aggregate price index = (ƩQ₁P₁/ƩQ₀P₁) × 100

Paashce’s weighted aggregate price index = (15,450.00/14,625.00) × 100

Paashce’s weighted aggregate price index = 105.64