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 7.50 7.75
B 2 1 630 1500
Show your work step by stepin answering the questions below:
i. Compute price relatives for each item in 2001 using 1989 as the base period.
ii. Compute an unweighted aggregate price index for the two items in 2001 using 1989
as the base period
iii. Compute a weighted aggregate price index for the two items using the Laspeyre’s
method.
iv. Compute a weighted aggregate price index for the two items using the Paasche
method.
i. Compute price relatives for each item in 2001 using 1989 as the base period:
Price Relative for Item A in 2001 = (Price in 2001 / Price in 1989) * 100
Price Relative for Item A in 2001 = (7.75 / 7.50) * 100
Price Relative for Item A in 2001 = 103.33
Price Relative for Item B in 2001 = (Price in 2001 / Price in 1989) * 100
Price Relative for Item B in 2001 = (1500 / 630) * 100
Price Relative for Item B in 2001 = 238.09
ii. Compute an unweighted aggregate price index for the two items in 2001 using 1989 as the base period:
Unweighted Aggregate Price Index = ((Price Relative for Item A + Price Relative for Item B) / 2)
Unweighted Aggregate Price Index = ((103.33 + 238.09) / 2)
Unweighted Aggregate Price Index = 170.71
iii. Compute a weighted aggregate price index for the two items using the Laspeyres method:
Laspeyres Price Index = ((Price in 2001 * Quantity in 1989) / (Price in 1989 * Quantity in 1989)) * 100
Laspeyres Price Index for Item A = ((7.75 * 1500) / (7.50 * 1500)) * 100
Laspeyres Price Index for Item A = 103.33
Laspeyres Price Index for Item B = ((1500 * 2) / (630 * 2)) * 100
Laspeyres Price Index for Item B = 238.10
Weighted Aggregate Price Index using Laspeyres method = (Laspeyres Price Index for Item A + Laspeyres Price Index for Item B) / 2
Weighted Aggregate Price Index using Laspeyres method = (103.33 + 238.10) / 2
Weighted Aggregate Price Index using Laspeyres method = 170.71
iv. Compute a weighted aggregate price index for the two items using the Paasche method:
Paasche Price Index = ((Price in 2001 * Quantity in 2001) / (Price in 1989 * Quantity in 2001)) * 100
Paasche Price Index for Item A = ((7.75 * 1800) / (7.50 * 1800)) * 100
Paasche Price Index for Item A = 103.33
Paasche Price Index for Item B = ((1500 * 1) / (630 * 1)) * 100
Paasche Price Index for Item B = 238.10
Weighted Aggregate Price Index using Paasche method = (Paasche Price Index for Item A + Paasche Price Index for Item B) / 2
Weighted Aggregate Price Index using Paasche method = (103.33 + 238.10) / 2
Weighted Aggregate Price Index using Paasche method = 170.71