Below is information on food items for the years 2000 and 2004
Below is information on food items for the years 2000 and 2004.
2000 2004
Item Price Quantity Price Quantity
Magarine (pound) 0.81 18 $0.89 27
Shortening (pound) 0.84 5 0.94 9
Milk (1/2 Gallon) 1.44 70 1.43 65
Potato Chips 2.91 27 3.07 33
A. Compute a simple price index for each of the four items. Use 2000 as the base period.
B. Compute a simple aggregate price index. Use 2000 as the base period.
C. Compute Laspeyres’ price index for 2004 using 2000 as the base period.
D. Compute Paasche’s index for 2004 using 2000 as the base period.
E. Determine Fisher’s ideal index using the values for the Laspeyres and Paasche indexes computed in the two previous problems.
F. Determine a value index for 2004 using 2000 as the base period.
Let P0 and Q0 denote the price and quantity of commodities in the base year (2000) and P1 and Q1 denote the price and quantity of commodities in the current year(2004)
A) The Simple price Index is given by the formula
Simple price Index = (P1/P0)*100
Simple price index for Margarine = (0.89/0.81)*100=109.88
Simple price index for Shortening = (0.94/0.84)*100=111.90
Simple price index for Milk = (1.43/1.44)*100 = 99.31
Simple price index for Potato chips = (3.07/2.91)*100=105.50
B) The Simple aggregate price Index is given by the formula
Simple aggregate price Index = [(∑P1)/(∑P0)]*100
= [(0.89+0.94+1.43+3.07)/(0.81+0.84+1.44+2.91)]*100
= (6.33/6)*100
= 105.50
C) The Laspeyres’ price index is given by the formula
Laspeyres’ price index = [(∑P1Q0)/(∑P0Q0)]*100
= [(0.89*18+0.94*5+1.43*70+3.07*27)/(0.81*18+0.84*5+1.44*70+2.91*27)]*100
= (203.71/198.15)*100
= 102.81
D) The Paasche’s index is given by the formula
Paasche’s index = [(∑P1Q1)/(∑P0Q1)]*100
= [(0.89*27+0.94*9+1.43*65+3.07*33)/(0.81*27+0.84*9+1.44*65+2.91*33)]*100
= (226.75/219.06)*100
= 103.51
E) The Fisher’s ideal index is the geometric mean of Laspeyre’s and Paasche’s Index.
Fisher’s ideal index = [(Laspeyres’ price index)* (Paasche’s index)](1/2)
= Sqrt(102.81*103.51)
= 103.16
F) The value Index is given by
Value Index = [(∑(P1/P0)/4]*100
= {[(0.89/0.81) + (0.94/0.84)) + (1.43/1.44) + (3.07/2.91)]/3}*100
= (4.2659/4)*100
= 106.65
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