Question

By using the data in the table below, calculate for 2005 with 2002 as base year:


2002 2005
Product p0 q0 p1 q1 p1q0 p0q0 p1q1 p0q1
I 60 50 70 40
II 50 20 40 40
III 30 30 30 40
Total A B C D E F


Find Fischer price index for 2005 with 2002 as base.

88.32


98.91


103.02


100


96.50

Answer 1

To calculate the Fischer Price Index for 2005 with 2002 as the base year, we first need to calculate the total values for each category in 2002 and 2005:

2002 Total (A) = (p0*q0) + (p1*q0) + (p1*q0)
2002 Total (B) = (p0*q1) + (p1*q1) + (p1*q1)

Now, let's calculate the totals for 2002:
I:
2002 Total (A) = (60*50) + (70*50) + (70*50) = 3000 + 3500 + 3500 = 10000
2002 Total (B) = (60*40) + (70*40) + (70*40) = 2400 + 2800 + 2800 = 8000

II:
2002 Total (A) = (50*20) + (40*20) + (40*20) = 1000 + 800 + 800 = 2600
2002 Total (B) = (50*40) + (40*40) + (40*40) = 2000 + 1600 + 1600 = 5200

III:
2002 Total (A) = (30*30) + (30*30) + (30*30) = 900 + 900 + 900 = 2700
2002 Total (B) = (30*40) + (30*40) + (30*40) = 1200 + 1200 + 1200 = 3600

Total 2002:
A = 10000 + 2600 + 2700 = 15300
B = 8000 + 5200 + 3600 = 16800

Now let's calculate the same totals for 2005:
I:
2005 Total (C) = (70*40) + (40*40) + (40*40) = 2800 + 1600 + 1600 = 6000
2005 Total (D) = (70*50) + (40*50) + (40*50) = 3500 + 2000 + 2000 = 7500

II:
2005 Total (C) = (40*40) + (40*40) + (40*40) = 1600 + 1600 + 1600 = 4800
2005 Total (D) = (40*20) + (40*20) + (40*20) = 800 + 800 + 800 = 2400

III:
2005 Total (C) = (30*40) + (30*40) + (30*40) = 1200 + 1200 + 1200 = 3600
2005 Total (D) = (30*30) + (30*30) + (30*30) = 900 + 900 + 900 = 2700

Total 2005:
C = 6000 + 4800 + 3600 = 14400
D = 7500 + 2400 + 2700 = 12600

Now, we can calculate the Fischer Price Index:
FPI = (Total 2005 / Total 2002) * 100
FPI = (14400 / 15300) * 100
FPI = 94.11

Therefore, the Fischer Price Index for 2005 with 2002 as the base year is 94.11.