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 quantity index for 2005 with 2002 as base.

Answer 1

To calculate the Fischer quantity index for 2005 with 2002 as base year, we will use the formula:

Fischer quantity index = (Σ(p0q1) / Σ(p0q0)) / (Σ(p1q1) / Σ(p1q0))

First, we need to calculate Σ(p0q0), Σ(p0q1), Σ(p1q0), and Σ(p1q1) for both years:

For 2002:
Σ(p0q0) = 60*50 + 50*20 + 30*30 = 3000 + 1000 + 900 = 4900
Σ(p0q1) = 60*40 + 50*40 + 30*40 = 2400 + 2000 + 1200 = 5600

For 2005:
Σ(p1q0) = 70*50 + 40*20 + 30*30 = 3500 + 800 + 900 = 5200
Σ(p1q1) = 70*40 + 40*40 + 30*40 = 2800 + 1600 + 1200 = 5600

Now we can plug these values into the formula to find the Fischer quantity index for 2005 with 2002 as base year:

Fischer quantity index = (Σ(p0q1) / Σ(p0q0)) / (Σ(p1q1) / Σ(p1q0))
= (5600 / 4900) / (5600 / 5200)
= (1.142857) / (1.076923)
= 1.060606

Therefore, the Fischer quantity index for 2005 with 2002 as base year is approximately 1.0606.