Consider the following two piece index series:

Question

2008=100 2012=100 2010=100
2007 94 A
2008 100 B
2009 115 C
2010 110 80 D
2011 90 E
2012 100 F
2013 115 G


Splice the two price index series to form one continuous series with 2010 as the base year.
Find the value of F.

Answer 1

To splice the two price index series into one continuous series, we need to express all indices in terms of 2010 = 100.

1. Convert the 2008 = 100 series to 2010 = 100:

   • 2007: 94 (2008=100 is the base year)
     • Conversion: \( \text{Index}_{2007} = \frac{94}{100} \times 110 = 103.33 \)
   • 2008: 100 (This is the base year)
     • Conversion: \( \text{Index}_{2008} = 100 \) for 2010=100 base.
   • 2009: 115
     • Conversion: \( \text{Index}_{2009} = \frac{115}{100} \times 110 = 126.5 \)
   • 2010: 110
     • Conversion: \( \text{Index}_{2010} = 100 \) for 2010=100 base.
   • 2011: Not provided.
   • 2012: Not provided.
   • 2013: 115
     • Conversion: \( \text{Index}_{2013} = \frac{115}{100} \times 110 = 126.5 \)

2. Convert the 2012 = 100 series to 2010 = 100:

   • 2010: 80
     • Conversion: \( \text{Index}_{2010} = 100 \) for 2010=100 base.
   • 2011: 90
     • Conversion: \( \text{Index}_{2011} = \frac{90}{100} \times 80 = 72 \)
   • 2012: 100
     • Conversion: \( \text{Index}_{2012} = 100 \) for 2010=100 base.
   • 2013: 115
     • Conversion: \( \text{Index}_{2013} = \frac{115}{100} \times 80 = 92 \)

Now we need to find \( F \) (the index for 2012 in the second series). We already noted that for 2012 in the second series, the index is 100 when taken as base in that series.

3. Spliced Series Output:
   • 2007: 103.33
   • 2008: 100
   • 2009: 126.5
   • 2010: 100
   • 2011: 72
   • 2012: 100
   • 2013: 92

Thus, the value of \( F \) in the 2010 base for 2012 is still 100.