Question 3.4: Weighted Index for Gasoline Cost Based on the following data...
Weighted Index for Gasoline Cost
Based on the following data, develop a weighted index for the price of a gallon of gasoline in 2014, when 1996 is the reference year having an index value of 99.2. The weight placed on regular unleaded gasoline is three times that of either premium or unleaded plus, because roughly three times as much regular unleaded is sold compared with premium or unleaded plus.
| Price (Cents/Gal) in Year | |||
| 1996 | 2010 | 2014 | |
| Premium | 114 | 240 | 315 |
| Unleaded plus | 103 | 230 | 305 |
| Regular unleaded | 93 | 221 | 285 |
In this example, k is 1996 and n is 2014. From Equation (3-2), the value of \bar{I_{2014}} is
\bar{I}_n= \frac{W_1 (C_{n1}/C{k}1)+ W_2(C_{n2}/C_{k2}) +···+W_M(C_{nM}/C_{kM})}{W_1+W_2 +···+W_M }\times \bar{I}_k (3-2)
\frac{(1)(315/114) + (1)(305/103) + (3)(285/93)}{1+1+3}\times 99.2 = 296Now, if the index in 2016, for example, is estimated to be 327, it is a simple matter to determine the corresponding 2016 prices of gasoline from \bar{I}_{2014} = 296:
Premium: 315 cents/gal \left(\frac{327}{296} \right) = 348 cents/gal,
Unleaded plus: 305 cents/gal \left(\frac{327}{296} \right) =337 cents/gal ,
Regular unleaded: 285 cents/gal \left(\frac{327}{296} \right) = 315 cents/gal.