15A trucking firm handles 4 commodities for a particular dis

   15.A trucking firm handles 4 commodities for a particular distributor.Total shipments for the commodities in 1996 and 2011 as well as the 1996 prices are reported in the following table

commodity              1996          2011       price/shipment 1996

A                              120             95              $1200

B                              86               75              $1800

C                              35              50               $2000

D                              60              70               $1500

Develop a weighted aggregate quantity index with a 1196 base. Comment on the growth or decline in quantities over the 1996-2011 period

Solution

In this case we will use price in year 1996 as weights.

Weighteed aggregate quantity indices = sumof(weights* quantity of corresponding commodity in year 2011) / sumof (weights* quantity of corresponding commodity in year 1996) * 100

= (95*1200 + 75*1800 + 2000*50 + 1500* 70)/ (1200* 120 + 1800* 86 + 2000*35 + 1500*60) *100

= 454000 / 458800 * 100 = 98.9538
As index is less than 100 we conclude that there is a decline in quantities exported over the period 1996 - 2011