A random sample of 100 households was selected to participate in a study to establish a composite price index for household utilities usage (i.e. electricity, sewage, water, telephone). The following average annual figures have been obtained:
|
householdutility
|
Price (R/unit)
|
Consumption (no. of units)
|
|
2008
|
2009
|
2010
|
2008
|
2009
|
2010
|
|
Electricity
|
1.97
|
2.05
|
2.09
|
745
|
812
|
977
|
|
Sewage
|
0.62
|
0.68
|
0.72
|
68
|
56
|
64
|
|
Water
|
0.29
|
0.31
|
0.35
|
296
|
318
|
378
|
|
Telephone
|
1.24
|
1.18
|
1.06
|
1 028
|
1 226
|
1 284
|
(a) Find the price relative for each household utility for 2010. Use 2008 as the base period. Interpret the meaning of each price relative value. Which utility showed the smallest change in price from 2008 to 2010? Justify.
(b) Calculate the composite price indexes for 2009 and 2010, with 2008 as the base period. Use each of the following methods:
(i) the Laspeyres weighted aggregates method
(ii) the Laspeyres weighted average of price relatives method.
(c) Interpret the values of these composite price indexes for 2009 and 2010.