Exam 24: Index Numbers

Correct Answer:

Verified

As the fruit and vegetable group is made up of six items, n = 6. Therefore
I_{2010, 2008} = [(2.95/2.98) + (2.37/2.32) + (2.44/2.69) + (4.59/3.72) + (1.95/2.20) + (2.35/2.57)] * 100 / 6 = 99.22%.
This index number indicates that fruit and vegetable prices in Melbourne have decreased by 0.78% in June 2010 compared to the June 2008 price level.

Correct Answer:

Verified

To construct the new series for the years 1985-1992 with 1990 = 100, we first determine an overlapping year of the two series. Here we can use 1989 for this purpose.
From the two CPI series, for the overlapping year 1989,
CPI₁₉₈₉
=
202.3 (base year 1980 = 100)
=
95.0 (base year 1990 = 100).
Therefore, for the year 1988:
CPI₁₉₈₈
=
187.3 (base year 1980 = 100)
=
187.3 *(95/202.3) (base year 1990 =100)
=
87.96 (base year 1990 = 100).
Similarly:
CPI₁₉₈₇
=
174.5 (base year 1980 = 100)
=
174.5* (95/202.3) (base year 1990 = 100)
=
81.95 (base year 1990 = 100).
That is, to convert the entries with base year 1980 = 100 for the years 1985 to 1988 into entries with base year 1990 = 100, we multiply each entry by the ratio 95.0/202.3 = .4696. The resulting series is shown in the last column of the following table: $$\begin{array}{l}\text { Consumer Price Index, 1985-92 }\\\begin{array} { | c | c | c | c | } \hline \text { Year } & \begin{array} { c } \text { Base year } \\( 1980 = 100 )\end{array} & \begin{array} { c } \text { Base year } \\( \mathbf { 1 9 9 0 } = \mathbf { 1 0 0 } )\end{array} & \begin{array} { c } \text { New series base year } \\( 1990 = 100 )\end{array} \\\hline 1985 & 148.7 & & 69.8 \\\hline 1986 & 162.6 & & 76.4 \\\hline 1987 & 174.5 & & 81.9 \\\hline 1988 & 187.3 & & 88.0 \\\hline 1989 & 202.3 & 95.0 & 95.0 \\\hline 1990 & & 100.0 & 100.0 \\\hline 1991 & & 105.3 & 105.3 \\\hline 1992 & & 107.3 & 107.3 \\\hline\end{array}\end{array}$$