Exam 24: Index Numbers

If the Laspeyres price index for a basket of goods is 128 and the Paasche price index for the same basket of goods for the same time period is 119, which of the following is the value of the Fischer price index, the geometric mean of these two indices? A 123.5 B 9 C 123.42 D None of these choices are correct.

A simple aggregate price index is the ratio of the sum of the prices of the n commodities in the current period to the sum in some base period, multiplied by 100.

The Fisher price index is the geometric mean of the Laspeyres price index and the Paasche price index.

The Australian Bureau of Statistics regularly publishes the average retail prices of selected items for each Australian capital city. The following table presents the prices of oranges, bananas, potatoes, tomatoes, carrots and onions in Melbourne during the June quarter in 2008 and 2010. Fruit and vegetable prices (\ /) Item June 2008 June 2010 Oranges 2.98 2.95 Bananas 2.32 2.37 Potatoes 2.69 2.44 Tomatoes 3.72 4.59 Carrots 2.20 1.95 Onions 2.57 2.35 Construct the average of relative price indexes for the fruit and vegetable group for June 2010 (with base June 2008 = 100).

Which of the following best describes the Australian consumer price index (CPI)? A The CPI is an economic indicator. B The CPI measures changes in the total price of a basket of goods and services. C In Australia, the Australian Bureau of statistics complies quarterly CPI for the eight capital cities as well as a weighted average. D All of these choices are correct.

Which of the following is the correct interpretation of a Paasche price index of 75, where the base year is 2009 and the current year is 2011? A According to the Paasche price index, prices have decreased by 75 \% from 2009 to 2011 . B According to the Paasche price index, prices have decreased by 25\% from 2011 to 2009 . C According to the Paasche price index, prices have decreased by 25\% from 2009 to 2011 D . None of these choices are correct.

In September 1997, a Brisbane family's weekly diet consisted of 6 kg of fish, 2 kg of beef and 2 kg of veal. One year later, because of the cost increases in these products, the family's diet has changed so that each week they consume 4 kg of chicken and 1 kg each of beef, veal, pork and fish. The prices are listed in the table below. $\quad\quad\quad\quad\text { September } 1997$$\quad\quad\quad\quad\quad\quad\text { September } 1998$ $\begin{array}{ccccc} \hline& \text { Price (\$) } & \text { Quantity (kg) } & \text { Price (\$) } & \text { Quantity (kg) } \\\text { Item } & p_{i 1997} & q_{i, 1997} & p_{i} 1998 & q_{i} 1998\\\hline\text { Beef } & 5.50 & 2 & 5.92 & 1 \\\text { Veal } & 7.48 & 2 & 8.06 & 1 \\\text { Pork } & 4.80 & 0 & 5.05 & 1\\\text { Chicken } & 3.62 & 0 & 3.45 & 4 \\\text { Fish } & 5.13 & 6 & 6.25 & 1\\\hline\end{array}$ Calculate the Laspeyres price index for 1998, using 1997 as the base.