Exam 18: Index Numbers

A simple price index is the ratio of the price of a commodity in the current period to its value in some base period, multiplied by 100.

Real GDP is real Nominal GDP divided by the CPI/100.

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.

Construct the index of average weekly earnings of Australian male employees for the period 2012-2016, using the data in the following table. Use 2012 as the base year. Average weekly earnings of Australian male employees, May 2012-May 2016 $\begin{array}{|c|c|}\hline {\text { Year }} & \text { Earnings (\$) } \\\hline 2012 & 1538.10 \\\hline 2013 & 1603.70 \\\hline 2014 & 1650.60 \\\hline 2015 & 1679.30 \\\hline 2016 & 1696.60 \\\hline\end{array}$ Source: Australian Bureau of Statistics, Australian Economic Indicators, ABS Cat. No. 6302.0, ABS, Canberra.

In 2002 your annual salary was $50 000 and in 2007 your annual salary is $75 000. The CPI in 2002 was 136 and the CPI in 2007 was 156.1. Which of the following is the percentage change in your real income from 2002 to 2007?

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?

The gross domestic product is often used as a measure of the economic performance of a country. The annual GDP and CPI (1990=100) for Australia for the years 2007-2015 is shown in the following table. Use the CPI data to deflate these figures to 2010 dollars. $\begin{array} { | l | c | c | } \hline \text { Year } & \text { GDP (millions of current \$) } & \text { CPI (1990=100) } \\\hline 2007 & 1128881 & 158.0 \\\hline 2008 & 1232583 & 164.8 \\\hline 2009 & 1251928 & 167.8 \\\hline 2010 & 1357034 & 172.6 \\\hline 2011 & 1445430 & 178.5 \\\hline 2012 & 1491046 & 181.4 \\\hline 2013 & 1524383 & 185.9 \\\hline 2014 & 1584578 & 190.4 \\\hline 2015 & 1609221 & 192.9 \\\hline\end{array}$ Source: Australian Bureau of Statistics, Australian Economic Indicators, ABS Cat. No. 1350.0, ABS, Canberra.

Which of the following best describes the Australian consumer price index (CPI)?

The table below lists two index number series for median household income of a particular country. Year Base Base 98 100 101 103 104 105 107 113 90 95 96 98 100 110 116 117 (a) Complete the 2000 index and the 2010 index by filling in the missing values. (b) Interpret the 2016 value using each index. (c) Which of your interpretations in part (b) do you prefer? Explain.

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?

In September 2015, 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. $\begin{array} { l c c c c } & { \text { September 2015 } } & { \text { September 2016 } } \\\hline & \text { Price (\$) } & \text { Quantity } ( \mathrm { kg } ) & \text { Price } ( \$ ) & \text { Quantity } ( \mathbf { k g } ) \\\text { Item } & \boldsymbol { p } _ { i , 2015 } & q _ { i } , 2015 & \boldsymbol { p } _ { i } , 2016 & q _ { i } , 2016 \\\hline \text { Beef } & 5.50 & 2 & 5.92 & 1 \\\text { Veal } & 7.48 & 2 & 8.06 & 1 \\\text { Pork } & 4.80 & 0 & 5.05 & 1 \\\text { Chicken } & 3.62 & 0 & 3.45 & 4 \\\text { Fish } & 5.13 & 6 & 6.25 & 1 \\\hline\end{array}$ Calculate the Laspeyres price index for 2016, using 2015 as the base.

The Fisher price index is the median of the Laspeyres price index and the Paasche price index.

What is the value of Real GDP in 2008 if Nominal GDP was 1 131 586 ($million) and CPI was 161.4?

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 2012 and 2014. Fruit and vegetable prices (\ /) Item June 2012 June 2014 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 a simple aggregate index of the prices for the fruit and vegetable group using June 2012 as the base period.

The All Ordinaries Index measures the average daily closing share prices of the 500 largest companies listed on the Australian Securities Exchange.

Which of the following is the value of annual real income for an annual salary of $85,000 when the CPI is 125?

In September 2015, 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. $\begin{array} { l c c c c } & { \text { September 2015 } } & { \text { September 2016 } } \\\hline & \text { Price (\$) } & \text { Quantity } ( \mathrm { kg } ) & \text { Price } ( \$ ) & \text { Quantity } ( \mathbf { k g } ) \\\text { Item } & \boldsymbol { p } _ { i , 2015 } & q _ { i } , 2015 & \boldsymbol { p } _ { i } , 2016 & q _ { i } , 2016 \\\hline \text { Beef } & 5.50 & 2 & 5.92 & 1 \\\text { Veal } & 7.48 & 2 & 8.06 & 1 \\\text { Pork } & 4.80 & 0 & 5.05 & 1 \\\text { Chicken } & 3.62 & 0 & 3.45 & 4 \\\text { Fish } & 5.13 & 6 & 6.25 & 1 \\\hline\end{array}$ Calculate the Paasche price index for 2016, using 2015 as the base.

Which of the following statements is correct?

Which of the following statements is correct?