The table below lists two index number series for median household income of a particular country. \[\begin{array} { | c | c | c | } \hline & \mathbf { 2 0 0 0 } & \mathbf { 2 0 1 0 } \\ \hline \text { Year } & \text { Base } & \text { Base } \\ \hline \mathbf { 1 9 9 9 } & 98 & \\ \hline \mathbf { 2 0 0 0 } & 100 & \\ \hline \mathbf { 2 0 0 1 } & 101 & \\ \hline \mathbf { 2 0 0 2 } & 103 & \\ \hline \mathbf { 2 0 0 3 } & 104 & \\ \hline \mathbf { 2 0 0 4 } & 105 & \\ \hline \mathbf { 2 0 0 5 } & 107 & \\ \hline \mathbf { 2 0 0 6 } & 113 & 90 \\ \hline \mathbf { 2 0 0 7 } & & 95 \\ \hline \mathbf { 2 0 0 8 } & & 96 \\ \hline \mathbf { 2 0 0 9 } & & 98 \\ \hline \mathbf { 2 0 1 0 } & & 100 \\ \hline \mathbf { 2 0 1 1 } & & 110 \\ \hline \mathbf { 2 0 1 2 } & & 116 \\ \hline \mathbf { 2 0 1 3 } & & 117 \\ \hline \end{array}\] (a) Complete the 2000 index and the 2010 index by filling in the missing values. (b) Interpret the 2013 value using each index. (c) Which of your interpretations in part (b) do you prefer? Explain.

(a) Use the multiplier 90/113 to fill in

The table below is the Laspeyres price index for a basket of goods related to the Computer IT industry. $\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \text { Year } & 1988 & 1989 & 1990 & 1991 & 1992 & 1993 & 1994 & 1995 & 1996 & 1997 & 1998 & 1999 \\ \hline \text { Base } & & & & & & & & & & & & \\ 1988 & 100 & 101.5 & 104.2 & 103.9 & 106.2 & 107.8 & 107.9 & 108 & 108.5 & 109 & 110 & 111.5 \\ \hline \begin{array}{c} \text { Base } \\ 2005 \end{array} & & & & & & & & & & & & \\ \hline \end{array}$ $\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \text { Year } & 2001 & 2002 & 2003 & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 & 2011 & 2012 \\ \hline \begin{array}{c} \text { Base } \\ 1988 \end{array} & 112.4 & 113.1 & 114 & 115.4 & 117 & 119.2 & 121.6 & 123.8 & 124.9 & 125.6 & 129.3 & 132.8 \\ \hline \begin{array}{c} \text { Base } \\ 2005 \end{array} & & & & & & & & & & & & \\ \hline \end{array}$ (a) Calculate and interpret the percentage price change from 2005 to 2013, using the 1988 base index. (b) Change the base of this index series to 2005. Explain why a base change may be useful. (c) Using the series with base 2005 that you created in part (b) recalculate the percentage price change from 2005 to 2013. Interpret. (d) Compare your answers from parts (a) and (c), in particular explain which value is a change in percentage points and which value is the percentage change.

(a) Percentage change = [(New - Old)/Old

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. \[\begin{array} { | l | c | c | } \hline { \text { Fruit and vegetable prices (\$/k) } } \\ \hline \text { Item } & \text { June 2008 } & \text { June 2010 } \\ \hline \text { Oranges } & 2.98 & 2.95 \\ \hline \text { Bananas } & 2.32 & 2.37 \\ \hline \text { Potatoes } & 2.69 & 2.44 \\ \hline \text { Tomatoes } & 3.72 & 4.59 \\ \hline \text { Carrots } & 2.20 & 1.95 \\ \hline \text { Onions } & 2.57 & 2.35 \\ \hline \end{array}\] Construct a simple aggregate index of the prices for the fruit and vegetable group using June 2008 as the base period.

I 2010,2008 = (2.95 + 2.37 + 2.44 + 4.59 + 1.95 +

Exam 24: Index Numbers

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 2013 value using each index. (c) Which of your interpretations in part (b) do you prefer? Explain.

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Question 21

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

(True/False)

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Question 22

The table below is the Laspeyres price index for a basket of goods related to the Computer IT industry. Year 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 Base 1988 100 101.5 104.2 103.9 106.2 107.8 107.9 108 108.5 109 110 111.5 Base 2005 Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Base 1988 112.4 113.1 114 115.4 117 119.2 121.6 123.8 124.9 125.6 129.3 132.8 Base 2005 (a) Calculate and interpret the percentage price change from 2005 to 2013, using the 1988 base index. (b) Change the base of this index series to 2005. Explain why a base change may be useful. (c) Using the series with base 2005 that you created in part (b) recalculate the percentage price change from 2005 to 2013. Interpret. (d) Compare your answers from parts (a) and (c), in particular explain which value is a change in percentage points and which value is the percentage change.

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Question 23

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 ( \/ k) 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 a simple aggregate index of the prices for the fruit and vegetable group using June 2008 as the base period.

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Question 24

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. $\begin{array}{lllll}&{\text { September } 1997} & &{\text { September } 1998} \\\hline &\text { Price }(\$) & \text { Quantity (kg) } & \text { Price (\$) } & \text { Quantity (kg) }\\\text { Item } & p_{i, 1997} & q_{i, 1997} & p_{i, 1998} & q_{i, 1998}\\\hline \text { Beef } & 5.50 & 2 & 5.92 & 1 \\\text { Veal } & 7.48 & 2 & 8.06 & 1 \\\text { Pork } & 4.80 & 0 & 5.05 & 1 \\\text { Chicken } & 3.62 & 0 & 3.45 & 4 \\\text { Fish } & 5.13 & 6 & 6.25 & 1\end{array}$ Calculate the Paasche price index for 1998, using 1997 as the base.

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Question 25

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

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