Exam 24: Index Numbers

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

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.

An average of relatives 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.

Which of the following statements is correct? A The price relative is a weighted price index. B The Laspeyres price index is an unweighted price index. C The Paasche price index is a weighted price index. D The Fischer price index is an unweighted price index.

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 2000 Base 1988 100 101.5 104.2 103.9 106.2 107.8 107.9 108 108.5 109 110 111.5 112 Base 1988 Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Base 1988 112.4 113.1 114 115.4 117 119.2 121.6 123.8 124.9 125.6 129.3 132.8 138.9 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.

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 a simple aggregate index of the prices for the fruit and vegetable group using June 2008 as the base period.

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? A 50 \% increase in real income from 2002 to 2007 . B 33.33\% increase in real income from 2002 to 2007 . C 30.69\% increase in real income from 2002 to 2007 . D None of these choices are correct.

What is the value of Real GDP in 2008 if Nominal GDP was 1 131 586 ($million) and CPI was 161.4? A 701 million dollars B 7011 million dollars C 701107 million dollars D None of these choices are correct.

Which of the following is the value of annual real income for an annual salary of $85,000 when the CPI is 125? A \ 680 per annum B \ 106250 per annum C \ 68000 per annum D None of these choices are correct.

Construct the index of average weekly earnings of Australian male employees for the period 1990-1998, using the data in the following table. Use 1990 as the base year. Average weekly earnings of Australian male employees, 1990-98 $\begin{array}{|c|c|}\hline \text { Year } & \text { Average earnings (\$) } \\\hline 1990 & 542.30 \\\hline 1991 & 574.10 \\\hline 1992 & 590.35 \\\hline 1993 & 605.23 \\\hline 1994 & 621.95 \\\hline 1995 & 645.10 \\\hline 1996 & 664.28 \\\hline 1997 & 682.35 \\\hline 1998 & 708.30 \\\hline\end{array}$ Source: Australian Bureau of Statistics, Australian Economic Indicators, ABS Cat. No. 1350.0, ABS, Canberra.

Real income is nominal income multiplied by the CPI (times 100).

The following are the two CPI series (one for 1985-1989 with base 1980 = 100 and the other for 1989-1992 with base 1990 = 100) published in various issues of ABS publications. Create a new CPI series for the period 1985-1992 with 1990 as the base year. $\text { Consumer price index with different base periods, Australia }$ Y ear Base period (=) Base period (=) 1985 148.7 1986 162.6 1987 174.5 1988 187.3 95.0 1989 202.3 100.0 1990 105.3 1991 107.3 1992

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 statements is correct? A The Paasche price index is al ways equal to the Laspeyres price index during periods of inflation. B The Laspeyres price index tends to underestimates price increases during periods of inflation. C The Paasche price index tends to overestimates price increases during periods of inflation. D The Laspeyres price index tends to overestimate price increases during periods of inflation.

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

The gross domestic product is often used as a measure of the economic performance of a country. The annual GDP of Australia for the years 1990-98 is shown in the following table. Use the CPI in Table 23.2 in the textbook (pp 966-7) to deflate these figures to 1993 dollars. $\begin{array} { | c | c | } \hline \text { Year } & \text { GDP (millions of current \$) } \\\hline 1990 & 382936 \\\hline 1991 & 395493 \\\hline 1992 & 404914 \\\hline 1993 & 425841 \\\hline 1994 & 448289 \\\hline 1995 & 473463 \\\hline 1996 & 507527 \\\hline 1997 & 531045 \\\hline 1998 & 563284 \\\hline\end{array}$ Source: Australian Bureau of Statistics, Australian Economic Indicators, ABS Cat. No. 1350.0, ABS, Canberra.

Which of the following is the correct interpretation of a Laspeyres price index of 135, where the base year is 2007 and the current year is 2010? A According to the Laspeyres price index, prices have risen by 35 \% from 2007 to 2010 . B According to the Laspeyres price index, prices have risen by 135\% from 2007 to 2010 . C According to the Laspeyres price index, prices have risen by 35\% from 2010 to 2007 . D None of these choices are correct.

Which of the following statements is correct? A The Paasche price index uses current period quantities as weights. B The Laspeyres price index uses current period quantities as weights. C The Paasche price index uses base period quantities as weight. D The Laspeyres price index uses base period prices as weights.

The table below lists two index number series for median household income of a particular country. 2000 2010 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.

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 Paasche price index for 1998, using 1997 as the base.