Deck 24: Index Numbers

Question 1

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

Answer 1

True

Question 2

Which of the following statements is correct?

A)The Paasche price index is always 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.

Answer 2

D

Question 3

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.

Answer 3

C

Question 4

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)$106 250 per annum
C)$68 000 per annum
D)None of these choices are correct.

Question 5

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.

Question 6

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

Question 7

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

Question 8

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

Question 9

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.

Question 10

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.

Question 11

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

Question 12

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)7 011 million dollars
C)701 107 million dollars
D)None of these choices are correct.

Question 13

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
$\begin{array}{|l|c|}\hline \text { Year } & \text { Average earnings (\$) } \\\hline 1990 & 542.30 \\\hline 1991 & 574.10 \\\hline 1992 & 590.35 \\\hline 1993 & 605.23 \\\hline 1994 & 621.95 \\\hline 1995 & 645.10 \\\hline 1996 & 664.28 \\\hline 1997 & 682.35 \\\hline 1998 & 708.30 \\\hline\end{array}$
Source: Australian Bureau of Statistics, Australian Economic Indicators, ABS Cat. No. 1350.0, ABS, Canberra.

Question 14

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.

Question 15

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.

Question 16

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.

Question 17

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.

Question 18

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

Question 19

The table below is the Laspeyres price index for a basket of goods related to the Computer IT industry. (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.

Question 20

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

Question 21

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. $$\text { Consumer price index with different base periods, Australia }$$
$\begin{array}{|c|c|c|}\hline \text { Year } & \begin{array}{c}\text { Baseperiod } \\(1980=100)\end{array} & \begin{array}{c}\text { Base period } \\(\mathbf{1 9 9 0}=\mathbf{1 0 0})\end{array} \\\hline 1985 & 148.7 & \\\hline 1986 & 162.6 & \\\hline 1987 & 174.5 & \\\hline 1988 & 187.3 & \\\hline 1989 & 202.3 & 100.0 \\\hline 1990 & & 105.3 \\\hline 1991 & & 107.3 \\\hline 1992 & & \\\hline\end{array}$

Question 22

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

Question 23

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.

Question 24

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 the average of relative price indexes for the fruit and vegetable group for June 2010 (with base June 2008 = 100).

Question 25

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. Source: Australian Bureau of Statistics, Australian Economic Indicators, ABS Cat. No. 1350.0, ABS, Canberra.