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Assignment

QUESTIONS

Part (A)

Consumer spending data in the following table are from the UK government: expenditure on food (series ABZV), and transport (series ADGT), in £ millions at current prices, from UK government website www.ons.gov.uk (downloaded 5th November 2011). The same table also includes a 'Consumer Price Index' for food (series DK9P) and transport (series DKA3).

Year

Food price index

Spending on food

Transport price index

Spending on transport

2001

94.9

60814

101.6

96954

2009

123.2

81185

99.7

122265

Calculate a proxy for the quantity of food an average consumer buys in each year, using this formula:Qfood = (food spending) / (food price index)

and similarly for transport.

Use the above data to calculate the Laspeyres Price Index for 2009. Show each step of your calculation. (30 marks in total)

Solution

Proxy for the quantity of food an average consumer buys in each year is given in the following calculations:

Formula:

Q (food) =

For 2001:

Q (food) =

Q (food) =

Q (food) = 640.82

Q (food) = 641 (due to rounding off)

For 2009

Q (food) =

Q (food) =

Q (food) = 658.96

Q (food) = 659 (due to rounding off)

Proxy for the quantity of transport an average consumer buys in each year is given in the following calculations:

Formula:

Q (transport) =

For 2001:

Q (transport) =

Q (food) =

Q (food) = 954.27

Q (food) = 954 (due to rounding off)

For 2009

Q (transport) =

Q (food) =

Q (food) = 1226.33

Q (food) = 1226 (due to rounding off)

Year

Food price index

Spending on food

Quantity of Food

Transport price index

Spending on transport

Total Quantity of Transport

2001

94.9

60814

641

101.6

96954

954

2009

123.2

81185

659

99.7

122265

1226

Calculating a Laspeyres Index

A Laspeyres Index is known as a “base-weighted” or “fixed-weighted” index because the price increases are weighted by the quantities in the base period. The Consumer Price Index is an example of a Laspeyres Index. In this example, 2005 will serve as the base year. Formally, the calculation is written,

L (base year) =

Where

jo refers to the base year value for good j,

t refers to the current year.

Below shows how to calculate the Laspeyres index for the given sum.

Calculating the base year for the Index (2001):

Index for the year 2001 can be calculated by the following formula:

L (base year) =

L (2001)

L (2001)

L (2001)

L (2001)

Then, typically, the value is multiplied by 100. So the base year value of the index will always be equal to 100.

Index Value = 1 x 100 = 100

Calculating Index Value of 2009

L (base year) =

L (2009)=

L (2009) =

L (2009)=

L (2009) =

Then, typically, the value is multiplied by 100. So the base year value of the index will always be equal to 100.

Index Value = 1.1 x 100 = 110

Part (B)

Work out a proxy for the quantity of food an average consumer buys in each year, using this formula:Qfood = (food spending) / (food price index)

Calculate this 'quantity proxy' for food, for each year. Repeat the process for transport, for 2001 and 2009. Work out the 'quantity proxy' for a household with the same food & transport budget, but which spent its entire budget on food. Next, calculate the 'quantity proxy' for a household which ...

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