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# Explain how economists use the concept of elasticity to distinguish between substitute goods and complementary goods.

## [CIE AS level May June 2017]

Step ➊ : Define ‘Cross elasticity of demand’ in the introduction.

Economists use the concept of Cross elasticity of demand (XED) to distinguish between substitutes and complementary goods. XED is a numerical measure of the responsiveness of the quantity demanded for one product following a change in the price of another related product, ceteris paribus. The values of XED can be positive or negative. This value depends on whether products are substitutes or complements.

The formula for cross elasticity of demand used is as follows :

XED =

% change in quantity demanded of product A

% change in the price of product B

Step ➋ : Explain how cross elasticity of demand is used to distinguish between substitute goods and complementary goods

Products that are substitutes for each other will have positive values for the XED whereas products that complements will have negative values of XED. This is illustrated in an example using the diagram below.

Figure A

➤ 2.1 Products that are substitutes for each other will have positive values for the XED.

Substitute goods are two alternative goods that could be used for the same purpose. Cars and motorbikes for example. If the price of cars goes up, then people will begin to turn to motorbikes because of its more favourable relative price. If the price of cars falls, then consumers will start to buy cars instead of motorbikes.

Assume the current average market price of a car is \$10,000 and current sales are 100 cars per day as shown in Figure A.

Following a 2% decrease in the price of motorbikes (a substitute product), demand for cars falls from 100 units to 98 units per day at the original price. The demand curve for cars shifts from D0 to D1.

The cross elasticity of demand can be calculated as follows;

XED =

2% fall in demand for cars
──────────────────────
2% decrease in price of motorbikes

= + 1

➤ 2.2 Products that are complements will have negative values of XED.

A complementary good or service is an item used in conjunction with another good or service. Cars and car tyres for example. If the price of cars tyres decrease, the quantity demanded for cars tyres will increase and so will the complementary demand for cars.

Consider that the average price of car tyres (a complement) falls by 5% . This encourages extra sales of cars tyres and cars as well. The demand for cars rises to 101 per day at the original price. The demand curve shifts from D0 to D2 in Figure A.

The cross elasticity calculation is:

XED =

1% increase in sales of cars
───────────────────
5% falling price of car tyres

= − 0.2

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Step ➌ : Conclude
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To conclude , products that are complements will have negative values of XED , products that are substitutes will have positive values of XED.

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♕ Mark schemes
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For knowledge and understanding of the concept of cross elasticity of demand: For an accurate formula (Up to 2 marks)

For recognition that substitutes have a positive coefficient (1 mark) and that complements have a negative coefficient (1 mark)

(4 marks maximum)

For application:

Using the formula to show why two goods with a positive coefficient are substitutes. (Up to 2 marks)
Using the formula to show why two goods with a negative coefficient are complements (Up to 2 marks)
(4 marks maximum)

Candidates need to display a strong grasp of the central concept and be able to apply it to explain how economists distinguish between substitutes and complements.
An ‘accurate formula’ is one that refers to the % change in quantity and price of the two goods. Allow credit for those candidates who do not provide the formula, but have a clear expression of what cross elasticity measures. Understanding of the measure is essential.

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♕ Examiner’s report
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This was the most popular of the essays available and this part of the question was answered well. There was clear understanding that economists use the concept of cross elasticity of demand to distinguish between substitutes and complementary goods. The formula was used to explain why substitutes have a positive coefficient and complements a negative coefficient. High marks were awarded here.

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