Price Elasticity of Demand Formulae
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Price Elasticity of Demand Formulae
A definition and the formula
All elasticities measure responsiveness.
In this case, the two key words are 'price' and 'demand', so the price elasticity of demand measures the responsiveness of the quantity demanded to a given price change. In the last 'topic' we discussed demand at some length. In most cases, the demand for a good rises when the price falls, ceteris paribus. The question is, by how much?
The following formula can be used to measure exactly how responsive demand is to a given price change:
So the algebraic terms mean: | E_{d} = The price elasticity of demand |
Δ = 'change in' | |
Q_{d} = Quantity demanded | |
P = Price |
Using the formula
You will only face questions that specifically ask you to calculate an elasticity in multiple-choice papers. Having said that, essay questions often appear where you need to analyse the significance of certain elasticities. Either way, it is important that you are confident in dealing with this, relatively simple, arithmetic formula.
Calculating the elasticity
Let's start with the easiest questions you might face:
The price of a CrispyChoc Bar in the local newsagent rises from 25p to 30p. As a result, the newsagent finds that the demand for this product falls from 80 bars a day to 40 bars a day. Find the price elasticity of demand.
At this point, it might be worth reviewing how to calculate percentage changes. Basically, you work out the change, divide this change by the original figure and then multiply the result by 100. Or, if you prefer the algebraic form:
So, the percentage change in quantity demanded is -40 (the change, or fall in demand) divided by 80 (the original amount demanded) multiplied by 100. -40 divided by 80 is -0.5. Multiply this by 100 and you get -50%.
The percentage change in price is +5 (the change in price) divided by 25 (the original price) multiplied by 100. 5 divided by 25 is 0.2. Multiply by 100 and you get 20%.
Now we can use the formula for the price elasticity of demand:
Notice that the answer is negative. This is because the price rose (positive) causing the quantity demanded to fall (negative). A negative divided by a positive is always negative. This is to be expected. The demand curve is nearly always downward sloping showing a negative relationship between price and quantity demanded. Because nearly all elasticities of demand are negative examiners often don't use the negative sign. The question will just state an elasticity of, say, 3. What they mean is -3, so don't get too confused!
Now try a couple for yourself. The answers will appear if you click the appropriate button:
A greengrocer decides to cut the price of his apples from 50p per lb to 45p per lb. He finds that his daily sales rise from 40lbs a day to 45lbs a day. What is the price elasticity of demand (ceteris paribus)?
The price of a litre of unleaded petrol rises from 80p to 84p (not again!). As a result, the quantity demanded at a local forecourt falls from 4000 to 3880 litres a day. What is the price elasticity of demand (ceteris paribus)?
Calculating demand and price changes from a given elasticity
Often, you will face the following type of question:
A greengrocer decides to cut the price of his bananas from 40p per lb to 32p per lb. The price elasticity of demand for this product is 2. He currently sells 80lbs of bananas a day. How many will he sell after the price cut?
The maths doesn't really get any harder than this in A level economics. That's meant to be a good thing, by the way!
The formula has three parts: E_{d}, %Q_{d} and %P. In the questions where you had to find the value of the elasticity, you were given two of the three parts and asked to find the third. In the question above, exactly the same thing has happened except the part you need to find has changed. Always write down the formula before you do your working:
Remember that although the elasticity is stated as '2', it is, in fact, -2:
Now we can rearrange the formula (remember that GCSE maths!):
(a minus times a minus is a plus).
So the demand for the greengrocer's bananas will rise by 40%. Initial sales were 80lbs a day, so sales after the price cut will be 112lbs a day (40% of 80 is 32. Add this to 80 to give 112.)
Now try a couple for yourself. Think carefully about the second question. The answers will appear if you click the appropriate button:
A publican decides to increase the price of Brand X lager from £2 a pint to £2.10 a pint. The price elasticity of demand for Brand X is 0.8. He currently sells 300 pints a day. What will the new demand be (ceteris paribus)?
The same publican sells best bitter for £1.50 a pint. He finds that, as a result of a price change, he is selling 242 pints of bitter compared with 220 pints before the price change. The price elasticity of demand for best bitter is 1.25. What is the new price (ceteris paribus)?