Elasticity
Elasticity is simply the measurement of how much something changes when something else changes.
In everyday life we can think of any number of things that will change based on something else. For example:
- If the temperature outside gets colder, how will this change the way I dress?
- If I push on the accelerator, how will this change the speed of my car?
- If I pull back on a rubber band and let it go, how far will it fly across the room?
These events describe relationships between variables. And that’s just what elasticity is.
Elasticity is the responsiveness of one variable to a change in another variable.
In economics we are concerned with the following variable relationships:
- If I change the price of my product, how will quantity demanded be affected?
- If I change consumer income, how will quantity demanded be affected?
- If the price of another product changes, how will this affect the quantity demanded for my product?
- If the price of my product changes, how will this affect quantity supplied?
Price Elasticity of Demand (PED)
Price Elasticity of Demand (PED) is the responsiveness of quantity demanded following a change in price.
In other words: if we change our price, what will happen to our quantity demanded?
The idea of Price Elasticity of Demand has been implicit ever since we’ve been talking about the demand curve. We know that if we change our price, we expect quantity demanded to change.
Price Elasticity of Demand simply gives us a way to measure this. We can use this measurement to predict what will happen following a price change and explain the implications for a business’ revenue.
Price Elastic Demand and Price Inelastic Demand
To describe how price affect quantity demanded, we use two terms: price elastic and price inelastic.
If demand is price elastic it means that Quantity Demanded changes more than proportionally following a change in price. This means that small changes in price will have large effects on our quantity demanded.
If demand is price inelastic, it means that Quantity Demanded changes less than proportionally following a change in price. This means that large changes in price will have small effects on our quantity demanded.
Note the language that is used to describe elasticity: more than proportional and less than proportional. This is very important because when measuring changes in price and quantity we are not interested in raw changes. Instead, we are interested in changes relative to the original quantity. To do this we will always compare price and quantity changes using percentages. Because we are using percentages, we can always say that changes are proportional.
Take the following example: say that we have two products, Product A and Product B. Product A sells 5 units per day, and Product B sells 100 units per day. We lower the price on both, and each sees daily sales increase by 1 unit per day.
They have both increased by the same amount- but Product A has seen a much larger proportional change. This is because, relative to the original sales of 5 units per day, an increase of 1 is fairly large (20% of the original). Product B also increases sales by 1 unit, but relative to 100 units per day, an increase of 1 is tiny (only 1% of the original). So even though they have both increased by the same amount, the proportional change is much different.
Link: Proportionality Warm Up Quesitons
It is always a good idea to use the idea of proportionality when describing how elastic something is.
The Sign of PED
Learning about the demand curve tells us the overall expected relationship between Price and Quantity Demanded: as Price goes up, Quantity Demanded goes down. The relationship is negative. This is the basis of the law of demand and is the reason why the demand curve slopes downwards.
Formula for PED
To describe the relationship between price and quantity demanded, we will use a formula to give a PED coefficient. This is a single number, which doesn’t have a unit or percentage sign. The formula uses calculations for changes in Quantity Demanded and Price:
The number that this formula generates describes how responsive, mathematically, your quantity demand will be to a change in price. So if your PED is -2, and you change your price by 10%, you can predict that your Quantity Demanded will change by:
2 x 10% = -20%
Notice how the formula uses percentage change for Quantity Demanded and Price. Using this, rather than raw figures, gives the proportional changes that we discussed earlier.
It is useful to know how to write out this formula using mathematical symbols, as shown here:
Finally, it is always useful to have a memory trick. “The Queen Rules over the People” is just catchy enough to remember, in a stressful exam situation, that Q always goes over P in the formula.
PED Coefficient and Elasticity
Say you have the following information:
- The price of rice increases by 10%. This has the effect of decreasing the quantity demanded for rice by 5%.
Is this product elastic or inelastic? And what will its PED coefficient be?
First, we can see that this product is price inelastic. We can tell by looking at the numbers. The price has changed by 10%, and this has only made a difference of 5% for the quantity demanded. We can see that price affects quantity demanded less than proportionally, so this product is inelastic.
To work out the PED coefficient we plug the numbers into the formula. Because percentage change in price is greater than the percentage change in Qd, we can see that this fraction is ‘bottom heavy.’ A ‘bottom heavy’ fraction will produce a decimal which is less than 1, which we can see in this answer: PED = -0.5.
Now consider this problem:
- The price of oranges decreases by 5%. This has the effect of increasing the quantity demanded by 7.5%.
Is this product elastic or inelastic? And what will its PED coefficient be?
First, we can see that this product is price elastic. The numbers show that quantity demanded increases by a greater proportional amount than price. This produces a ‘top heavy’ fraction, which will produce a decimalised answer which is greater than 1: PED = -1.5.