Price Elasticity of Demand (PED)
A measure of the responsiveness of quantity demanded when there is a price change.
The Formula for PED
Price elasticity of demand is defined as the percentage change in quantity demanded divided by the percentage change in price.
$$ \mathrm{PED} = \frac{\%\Delta Q_d}{\%\Delta P}$$
Where:
- $\%\Delta Q_d$ = Percentage change in quantity demanded
- $\%\Delta P$ = Percentage change in price
To calculate percentage changes, use this formula:
$$\%\Delta X = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100$$
This gives you the percentage change from Old Value to New Value
NoteThe formula above works for linear (straight-line demand curves) and is a good approximation for others.
The exact percentage change and elasticity for non-linear curves concerns the derivative which is not part of this syllabus.
Therefore, using the above formulas, PED can be written as:
$$ \mathrm{PED} = \frac{\frac{Q_{new}-Q_{old}}{Q_{old}}\times 100}{\frac{P_{new}-P_{old}}{P_{old}}\times 100} = \frac{\frac{Q_{new}-Q_{old}}{Q_{old}}}{\frac{P_{new}-P_{old}}{P_{old}}}=\frac{\frac{\Delta Q}{Q_{old}}}{\frac{\Delta P}{P_{old}}} $$
ExampleIf we know that
- At a price $P_1 = \$ 50$ people buy $Q_1=30$ bars of chocolate.
- At a price $P_2 = \$ 100$ people buy $Q_2 = 15$ bars of chocolate.
Then we can calculate the $PED$ by using the formula above.
- $\%\Delta P = \frac{100-50}{50}\times 100 = \% 100$, since the price doubled.
- $\%\Delta Q_d = \frac{15 - 30}{30}\times 100 = - \% 50$.
Hence the price elasticity of demand would be:
$$ PED = \frac{-\% 50}{\% 100} = -\frac{1}{2}$$
NoteFor the example above, we would get a different $PED$ if we used $P_2,Q_2$ as our initial values and $P_1,Q_1$ as the new one (you can try this yourself)
Hence, the above $PED$ would be written as the price elasticity of demand at $\mathbf{P_1}$ because at $P_2$ the value is different.
As we can see, the price elasticity of demand is negative.
- That is because of the law of demand, the percentage change of quantity demanded will be in the inverse of the percentage change of price.
- Therefore PED is mathematically always negative.
However, for easier interpretation, economists use the absolute value of PED such that the PED calculated will just be noted as $\frac{1}{2}$ instead of $-\frac{1}{2}$.
Degrees of PED: Theoretical Range of Values
PED values help classify demand into different categories (we take the absolute values):
Price Inelastic
- When $0 < PED < 1$, the demand is called price inelastic.
- Here, the percentage change in quantity demanded is less than the percentage change in price.
- Therefore $PED$ is smaller than 1 and the quantity demanded is highly unresponsive.
Price Elastic
- When $1 < PED < \infty$, the demand is called price elastic.
- Here, the percentage change in quantity demanded is more than the percentage change in price.
- Therefore $PED$ is greater than 1 and the quantity demanded is greatly responsive.
Special values of PED
Figure 1 below showcases the three special values the PED of a demand curve can take.
Unit Elastic
- When $PED = 1$, the demand is called unit price elastic.
- Here, the percentage change in quantity demanded is equal to the percentage change in price.
- Therefore $PED$ is equal to 1 and the quantity demanded is exactly as responsive to the price.
Why is the unit elastic demand curve in Figure 1 unit elastic if it appears steep and the x and y axis have the same scale?
Many students make the mistake of thinking the demand on the left diagram in Figure 1 is inelastic, since the axis have the same scale and it is clearly steep.
However, this is not the case. Remember:
PED is defined as the percentage change in quantity demanded divided by the percentage change in price.
The formula of PED is:
$$PED=\frac{\%\Delta Q_d}{\%\Delta P}
Where:
- $\%\Delta Q_d = \frac{Quantity Demanded_initial - Quantity Demanded_final}{Quantity Demanded_final} \times 100$
- $\%\Delta P = \frac{Price_intial - Price_final}{Price_final} \times 100$
If we calculate the PED for the demand curve shown:
- $\%\Delta Q_d = \frac{2-4} {2} \times 100 = \frac{-2}{2} \times 100 = -100\%$
- $\%\Delta P = \frac{6-3} {3} \times 100 = \frac{3}{3} \times 100 = 100\%$
Therefore, the PED is:
$$PED = \frac{-100\%} {100\%} = -1$$
As we explained, we always take the absolute value of the PED. Hence PED = 1.
This is because the PED is calculated as a percentage change, not as a change.
Perfectly Inelastic
- When $PED = 0$, the demand is called perfectly price inelastic.
- Here, the percentage change in quantity demanded is always at zero regardless of what happens to the price.
- Therefore $PED$ is 0 and the quantity demanded is perfectly unresponsive.
Perfectly Elastic
- When $PED = \infty$, the demand is called perfectly price elastic.
- A small price fall causes people to buy an infinite amount, and a small price increase causes people to buy nothing.
- Therefore $PED$ is infinite and the quantity demanded is perfectly responsive.
Why is the unit elastic demand curve curved?
In the given unit elastic demand curve, the price elasticity of demand (PED) is equal to 1.
This happens when the percentage change in quantity demanded is exactly equal to the percentage change in price at all points along the curve. Looking at the figure:
- When the price decreases from 4 to 2 (a 50% decrease), the quantity demanded increases from 1 to 2 (a 50% increase).
- Similarly, when the price falls from 2 to 1 (a 50% decrease), the quantity rises from 2 to 4 (a 50% increase).
Since the percentage change in quantity is equal to the percentage change in price in both cases, the PED is exactly 1 at all points.
Common MistakeStudents often confuse PED with the slope of the demand curve. Remember, PED measures percentage changes, not the steepness of the curve.
Determinants of PED
Several factors influence how responsive consumers are to price changes:
- Number and closeness of substitutes.
- Degree of necessity.
- Proportion of income spent.
- Time.
Number and Closeness of Substitutes
The more substitutes available, the more elastic the demand.
- If price changes happen, people can easily switch over to the substitute goods. Hence, the quantity demanded is quite responsive (elastic).
- If fewer substitutes are available, there is not many alternatives to switch to and therefore the quantity demanded is less responsive (inelastic).
A specific type of toothbrush has many substitutes. If the prices of one noticeably increase, most people would just switch to a cheaper one.
Further, it is important to know how close these substitutes are to each other, since they are a determining factor on whether consumers want to switch.
- If two substitutes are closer, consumers wouldn't mind switching over. This makes the demand more elastic.
- If they aren't very good substitutes of each other, consumers still might not switch.
Sprite and 7UP are much closer substitutes of each other than Sprite and Almond Milk.
Another important factor is the broadness of the product.
- If we look at broad categories of products (Food, Water, Coffee etc.) then they will likely have fewer substitutes.
