Price Elasticity of Supply
A measure of the responsiveness of quantity supplied when there is a change in price.
Price elasticity of supply is defined as the percentage change in quantity supplied divided by the percentage change in price:
$$ \mathrm{PES} = \frac{\%\Delta Q_s}{\%\Delta P}$$
Where:
- $\%\Delta Q_s$ = Percentage change in quantity supplied
- $\%\Delta P$ = Percentage change in price
Therefore, using the above formulas, PES can be written as:
$$ \mathrm{PES} = \frac{\frac{Q_{new}-Q_{old}}{Q_{old}}\times 100}{\frac{P_{new}-P_{old}}{P_{old}}\times 100} = \frac{\frac{Q_{new}-Q_{old}}{Q_{old}}}{\frac{P_{new}-P_{old}}{P_{old}}}=\frac{\frac{\Delta Q}{Q_{old}}}{\frac{\Delta P}{P_{old}}} $$
NoteThe expanded format of writing PES is provided here as in exam papers, they might ask you to calculate the percentage change in quantity supplied and price to figure out the PES!
As observed above, it is almost identical to $PED$ but rather focuses on the quantity supplied.
ExampleIf we know that:
- At a price $P_1 = \$ 50$ producers supply $Q_1=15$ bars of chocolate
- At a price $P_2 = \$ 100$ producers supply $Q_2 = 25$ bars of chocolate.
Then we can calculate the $PES$ at $P=50$ by using the formula above.
- $\%\Delta P = \frac{100-50}{50}\times 100 = 100\%$ since the price doubled
- $\%\Delta Q = \frac{25 - 15}{15}\times 100 \approx 66.66\%$
Hence the price elasticity of supply would be:
$$ PES = \frac{\%\Delta Q_s}{\%\Delta P} = \frac{66.66..}{100} = \frac{2}{3}$$
NoteFor the example above, we would get a different $PES$ 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 make sure to write "PES at P = initial price".
As we can see, the price elasticity of supply is positive.
- This is due to the law of supply, where the percentage change of quantity supplied will be in the same direction as that of price.
- Therefore PES is mathematically always positive.
Degrees of PES: Theoretical Range of Values
PES values help classify supply into different categories.
Relative PES cases
Price Inelastic
- When $0 < PES < 1$, the supply is called price inelastic.
- Here, the percentage change in quantity supplied is less than the percentage change in price
- Therefore $PES$ is smaller than 1 and the quantity supplied is greatly unresponsive
Now think of seasonal fruits
- If prices rises, even by a lot, it is almost impossible to increase the quantity supplied of seasonal fruits in a certain period of time.
- Because seasonal fruits only grow at specific times of the year and take time to grow.
- Producers cannot easily increase the quantity and thus quantity supplied doesn't rise by much.
Price Elastic
- When $1 < PES < \infty$, the supply is called price elastic.
- Here, the percentage change in quantity supplied is more than the percentage change in price.
- Therefore $PES$ is greater than 1 and the quantity supplied is greatly responsive.
Think of taxis
- Relatively easy to work as a taxi driver, whether it is part-time of full time alongside ease of access with online apps.
- Even if prices rise by a bit, by offering drivers a higher commission, a lot more drivers are likely willing to accept commission due to competition.
- Or new drivers can easily join to get a portion of the cut.
- Hence the quantity supplied of taxis will increase.
Example Diagrams
The figure above shows the supply curve of a good that has a high PES or in other words, is elastic.
- There is a higher increase in quantity supplied compared to the change in price.
- The curve is relatively flatter and starts from the y axis.
The figure above shows the supply curve of a good that has a low PES or in other words, is inelastic.
- There is a lower increase in quantity supplied compared to the change in price.
- The curve is relatively steeper and starts from the x axis.
Usually, the flatter curve represents a high elasticity and the curve that is steeper represents a low elasticity (inelasticity).
Common MistakeAs stated before, you can only compare flatter with steeper if two curves intersect on the same set of axes/graph, otherwise, you can't due to scaling differences!
