Price Elasticity of Demand (PED)
A measure of the responsiveness of quantity demanded when there is a price change.
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:
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
The 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:
$$ \mathrm{PED} = \frac{\frac{Q_{new}-Q_{old}}{Q_{old}}\times 100}{\frac{P_{new}-P_{old}}{P_{old}}\times 100} = \frac{\frac{Q_{new}-Q_{old}}{Q_{old}}}{\frac{P_{new}-P_{old}}{P_{old}}}=\frac{\frac{\Delta Q}{Q_{old}}}{\frac{\Delta P}{P_{old}}} $$
If we know that
Then we can calculate the $PED$ by using the formula above.
Hence the price elasticity of demand would be:
$$ PED = \frac{-\% 50}{\% 100} = -\frac{1}{2}$$
For 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.
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 $-\frac{1}{2}$.
PED values help classify demand into different categories (we take the absolute values):
Figure 1 below showcases the three special values the PED of a demand curve can take.
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:
$$PED=\frac{\%\Delta Q_d}{\%\Delta P}
Where:
If we calculate the PED for the demand curve shown:
Therefore, the PED is:
$$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.
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