Hi I was given the following price vs quantity values.

Price   Quantity Demanded
4   221
5   210
6   185
7   162
8   144
9   122
10  102
11  81
12  61
13  46
14  25

The graph was plotted as shown below.

enter image description here

The equation was, $Y = -0.0496 X + 15.133$. What I need to know is, I was asked to find the PED when price is $\$7.5$.

Then what I did was, I found the quantity at price $7.5$ substituting to the price quantity equation. And then found the PED using the equation

enter image description here

The quantity derived for price $7.5$ was $153.89$. Then I calculated the PED as below. Is it correct?

$$\frac{(153.89-144)/144}{(7.5-8)/8} = 1.099$$

May I know whether this calculation is correct?

  • $\begingroup$ Is Y = -0.0496 X + 15.133 your formula for quantity demanded? $\endgroup$ – Ali Apr 22 '19 at 16:51

The answer will vary slightly depending on which notion of elasticity you're using.

Arc elasticity (or midpoint elasticity) uses the formula \begin{equation} \epsilon^\text{arc}=\frac{Q_1-Q_0}{P_1-P_0}\cdot\frac{\frac12(Q_0+Q_1)}{\frac12(P_0+P_1)}, \end{equation} where $\frac12(Q_0+Q_1)$ is the midpoint between $Q_0$ and $Q_1$. Note that in your case, $7.5$ is the midpoint between $7$ and $8$.

Point elasticity uses the formula \begin{equation} \epsilon^\text{point}=\frac{\mathrm dQ}{\mathrm dP}\cdot\frac{P}{Q}. \end{equation} Here, $\frac{\mathrm dQ}{\mathrm dP}$ is the derivative of the demand function (evaluated at the point you want to calculate the elasticity, but it will be constant if demand is linear), and in your case, $P=7.5$ and $Q$ is the quantity demanded corresponding to that price.

  • $\begingroup$ Thanks alot Herr. :) Corrected it . I'm having another small question. The PED value I received at price 7.5 is, 0.9641. Does it mean this is inelastic since it is smaller than 1. What Can I do to increase the revenue of the product. Increase or decrease the product $\endgroup$ – Hiru Apr 23 '19 at 2:46
  • $\begingroup$ @Hiru: If you assume linear demand, then there is a nice property you can use. Suppose $Q^*$ is the quantity where $\epsilon=1$, then we must have $\epsilon >1$ for all $Q<Q^*$ and $\epsilon <1$ for all $Q>Q^*$. $\endgroup$ – Herr K. Apr 23 '19 at 3:42

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