Question

Explain Ratio method and Geometric method of measuring price elasticity of demand.

Answer 1

(A) RATIO METHOD OR PROPORTIONATE METHOD:
This method is also known as Arithmetic Method. In this method we compare the percentage of change in demand with percentage of change in price. When we divide the percentage of change in demand by the percentage of change in price, we get Elasticity of demand.
$Ed=\frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in Price}}$
Symbolically:
$Ed=\frac{△Q}{Q}÷\frac{△P}{P}=\frac{△Q}{Q}\times \frac{P}{△P}$
$Ed=\frac{△Q}{△P}\times \frac{P}{Q}$
$△Q=$ Change in demand $(Original-newquantity)$
$△P=$ Change in price $(Original-newprice)$
$Q=$ Original quantity
$P=$ Original price
By applying the above formula we can calculate and find the type of elasticity. If the result is one, then elasticity is unitary. If it is more than one it is relatively elastic and if it is less than one it is relatively inelastic.
Eg.

Price $\left(P\right)$	Quantity demanded (D)
$Rs.8$	$10$
$Rs.6$	$14$

$Ed=\frac{△Q}{△P}\times \frac{P}{Q}\left[△Q\right(\text{Change in Qty})=(10-14)=-4,OriginalQty=10,△P(\text{Change in price})=(6-8)=-2,Originalprice=8]$
$=\frac{-4}{-2}\times \frac{8}{10}=\frac{8}{5}$
$=1.6(e>1)$
So the commodity has Relatively Elastic Demand $e>1$.
If the Answer was $<1$ then it would have been relatively inelastic.
(B) GEOMETRIC METHOD/ POINT METHOD:
In this method given by Prof. Marshall we will be able to find out elasticity at a point on a given demand curve. To find out elasticity at any given point ${}^{\prime }{P}^{\prime }$ on a linear demand curve $DD$ (Straight Line) extend the demand curve towards $Y$ axis and $X$ axis to meet at point $A$ and $B$ respectively as shown in the diagram. Then measure the distance of segment $PA$ and segment $PB$. Then divide the distance of lower segment $PB$ by upper segment $PA$.
Point Elasticity of demand $=\frac{\text{Lower segment of the demand curve}}{\text{Upper segment of the demand curve}}$
Suppose the distance of lower segment $PB$ is $6cm$ and upper segment $PA$ is $4cm$.
$\frac{6}{4}=\frac{PB}{PA}=1.5$
Then Elasticity at point $"P"$ is $1.5$ which is $e>1$. So demand is Relatively Elastic. On a given linear demand curve elasticity of demand at different point is different as shown in the diagram.
Now to find elasticity of demand on a non-linear demand curve on given point $"P"$ as shown in the diagram. First draw a tangent line $AB$ to meet $Y$ and $X$ axis at point $A$ and $B$. Then divide the lower Seg $PB$ by the upper Seg $PA$ i.e. $\frac{PB}{PA}$.
Suppose distance $PA$ is $8cm$ and $PB$ is $4cm$, then $ED=\frac{4}{8}=0.5$ i.e. $e<1$. It is a case of Relatively Inelastic demand.