Question

Define elasticity of supply and find the price from the given statement:

If Es of a good is 2 and a firm supplies 200 units at price of Rs 8 per unit, then at what price will the firm supply 250 units. What is the conclusion?

Answer 1

We define elasticity of supply of a good as the amount of the change in the quantity demanded of a good due to one percent change in the good's price.

Elasticity of supply $=\frac{\delta Q}{\delta P}=\frac{\frac{Q_2-Q_1}{Q1}}{\frac{P_2-P_1}{P_1}}$

Given : Elasticity of supply (Es)$= 2 \space \space$

$0.125 = \frac{(X - 8)}{8}$

P₁ = 8  and Q₁ = 200

P₂ = ? and Q₂ = 250

% change in quantity supplied$= \frac{(250−200)}{200} = 0.25 = 25\%$

so, using formula , we have :$2 = \frac{25\%}{\% \space \delta\space in P}$

% change in P$=\frac{ (P2 − 8) ×100}{8}= \frac{25\%}{2} = 12.5\%$

$(P_2 − 8)×100 = 100$

$(P_2 − 8) =\frac{ 100}{100} = 1$

$P_2 − 8 = 1$

$P_2 = 1 + 8 = 9$

Thus, $P_2$ is Rs 9 or the price is Rs 9 when the quantity sold is 250 units.

 

The conclusion is that the supply of the good is elastic as the Es is more than 1 and any change in price causes more than proportional change in quantity demanded.