Question

Find the elasticity of supply for supply function$x = 2{p^2} + 5$, when $p = 3$.
A. $\dfrac{{23}}{{36}}$
B. $\dfrac{{36}}{{23}}$
C. $\dfrac{{63}}{{32}}$
D. None of these

Answer 1

Hint: We will differentiate the value of $x$with respect to $p$.Further we will use the formula of elasticity of supply to get the answer. By using the formula for elasticity of supply$ = \dfrac{{change\,in\,\,su\,pply}}{{actual\,su\,pply}} \times \dfrac{{\,\,\,\,actual\,price\,\,\,\,}}{{change\,in\,price}}$.

Complete step-by-step answer:
The given supply function
$x = 2{p^2} + 5$
We will do differentiate the value of $x$with respect to $p$,we have
$\dfrac{{dx}}{{dp}} = 2 \times 2p$
$\dfrac{{dx}}{{dp}} = 4p$
By using the formula of Elasticity of supply, we will get
Elasticity of supply$ = \dfrac{{dx}}{{dp}} \times \dfrac{p}{x}$
Elasticity of supply $ = 4p \times \dfrac{p}{{2{p^2} + 5}}$
Elasticity of supply $ = \dfrac{{4{p^2}}}{{2{p^2} + 5}}$ $\left( i \right)$
We will put the value of p, $p = 3$in equation$\left( i \right)$,we have
Elasticity of supply$ = \dfrac{{4{{\left( 3 \right)}^2}}}{{2{{\left( 3 \right)}^2} + 5}}$
Elasticity of supply $ = \dfrac{{36}}{{23}}$
So, the correct answer is “Option B”.

Note: Elasticity of supply is the degree of responsiveness of quantity supplied to a change in price. The elasticity of supply establishes a quantitative relationship between the supply of a commodity and its price.