Calculating Elasticity of Supply Using Point Method

The question asks to find the elasticity of supply ($E_s$) using the point method for the given supply function $q = -100 + 10p$ when the price ($p$) is ₹ 15.

Formula for Point Elasticity of Supply

The formula for point elasticity of supply is:

$E_s = \frac{dq}{dp} \times \frac{p}{q}$

Step-by-Step Calculation

1. Determine the derivative $\frac{dq}{dp}$:

   Given the supply function $q = -100 + 10p$.

   Differentiating $q$ with respect to $p$, we get:

   $\frac{dq}{dp} = \frac{d}{dp}(-100 + 10p) = 10$

2. Calculate the quantity ($q$) at the given price ($p = ₹ 15$):

   Substitute $p = 15$ into the supply function:

   $q = -100 + 10 \times 15$

   $q = -100 + 150$

   $q = 50$

3. Calculate the Elasticity of Supply ($E_s$):

   Now, substitute the values of $\frac{dq}{dp}$, $p$, and $q$ into the elasticity formula:

   $E_s = \frac{dq}{dp} \times \frac{p}{q}$

   $E_s = 10 \times \frac{15}{50}$

   Simplify the expression:

   $E_s = 10 \times \frac{3}{10}$

   $E_s = 3$

Therefore, the elasticity of supply when the price is ₹ 15 is 3.