Answer :
Answer:
Step-by-step explaTo calculate the point elasticity of supply for the given supply function \( p = 25 + 0.5q \) when the price is increasing to Rs 90, we need to follow these steps:
1. **Find the quantity supplied (\(q\)) when the price (\(p\)) is Rs 90.**
2. **Determine the derivative of the supply function with respect to \(q\) (\( \frac{dp}{dq} \)).**
3. **Use the formula for the point elasticity of supply:**
\[ E_s = \frac{dq}{dp} \times \frac{p}{q} \]
### Step 1: Find the quantity supplied (\(q\)) when \( p = 90 \)
Given the supply function:
\[ p = 25 + 0.5q \]
Set \( p = 90 \) and solve for \( q \):
\[ 90 = 25 + 0.5q \]
\[ 90 - 25 = 0.5q \]
\[ 65 = 0.5q \]
\[ q = \frac{65}{0.5} \]
\[ q = 130 \]
So, when the price is Rs 90, the quantity supplied is 130 units.
### Step 2: Determine the derivative of the supply function (\( \frac{dp}{dq} \))
The given supply function is:
\[ p = 25 + 0.5q \]
The derivative of \( p \) with respect to \( q \) is:
\[ \frac{dp}{dq} = 0.5 \]
### Step 3: Use the point elasticity of supply formula
The point elasticity of supply \( E_s \) is given by:
\[ E_s = \frac{dq}{dp} \times \frac{p}{q} \]
First, find \( \frac{dq}{dp} \) by taking the reciprocal of \( \frac{dp}{dq} \):
\[ \frac{dq}{dp} = \frac{1}{\frac{dp}{dq}} = \frac{1}{0.5} = 2 \]
Now, substitute the values of \( p \), \( q \), and \( \frac{dq}{dp} \) into the elasticity formula:
\[ E_s = 2 \times \frac{90}{130} \]
\[ E_s = 2 \times \frac{9}{13} \]
\[ E_s = \frac{18}{13} \]
Therefore, the point elasticity of supply when the price is increasing to Rs 90 is:
\[ E_s = \frac{18}{13} \approx 1.38 \]
So, the elasticity of supply at this point is approximately 1.38.nation:
