To calculate the point elasticity of demand, we use the following formula:

$\text{Elasticity of demand} (E_d) = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$

We can express the formula in terms of the actual values Sarah provides:

$E_d = \frac{\frac{Q_2 - Q_1}{Q_1}}{\frac{P_2 - P_1}{P_1}}$

Where:

• $Q_1 = 200$ (initial quantity sold)
• $Q_2 = 150$ (new quantity sold)
• $P_1 = 2$ (initial price in Rands)
• $P_2 = 2.50$ (new price in Rands)

Step 1: Calculate the percentage change in quantity demanded

$\frac{Q_2 - Q_1}{Q_1} = \frac{150 - 200}{200} = \frac{-50}{200} = -0.25$

Step 2: Calculate the percentage change in price

$\frac{P_2 - P_1}{P_1} = \frac{2.50 - 2}{2} = \frac{0.50}{2} = 0.25$

Step 3: Calculate the elasticity of demand

$E_d = \frac{-0.25}{0.25} = -1$

Conclusion:

The point elasticity of demand for Sarah's cupcakes is $-1$, indicating unitary elasticity. This means that the percentage change in quantity demanded is exactly proportional to the percentage change in price.

Would you like further clarification or more details on this?

Here are 5 related questions you might want to explore:

1. What does unitary elasticity imply about Sarah's pricing strategy?
2. How would a higher elasticity (e.g., $E_d = -2$) affect her revenue?
3. What factors could cause the elasticity of Sarah's cupcakes to change over time?
4. How could Sarah find the optimal price for maximizing revenue?
5. Can Sarah's demand elasticity differ on weekends compared to weekdays?

Tip: Elasticity is often negative because of the inverse relationship between price and quantity demanded—be mindful of the sign when interpreting the results.