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

$E_d = \frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}}$

Step 1: Calculate the percentage change in quantity demanded

Sarah initially sold 200 cupcakes per day, and after the price increase, she sells 150 cupcakes per day.

$\%\text{ change in quantity demanded} = \frac{\text{New Quantity} - \text{Old Quantity}}{\text{Old Quantity}} \times 100$ $\%\text{ change in quantity demanded} = \frac{150 - 200}{200} \times 100 = \frac{-50}{200} \times 100 = -25\%$

Step 2: Calculate the percentage change in price

The price increased from R2 to R2.50.

$\%\text{ change in price} = \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \times 100$ $\%\text{ change in price} = \frac{2.50 - 2}{2} \times 100 = \frac{0.50}{2} \times 100 = 25\%$

Step 3: Calculate the point elasticity of demand

Now that we have both percentage changes, we can calculate the elasticity.

$E_d = \frac{-25\%}{25\%} = -1$

Conclusion:

The point elasticity of demand for Sarah's cupcakes is -1, which indicates unitary elastic demand. This means that the percentage decrease in quantity demanded is equal to the percentage increase in price.

Would you like more details or clarification on this?

Relative questions:

1. What does unitary elasticity indicate about consumer behavior?
2. How would a further price increase affect Sarah’s sales if demand remains unitary elastic?
3. Can you think of examples where demand might be perfectly elastic or inelastic?
4. What would the elasticity be if sales had dropped to 100 cupcakes instead of 150?
5. How can Sarah use this elasticity information to optimize her pricing strategy?

Tip:

Understanding price elasticity helps businesses decide on pricing strategies by showing how sensitive consumers are to price changes.