Suppose Sarah initially sells her cupcakes for R2 each and observes that she sells
200 cupcakes per day. After increasing the price to R2.50, she notices a decrease in
sales to 150 cupcakes per day. Calculate the point elasticity of demand for Sarah's
cupcakes. (3 Marks)

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.

Suppose Sarah initially sells her cupcakes for R2 each and observes that she sells 200 cupcakes per day. After increasing the price to R2.50, she notices a decrease in sales to 150 cupcakes per day. Calculate the point elasticity of demand for Sarah's cupcakes. (3 Marks)

Discover how to calculate the point elasticity of demand for Sarah's cupcakes when prices rise from R2 to R2.50 and sales decrease from 200 to 150 units. This problem covers key economics concepts such as percentage change and demand elasticity. Suitable for Grades 10-12 students.

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