The point elasticity of demand measures the responsiveness of the quantity demanded to a change in price. It is given by the formula:

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

Where:

• $\%\ \text{change in quantity demanded} = \frac{\text{new quantity} - \text{old quantity}}{\text{old quantity}} \times 100$
• $\%\ \text{change in price} = \frac{\text{new price} - \text{old price}}{\text{old price}} \times 100$

Step 1: Calculate the percentage change in quantity demanded

The initial quantity (old quantity) is 200 cupcakes, and the new quantity is 150 cupcakes.

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

Step 2: Calculate the percentage change in price

The initial price (old price) is R2, and the new price is R2.50.

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

Step 3: Calculate the point elasticity of demand

Now, we can substitute the values into the elasticity formula:

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

Conclusion:

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

Would you like further clarification or details?

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Here are 5 related questions for further exploration:

1. How does the concept of elasticity affect Sarah’s pricing decisions?
2. What factors could influence the elasticity of demand for cupcakes?
3. If Sarah reduced the price to R1.50, what could happen to demand based on this elasticity?
4. How can Sarah determine the optimal price to maximize revenue?
5. How does price elasticity differ from income elasticity of demand?

Tip: Inelastic demand (|E| < 1) means consumers are less sensitive to price changes, while elastic demand (|E| > 1) indicates high sensitivity to price changes.