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

\[
\text{Elasticity of demand (E_d)} = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}}
\]

We can break down the steps as follows:

1. **Initial price (P₁):** R2.00
2. **New price (P₂):** R2.50
3. **Initial quantity demanded (Q₁):** 200 cupcakes
4. **New quantity demanded (Q₂):** 150 cupcakes

### Step 1: Calculate the percentage change in quantity demanded
\[
\%\ \text{change in quantity} = \frac{Q_2 - Q_1}{Q_1} \times 100 = \frac{150 - 200}{200} \times 100 = \frac{-50}{200} \times 100 = -25\%
\]

### Step 2: Calculate the percentage change in price
\[
\%\ \text{change in price} = \frac{P_2 - P_1}{P_1} \times 100 = \frac{2.50 - 2.00}{2.00} \times 100 = \frac{0.50}{2.00} \times 100 = 25\%
\]

### Step 3: Calculate the elasticity of demand
\[
E_d = \frac{-25\%}{25\%} = -1
\]

Thus, the point elasticity of demand is **-1**. This indicates that the demand for Sarah's cupcakes is unit elastic, meaning the percentage change in quantity demanded is exactly equal to the percentage change in price.

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Would you like further details or explanations on any part of the calculation? Here are five related questions that build on this:

1. What does it mean if the elasticity of demand is greater than or less than 1?
2. How does point elasticity differ from arc elasticity?
3. What factors could affect the elasticity of demand for Sarah's cupcakes?
4. How would total revenue change if the price elasticity of demand is elastic versus inelastic?
5. Can the point elasticity of demand ever be positive? Why or why not?

**Tip:** A negative elasticity of demand is typical because price and quantity demanded usually move in opposite directions.

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.

Learn how to calculate the point elasticity of demand for Sarah's cupcakes as she increases the price from R2 to R2.50, resulting in a decrease in daily sales from 200 to 150. This solution involves key economics concepts such as percentage change and price elasticity of demand. Suitable for high school or first-year university economics students.

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