If the price elasticity of demand for a good is - 4.0, then a 10 percent increase in price would result in a

The price elasticity of demand (PED) measures how the quantity demanded of a good responds to changes in its price. It is calculated using the formula:

\[
\text{Price Elasticity of Demand (PED)} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}
\]

Given that the PED for this good is \(-4.0\) and there is a 10% increase in price, we want to determine the resulting percentage change in quantity demanded.

### Step-by-step solution:

1. **Identify the given values:**
   - PED = \(-4.0\)
   - \(\% \text{ change in price} = +10\%\)

2. **Rearrange the formula to find the percentage change in quantity demanded:**

   \[
   \% \text{ change in quantity demanded} = \text{PED} \times \% \text{ change in price}
   \]

3. **Substitute the given values:**

   \[
   \% \text{ change in quantity demanded} = -4.0 \times 10\%
   \]

4. **Calculate the result:**

   \[
   \% \text{ change in quantity demanded} = -40\%
   \]

### Conclusion:

A 10% increase in the price of this good would result in a 40% decrease in the quantity demanded. The negative sign indicates that the quantity demanded moves in the opposite direction of the price change, which is typical for most goods.

Would you like more details or have any questions about this explanation?

Here are 5 related questions to consider:
1. What does a PED value greater than 1 (in absolute terms) indicate about a good's demand?
2. How would a PED of \(-0.5\) affect quantity demanded if the price increases by 10%?
3. What are some factors that might influence the price elasticity of demand for a product?
4. How does the concept of elasticity relate to revenue changes for a business?
5. What is the difference between elastic and inelastic demand?

**Tip:** A product with a higher absolute value of PED (e.g., -4) is considered highly elastic, meaning that consumers are very responsive to price changes.

Explore how a 10% price increase for a good with a price elasticity of demand of -4.0 results in a 40% decrease in quantity demanded. Understand the price elasticity formula and how it impacts consumer demand. Suitable for high school economics students.

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