If the price elasticity of demand for used cars priced between $4,000 and $6,000 is −0.75 (using the mid-point method), what will be the percentage change in the quantity demanded when the price of a used car falls from $6,000 to $4,000?

**Instructions:** Round your answer to the nearest whole number.

____ percent

To find the percentage change in the quantity demanded when the price of a used car falls from $6,000 to $4,000, we'll use the price elasticity of demand formula:

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

Given:
- Price elasticity of demand ($ E_d $) = −0.75
- Initial price ($ P_1 $) = $6,000
- Final price ($ P_2 $) = $4,000

First, calculate the percentage change in price using the midpoint method:

\[
\%\ \text{change in price} = \frac{P_2 - P_1}{\frac{P_1 + P_2}{2}} \times 100
\]

Substitute the values:

\[
\%\ \text{change in price} = \frac{4000 - 6000}{\frac{6000 + 4000}{2}} \times 100
= \frac{-2000}{5000} \times 100
= -40\%
\]

Now, use the elasticity formula to find the percentage change in quantity demanded:

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

Rearranging the formula to solve for the percentage change in quantity demanded:

\[
\%\ \text{change in quantity demanded} = E_d \times \%\ \text{change in price}
= -0.75 \times -40 = 30\%
\]

Thus, the percentage change in the quantity demanded is **30%**.

Would you like further details or have any questions?

Here are five related questions to expand on the topic:

1. How does price elasticity of demand differ for different products?
2. What is the midpoint method, and why is it used in elasticity calculations?
3. How would the quantity demanded change if the elasticity were greater than 1?
4. What factors influence the price elasticity of demand for a product?
5. How does price elasticity affect a company's pricing strategy?

**Tip:** A negative elasticity value indicates that the demand decreases when the price increases, which is common for most goods.

If the price elasticity of demand for used cars priced between $4,000 and $6,000 is −0.75 (using the mid-point method), what will be the percentage change in the quantity demanded when the price of a used car falls from $6,000 to $4,000?

Understand how to calculate the percentage change in quantity demanded using the price elasticity of demand for used cars priced between $4,000 and $6,000. This example uses the mid-point method and involves detailed steps with a final answer of a 30% increase in demand.

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