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We are given the demand function $ q = 2400p^{-0.4} $ and a price of $ p = 11 $. We need to calculate the elasticity of demand $ \varepsilon $, which is defined as:

\[
\varepsilon = \left( \frac{dq}{dp} \cdot \frac{p}{q} \right)
\]

### Step-by-step solution:

1. **Find the derivative $ \frac{dq}{dp} $:**
   The demand function is $ q = 2400p^{-0.4} $, so we differentiate it with respect to $ p $:

   \[
   \frac{dq}{dp} = 2400 \cdot (-0.4) \cdot p^{-1.4}
   \]
   Simplifying:
   \[
   \frac{dq}{dp} = -960 p^{-1.4}
   \]

2. **Substitute $ p = 11 $ into the demand function:**
   Now, we find the quantity $ q $ when $ p = 11 $:

   \[
   q = 2400 \cdot (11)^{-0.4}
   \]
   Using a calculator:
   \[
   q \approx 2400 \cdot 0.5156 = 1237.44
   \]

3. **Substitute $ p = 11 $ into $ \frac{dq}{dp} $:**
   Now, substitute $ p = 11 $ into the derivative:

   \[
   \frac{dq}{dp} = -960 \cdot (11)^{-1.4}
   \]
   Using a calculator:
   \[
   \frac{dq}{dp} \approx -960 \cdot 0.3865 = -370.06
   \]

4. **Calculate the elasticity of demand $ \varepsilon $:**
   Now, use the formula for elasticity:

   \[
   \varepsilon = \frac{dq}{dp} \cdot \frac{p}{q} = -370.06 \cdot \frac{11}{1237.44}
   \]

   Using a calculator:

   \[
   \varepsilon \approx -370.06 \cdot 0.00889 = -3.29
   \]

### Conclusion:
- The elasticity of demand is approximately $ \varepsilon = -3.29 $.
- Since $ |\varepsilon| > 1 $, the demand is **elastic**.

Would you like further details or clarifications?

Here are 5 questions related to elasticity of demand:
1. What factors influence whether a product has elastic or inelastic demand?
2. How does elasticity affect a firm's pricing strategy?
3. What is the difference between price elasticity of demand and income elasticity of demand?
4. How can businesses use elasticity to predict changes in revenue?
5. Can elasticity change at different price points?

**Tip:** Elasticity is often higher for luxury goods than for necessities, as consumers are more sensitive to price changes in non-essential items.

Find the elasticity of demand for a product if the demand function is q = 2400p^(-0.4) and each unit of the product is currently selling for $11. Round to 2 decimal places, if necessary.

Learn how to calculate the elasticity of demand for a product where the demand function is q = 2400p^(-0.4) and the price is $11. Step-by-step breakdown, including differentiation and elasticity formula. Ideal for economics or calculus students.

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