QuestionJuly 16, 2025

The weekly sales of an item is given by q=60-4p^2 Find the price elasticity of the demand function in terms of the price. E(p)=square

The weekly sales of an item is given by q=60-4p^2 Find the price elasticity of the demand function in terms of the price. E(p)=square
The weekly sales of an item is given by q=60-4p^2 Find the price elasticity of the demand function in terms of the price. E(p)=square

Solution
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Answer

\( E(p) = \frac{-8p^2}{60 - 4p^2} \) Explanation 1. Find the derivative of demand function The demand function is \( q = 60 - 4p^2 \). Differentiate with respect to ( p ): \( \frac{dq}{dp} = -8p \). 2. Use the elasticity formula **Elasticity formula**: \( E(p) = \left( \frac{dq}{dp} \right) \cdot \left( \frac{p}{q} \right) \). 3. Substitute values into the formula Substitute \( \frac{dq}{dp} = -8p \), \( q = 60 - 4p^2 \) into the formula: \[ E(p) = (-8p) \cdot \left( \frac{p}{60 - 4p^2} \right) \] Simplify: \[ E(p) = \frac{-8p^2}{60 - 4p^2} \]

Explanation

1. Find the derivative of demand function<br /> The demand function is \( q = 60 - 4p^2 \). Differentiate with respect to ( p ): \( \frac{dq}{dp} = -8p \).<br />2. Use the elasticity formula<br /> **Elasticity formula**: \( E(p) = \left( \frac{dq}{dp} \right) \cdot \left( \frac{p}{q} \right) \).<br />3. Substitute values into the formula<br /> Substitute \( \frac{dq}{dp} = -8p \), \( q = 60 - 4p^2 \) into the formula: <br />\[ E(p) = (-8p) \cdot \left( \frac{p}{60 - 4p^2} \right) \]<br /> Simplify: <br />\[ E(p) = \frac{-8p^2}{60 - 4p^2} \]
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