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 elasticity formula **Price Elasticity** is given by \( E(p) = \left(\frac{dq}{dp}\right) \cdot \frac{p}{q} \). 3. Substitute values into elasticity formula Substitute \( \frac{dq}{dp} = -8p \), \( q = 60 - 4p^2 \) into the formula: \( E(p) = (-8p) \cdot \frac{p}{60 - 4p^2} \). 4. Simplify the expression 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 elasticity formula<br /> **Price Elasticity** is given by \( E(p) = \left(\frac{dq}{dp}\right) \cdot \frac{p}{q} \).<br />3. Substitute values into elasticity formula<br /> Substitute \( \frac{dq}{dp} = -8p \), \( q = 60 - 4p^2 \) into the formula: \( E(p) = (-8p) \cdot \frac{p}{60 - 4p^2} \).<br />4. Simplify the expression<br /> Simplify: \( E(p) = \frac{-8p^2}{60 - 4p^2} \).
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