The weekly sales of an item is given by $$ q=45-4 p^{2} $$. Find the price elasticity of the demand function in terms of the price. $$ E(p)= $$

Question

UpStudy AI · Accepted Answer

The price elasticity of demand $$ E(p) $$ measures how sensitive the quantity demanded is to a change in price. It is defined as:

$$
E(p) = \frac{dq}{dp} \times \frac{p}{q}
$$

Given the demand function:

$$
q = 45 - 4p^2
$$

1. **Differentiate $$ q $$ with respect to $$ p $$:**

$$
\frac{dq}{dp} = -8p
$$

2. **Substitute $$ \frac{dq}{dp} $$ and $$ q $$ into the elasticity formula:**

$$
E(p) = (-8p) \times \frac{p}{45 - 4p^2} = \frac{-8p^2}{45 - 4p^2}
$$

**Final Expression for Price Elasticity of Demand:**

$$
E(p) = \frac{-8p^{2}}{45 - 4p^{2}}
$$

Answer:
After simplifying, elasticity is –8 p² divided by (45 minus four p²). Thus,

E(p) = −8 p² ⁄ (45 − 4p²)
E(p) = $$\frac{-8p^{2}}{45 - 4p^{2}}$$

The weekly sales of an item is given by \( q=45-4 p^{2} \). Find the price elasticity of the demand function in terms of the price. \( E(p)= \)