Use the price-demand equation below to find , the elasticity of demand.

Ask by Dawson Johnston. in the United States

Nov 24,2024

Question

Use the price-demand equation below to find $$ E(p) $$, the elasticity of demand. $$ \quad x=f(p)=5200-4 p^{2} $$

UpStudy AI · Accepted Answer

To find the elasticity of demand $$ E(p) $$ using the price-demand equation $$ x = f(p) = 5200 - 4p^2 $$, we can use the formula for elasticity of demand:

$$
E(p) = \frac{dx/dp}{x/p}
$$

where $$ x $$ is the quantity demanded and $$ p $$ is the price.

### Step 1: Find $$ \frac{dx}{dp} $$

First, we need to differentiate $$ f(p) $$ with respect to $$ p $$:

$$
f(p) = 5200 - 4p^2
$$

Taking the derivative:

$$
\frac{dx}{dp} = \frac{d}{dp}(5200 - 4p^2) = -8p
$$

### Step 2: Substitute $$ x $$ and $$ \frac{dx}{dp} $$ into the elasticity formula

Now we can substitute $$ x $$ and $$ \frac{dx}{dp} $$ into the elasticity formula:

$$
E(p) = \frac{-8p}{(5200 - 4p^2)/p}
$$

### Step 3: Simplify the expression

We can simplify the expression:

$$
E(p) = \frac{-8p^2}{5200 - 4p^2}
$$

### Final Expression for Elasticity of Demand

Thus, the elasticity of demand $$ E(p) $$ is given by:

$$
E(p) = \frac{-8p^2}{5200 - 4p^2}
$$

This expression represents the elasticity of demand in terms of the price $$ p $$.
The elasticity of demand $$ E(p) $$ is given by $$ E(p) = \frac{-8p^2}{5200 - 4p^2} $$.

Use the price-demand equation below to find , the elasticity of demand.

Upstudy AI Solution

Answer

Solution

Step 1: Find

Step 2: Substitute and into the elasticity formula

Step 3: Simplify the expression

Final Expression for Elasticity of Demand

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