Given the demand function $D(p)=\frac{300}{p}$ Find the Elasticity of Demand at a price of $\$ 63$

Step 1 ：Given the demand function \(D(p)=\frac{300}{p}\), we are asked to find the elasticity of demand at a price of $63.

Step 2 ：The elasticity of demand (E) is calculated using the formula: \(E = p \cdot \frac{D'(p)}{D(p)}\), where \(D'(p)\) is the derivative of the demand function with respect to price.

Step 3 ：First, we find the derivative of the demand function, which is \(D'(p) = -\frac{300}{p^2}\).

Step 4 ：Then, we substitute the price \(p=63\) into the elasticity formula to find the elasticity of demand at this price.

Step 5 ：Doing so, we find that the elasticity of demand at a price of $63 is -1.

Step 6 ：This means that a 1% increase in price would lead to a 1% decrease in quantity demanded, and vice versa. This is characteristic of a unit elastic demand, where the percentage change in quantity demanded is exactly equal to the percentage change in price.

Step 7 ：Final Answer: The Elasticity of Demand at a price of $63 is \(\boxed{-1}\).