Final answer:
The elasticity of demand at a price of $10 is -1.6. This indicates that the demand is elastic, as the absolute value is greater than 1, meaning the quantity demanded will change significantly with a change in price.
Step-by-step explanation:
The student's question involves finding the elasticity of demand for a product given a specific demand curve, q = 900 - 4p², at a price of $10, and determining if the demand is elastic, inelastic, or neither at that price point.
Calculating Elasticity of Demand
The price elasticity of demand (PED) is calculated using the formula:
PED = (dq/dp) * (p/q)
Where:
- dq/dp is the derivative of the demand with respect to the price.
- p is the price.
- q is the quantity demanded at that price.
We first calculate the derivative of the demand curve:
dq/dp = -8p
At a price of $10, we calculate q:
q = 900 - 4(10)² = 500
Substitute these values into the PED formula:
PED = (-8 * 10) * (10 / 500) = -1.6
The absolute value of the elasticity is 1.6, which indicates the demand is elastic, since the value is greater than 1.