Final answer:
The point elasticity of demand for the product when q = 5 is -5.5. This is calculated by first finding the derivative of the demand function and then using the price elasticity formula, taking into account the price and quantity at q = 5.
Step-by-step explanation:
The point elasticity of demand for the manufacturer's product when q = 5 can be determined by applying the elasticity formula: the percentage change in quantity demanded divided by the percentage change in price. To compute this, we first find the derivative of the demand function p = 300 - q² with respect to q, which gives us -2q. The price elasticity of demand at a specific point is calculated using the formula: Elasticity (E) = (p/q) × (dq/dp)
Where:
- “p/q” is the price divided by the quantity,
- “dq/dp” is the derivative of quantity with respect to price, which is the reciprocal of the derivative of price with respect to quantity since dp/dq = -2q.
At q = 5, the price p is given by the demand function as:p = 300 - q² = 300 - 5² = 300 - 25 = 275
The point elasticity of demand at q = 5: E = (275 / 5) × (1 / -2 × 5) = 55 × (-1/10) = -5.5
Therefore, the point elasticity of demand when q = 5 is -5.5.