Final answer:
The elasticity of demand at a price of $11 for the demand function D(p) = -8p + 221 is calculated to be 0.662, indicating that demand is inelastic at this price point.
Step-by-step explanation:
In the given scenario, the elasticity of demand at a price of $11 is calculated using the formula: Elasticity = (p/q) * (dD/dp), where p is the price, q is the quantity, and dD/dp is the derivative of the demand function. The demand function D(p) = -8p + 221 yields a derivative of -8, as it is a linear function. Substituting the price p = $11 into the demand function, we find D($11) = 133.
Calculating the elasticity at p = $11, we get Elasticity = (11/133) * (-8) = -0.662. Taking the absolute value, the elasticity is 0.662, indicating an inelastic demand. The demand curve is inelastic because the elasticity value is less than one, suggesting that the percentage change in quantity demanded is less than the percentage change in price, emphasizing a relatively unresponsive consumer demand to price fluctuations.