The demand for a monopolist's output is 3,000/(p + 2)², where p is the price it charges.At a price of $3, the elasticity of demand for the monopolist's output is A)-1. B)-2.60. C)-2.10. D)-1.60. E)-1.10.

Question

Quizplus · Accepted Answer

To find the elasticity of demand at a price of $3, we need to use the following formula: Elasticity of demand = (% change in quantity demanded)/(% change in price) To calculate the % change in quantity demanded, we need to find Qd at two different prices, say $3 and $3.10: Qd at $3 = 3,000/(3F1F1F1S1 + F1F1F10 2)² = 3,000/(9S1 + S1) = 250 Qd at $3.10 = 3,000/(3.1F1F1F1S1 + F1F1F10 2)² = 3,000/(9.31S1 + S1) = 241.39 % change in quantity demanded = [(Qd at $3.10 - Qd at $3)/Qd at $3] * 100% = [(241.39 - 250)/250] * 100% = -3.44% To calculate the % change in price, we need to use the initial price of $3: % change in price = [(new price - old price)/old price] * 100% = [(3.10 - 3)/3] * 100% = 3.33% Now we can calculate the elasticity of demand: Elasticity of demand = (% change in quantity demanded)/(% change in price) = -3.44%/3.33% = -1.03 Since the absolute value of elasticity is greater than 1, the demand is elastic. To find the numerical value of the elasticity, we need to multiply it by the price: Numerical value of elasticity = -1.03 * $3 = -$3.09 The correct answer is D, F1F1F1S1F1F1F101.60.

The Demand for a Monopolist's Output Is 3,000/(p + 2)2

The Demand for a Monopolist's Output Is 3,000/(p + 2)²