Asked by Khristy Ramirez on Jul 08, 2024
Verified
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.
Elasticity of Demand
An indicator of the degree to which demand for a product changes in response to a variation in its price, shown as a percentage.
- Investigate the link between price elasticity of demand and the strategies for setting prices in monopolistic markets.
Verified Answer
SB
Sabino BoyzoJul 14, 2024
Final Answer :
D
Explanation :
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/(3 + 2)2 = 3,000/(9S1 + S1) = 250
Qd at $3.10 = 3,000/(3.1 + 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, 1.60.
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/(3 + 2)2 = 3,000/(9S1 + S1) = 250
Qd at $3.10 = 3,000/(3.1 + 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, 1.60.
Learning Objectives
- Investigate the link between price elasticity of demand and the strategies for setting prices in monopolistic markets.