Renee wants to start offering online music lessons and needs to decide how much to charge for a one hour session in order to compete effectively with in-person music lessons. Based on Renee's understanding of the total market for online and in-person music lessons, she predicts that at a price of $40 per session, demand for her online lessons would be 20% of the total market, while at a price of $60 per lesson, demand would be 5% of the total market. It cannot be assumed that the demand curve is linear. Calculate the midpoint price elasticity of demand for online music lessons. Round your answer to the nearest two decimal places, giving a positive value for elasticity.
Question
Renee wants to start offering online music lessons and needs to decide how much to charge for a one hour session in order to compete effectively with in-person music lessons. Based on Renee's understanding of the total market for online and in-person music lessons, she predicts that at a price of 60 per lesson, demand would be 5% of the total market. It cannot be assumed that the demand curve is linear.
Calculate the midpoint price elasticity of demand for online music lessons. Round your answer to the nearest two decimal places, giving a positive value for elasticity.
Solution
The midpoint price elasticity of demand is calculated using the formula:
Elasticity = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))
Where: Q1 is the initial quantity demanded, Q2 is the final quantity demanded, P1 is the initial price, and P2 is the final price.
In this case, we have:
Q1 = 20% of the total market Q2 = 5% of the total market P1 = 60
Substituting these values into the formula, we get:
Elasticity = ((0.05 - 0.20) / ((0.05 + 0.20) / 2)) / ((60 - 40) / ((60 + 40) / 2))
Solving the above equation, we get:
Elasticity = -1.5 / 0.5 = -3
Since we are asked to provide a positive value for elasticity, we take the absolute value of -3, which is 3. Therefore, the midpoint price elasticity of demand for online music lessons is 3.00.
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