Calculate the mid-point elasticity of demand. Please review chapter 6 before taking this assignment. Question: The online bookseller wants to increase its total revenue by offering 10% discount on every book it sells.Its custmers are divided in 2 groups Group A and group B Volume of sales before the discount for Group A= sales for $1.55 million per week and for the Group B= sales for $ 1.50 million per week After the discount of 10% the volume of sales for the Goup A = $ 1.65 million and for the Group B= $1.70 million per week a) Using mid-point method,calculate the price elasticity of Demand both for group A and Group B ( 10 points) b)Explain how the discount will affect the total revenue in each group ( 10 points)
To calculate the mid-point elasticity of demand, we need to use the following formula:
E = [(Q2 - Q1) / ((Q1 + Q2) / 2)] / [(P2 - P1) / ((P1 + P2) / 2)]
Where:
E = Elasticity of Demand
Q1 = Initial quantity of sales
Q2 = Quantity of sales after the change
P1 = Initial price
P2 = Price after the change
For Group A:
Q1 = $1.55 million
Q2 = $1.65 million
P1 = 1 (since it represents 100% of the price)
P2 = 0.9 (10% discount = 90% of the original price)
Calculating the mid-point elasticity for Group A:
E = [(Q2 - Q1) / ((Q1 + Q2) / 2)] / [(P2 - P1) / ((P1 + P2) / 2)]
= [(1.65 - 1.55) / ((1.55 + 1.65) / 2)] / [((0.9 - 1) / ((1 + 0.9) / 2))]
= [(0.1) / (3.2)] / [(-0.1) / (1.45)]
= 0.03125 / -0.0689655
= -0.4531 (approximately)
For Group B:
Q1 = $1.50 million
Q2 = $1.70 million
P1 = 1 (since it represents 100% of the price)
P2 = 0.9 (10% discount = 90% of the original price)
Calculating the mid-point elasticity for Group B:
E = [(Q2 - Q1) / ((Q1 + Q2) / 2)] / [(P2 - P1) / ((P1 + P2) / 2)]
= [(1.70 - 1.50) / ((1.50 + 1.70) / 2)] / [((0.9 - 1) / ((1 + 0.9) / 2))]
= [(0.20) / (3.2)] / [(-0.1) / (1.45)]
= 0.0625 / -0.0689655
= -0.9063 (approximately)
b) To understand how the discount will affect the total revenue in each group, we need to consider the concepts of elasticity and the relationship between price and quantity.
The elasticity values for both Group A and Group B are negative, indicating that the demand is price-sensitive. A value greater than 1 indicates elastic demand, while a value less than 1 indicates inelastic demand.
For Group A, the elasticity is -0.4531, which means that a 1% decrease in price will lead to a 0.4531% increase in quantity demanded. This suggests that the demand for Group A is relatively inelastic, meaning customers are not very responsive to price changes.
For Group B, the elasticity is -0.9063, which means that a 1% decrease in price will lead to a 0.9063% increase in quantity demanded. This suggests that the demand for Group B is relatively more elastic than Group A, meaning customers are more responsive to price changes.
Now, to analyze how the discount will affect the total revenue for each group:
- For Group A, since the demand is relatively inelastic (-0.4531), reducing the price by 10% may not lead to a significant increase in quantity demanded. As a result, the total revenue might not increase significantly, or it could potentially decrease.
- For Group B, the demand is relatively more elastic (-0.9063), meaning customers are more responsive to price changes. Thus, reducing the price by 10% could lead to a larger increase in quantity demanded, resulting in a potential increase in total revenue.
It's important to note that these conclusions are based on the assumption that no other factors, such as competitors' actions or changes in customer preferences, influence demand or revenue.
Remember to review Chapter 6 for a more comprehensive understanding of elasticity of demand and its impact on total revenue.