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)
So do you need help figuring out the steps you must take to solve the problem? Do you have an answer already that you want checked?
To calculate the mid-point elasticity of demand, we can use the following formula:
Price Elasticity of Demand = (ΔQ/((Q1+Q2)/2)) / (ΔP/((P1+P2)/2))
Where:
- ΔQ represents the change in quantity demanded
- Q1 and Q2 represent the initial and final quantities demanded, respectively
- ΔP represents the change in price
- P1 and P2 represent the initial and final prices, respectively
In this case, we have the following information:
- For Group A:
- Q1 = $1.55 million
- Q2 = $1.65 million
- ΔQ = Q2 - Q1 = $1.65 million - $1.55 million = $0.10 million
- For Group B:
- Q1 = $1.50 million
- Q2 = $1.70 million
- ΔQ = Q2 - Q1 = $1.70 million - $1.50 million = $0.20 million
- The discount is 10%, which means ΔP = 0.10P1
Now let's calculate the mid-point elasticity of demand for both Group A and Group B:
a) Group A:
- P1 = $1.00 (100% of the original price)
- P2 = $0.90 (90% of the original price)
- ΔP = 0.10 * $1.00 = $0.10
Using the formula mentioned above, we have:
Price Elasticity of Demand (Group A) = (0.10 / ((1.55 + 1.65) / 2)) / (0.10 / ((1.00 + 0.90) / 2))
b) Group B:
- P1 = $1.00 (100% of the original price)
- P2 = $0.90 (90% of the original price)
- ΔP = 0.10 * $1.00 = $0.10
Using the formula mentioned above, we have:
Price Elasticity of Demand (Group B) = (0.20 / ((1.50 + 1.70) / 2)) / (0.10 / ((1.00 + 0.90) / 2))
To calculate the total revenue effect of the discount in each group, we need to determine the direction of demand elasticity.
- If the price elasticity of demand is greater than 1, demand is elastic, and a price decrease will increase total revenue.
- If the price elasticity of demand is less than 1, demand is inelastic, and a price decrease will decrease total revenue.
- If the price elasticity of demand is exactly 1, demand is unit elastic, and a price decrease will not change total revenue.
Now let's analyze the results:
a) Group A:
- If the price elasticity of demand for Group A is greater than 1, the discount will increase total revenue.
- If the price elasticity of demand for Group A is less than 1, the discount will decrease total revenue.
- If the price elasticity of demand for Group A is equal to 1, the discount will not impact total revenue.
b) Group B:
- If the price elasticity of demand for Group B is greater than 1, the discount will increase total revenue.
- If the price elasticity of demand for Group B is less than 1, the discount will decrease total revenue.
- If the price elasticity of demand for Group B is equal to 1, the discount will not impact total revenue.
To determine the exact impact on total revenue, we need to calculate the percentage change in total revenue using the formula:
Percentage Change in Total Revenue = Percentage Change in Quantity Demanded + Percentage Change in Price
By comparing the absolute values of the percentage changes in quantity demanded and price, we can determine the overall impact on total revenue.