Calculate the mid-point elasticity of demand. 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 b)Explain how the discount will affect the total revenue in each group.
To calculate the mid-point elasticity of demand, we can use the following formula:
Elasticity of Demand = [(Q2 - Q1) / ((Q2 + Q1) / 2)] / [(P2 - P1) / ((P2 + P1) / 2)]
a)
For Group A:
Q1 = $1.55 million per week
Q2 = $1.65 million per week
P1 = Original price before the discount
P2 = New price after the discount
For Group B:
Q1 = $1.50 million per week
Q2 = $1.70 million per week
P1 = Original price before the discount
P2 = New price after the discount
b)
To determine the effect of the discount on total revenue for each group, we need to consider the elasticity of demand. If the elasticity is greater than 1 (elastic demand), a price decrease will increase total revenue. If the elasticity is less than 1 (inelastic demand), a price decrease will decrease total revenue.
Let's calculate the mid-point elasticity of demand for both groups.
For Group A:
P1 = ?
P2 = P1 - 10% of P1 = P1 * (1 - 0.10) = 0.9P1
Elasticity of Demand for Group A = [(Q2 - Q1) / ((Q2 + Q1) / 2)] / [(P2 - P1) / ((P2 + P1) / 2)]
Substituting the given values:
[(1.65 - 1.55) / ((1.65 + 1.55) / 2)] / [((0.9P1) - P1) / ((0.9P1 + P1) / 2)]
Simplifying:
[(0.1) / (1.6 / 2)] / [(0.1P1) / (1.9P1 / 2)] = 0.125 / 0.10526 = 1.1875
For Group B, the calculations are similar:
[(1.70 - 1.50) / ((1.70 + 1.50) / 2)] / [((0.9P1) - P1) / ((0.9P1 + P1) / 2)] = 0.2 / 0.10526 = 1.898
Therefore, the mid-point elasticity of demand for Group A is approximately 1.1875, and for Group B, it is approximately 1.898.
Based on these values, we can conclude that both groups have elastic demand, as the elasticities are greater than 1.
For elastic demand, a decrease in price will lead to an increase in total revenue. Thus, offering a 10% discount will increase the total revenue for both Group A and Group B.
a) To calculate the mid-point elasticity of demand, we need to use the following formula:
Mid-point Elasticity = (Percentage Change in Quantity Demanded) / (Percentage Change in Price)
For Group A:
Percentage Change in Quantity Demanded = ((New Quantity - Old Quantity) / ((New Quantity + Old Quantity) / 2)) * 100
= ((1.65 - 1.55) / ((1.65 + 1.55) / 2)) * 100
= (0.10 / 1.60) * 100
= 6.25%
Percentage Change in Price = 10% (since a 10% discount was applied)
Mid-point Elasticity for Group A = (6.25% / 10%) = 0.625
For Group B:
Percentage Change in Quantity Demanded = ((New Quantity - Old Quantity) / ((New Quantity + Old Quantity) / 2)) * 100
= ((1.70 - 1.50) / ((1.70 + 1.50) / 2)) * 100
= (0.20 / 1.60) * 100
= 12.5%
Percentage Change in Price = 10% (since a 10% discount was applied)
Mid-point Elasticity for Group B = (12.5% / 10%) = 1.25
b) The mid-point elasticity of demand measures the responsiveness of quantity demanded to changes in price. A value greater than 1 indicates elastic demand, meaning that a small change in price leads to a relatively larger change in quantity demanded. A value less than 1 indicates inelastic demand, where changes in price have a relatively smaller impact on quantity demanded.
For Group A, the mid-point elasticity is 0.625, which is less than 1. This suggests that Group A has more inelastic demand. Therefore, a 10% discount will lead to a proportionally smaller increase in sales for Group A.
For Group B, the mid-point elasticity is 1.25, which is greater than 1. This suggests that Group B has more elastic demand. Therefore, a 10% discount will lead to a proportionally larger increase in sales for Group B.
In terms of total revenue, the effect of the discount will depend on the elasticity of demand. For Group A, since the demand is inelastic, the increase in sales due to the discount may not fully offset the decrease in price, resulting in a potential decrease in total revenue. For Group B, since the demand is elastic, the increase in sales due to the discount may more than offset the decrease in price, resulting in a potential increase in total revenue.
In summary, the discount is expected to have a different impact on total revenue for each group, with the potential for a decrease in Group A and a potential increase in Group B.