Final answer:
a. The price elasticity when the price changes from $6 to $5 is 2.2.
b. The price elasticity when the price changes from $4 to $5 is -18.
c. The range of price that makes total revenue increase when the price increases is when the price is below $4.
d. The price that yields the highest total revenue is $5.
Step-by-step explanation:
a. To compute the price elasticity when the price changes from $6 to $5, we will use the midpoint elasticity formula. The formula is Price Elasticity = (Change in Quantity / Average Quantity) / (Change in Price / Average Price).
Average Quantity = (Q1 + Q2) / 2 = (120 + 80) / 2 = 100
Change in Quantity = Q2 - Q1 = 80 - 120 = -40
Average Price = (P1 + P2) / 2 = (6 + 5) / 2 = 5.5
Change in Price = P2 - P1 = 5 - 6 = -1
Using the given values, we can calculate the price elasticity:
Price Elasticity = (-40 / 100) / (-1 / 5.5) = 2.2
b. To compute the price elasticity when the price changes from $4 to $5, we will use the same formula. Using the given values:
Average Quantity = (Q1 + Q2) / 2 = (120 + 80) / 2 = 100
Change in Quantity = Q2 - Q1 = 80 - 120 = -40
Average Price = (P1 + P2) / 2 = (4 + 5) / 2 = 4.5
Change in Price = P2 - P1 = 5 - 4 = 1
Price Elasticity = (-40 / 100) / (1 / 4.5) = -18
c. To determine the range of price that makes total revenue increase when the price increases, we need to consider the price elasticity. When the price elasticity is greater than 1, total revenue will increase when the price increases. From part b, we can see that the price elasticity was -18, which is less than 1.
Therefore, the range of price that makes total revenue increase when the price increases is when the price is below $4.
d. The price that yields the highest total revenue can be found when the price elasticity is 1. This means that total revenue is maximized at that price. From part a, we found that the price elasticity was 2.2, which is greater than 1. Therefore, the price that yields the highest total revenue is when the price is $5.