Question

This question examines the market for mangos. You will use a demand function to construct the demand schedule, calculate the price elasticity of demand at different points along a linear demand curve, and identify the likely effects of price changes on total revenue.

Below, you are provided with the demand function for mangos. If you plug any price into the formula for the demand function, you get the quantity demanded at that price.
Q = 150 – 25P
Task 1. Use the table below to find the quantity of mangos demanded at each price.
Price Quantity of Mangos Demanded
$1
2
3
4
5
Task 2. Calculate the price elasticity of demand when the price falls from $5 to $4.
Task 3. When the price of a mango falls from $5 to $4, does total revenue fall or rise? How do you know?
Task 4. When the price of a mango falls from $3 to $2, does total revenue fall or rise?

Answer 1

Task 1. Use the table below to find the quantity of mangos demanded at each price.

For a price of $1, the quantity demanded of mangos is:

Q = 150 - 25 ($1)

Q = 125

For $2:

Q = 150 - 25 ($2)

Q = 150 - 50

Q = 100

For $3

Q = 150 - 25 ($3)

Q = 150 - 75

Q = 75

For $4

Q = 150 - 25 ($4)

Q = 150 - 100

Q = 50

For $5

Q = 150 - 25 ($5)

Q = 150 - 125

Q = 25

Task 2. Calculate the price elasticity of demand when the price falls from $5 to $4.

The formula is

Price Elasiticy of Demand (PED) = ((Q2 - Q1) / (Q2 + Q1) / 2 ) / ((P2 - P1) / ((P2 + P1) / 2)

Now, we plug the amounts into the formula

PED = ((50 - 25) / (50 + 25) / 2) / ((4 - 5) / (4 + 5) / 2)

PED = 0.1666 / -0.0556

PED = -3

We take the absolute value, 3, which is a PED higher than 1, meaning that demand is elastic: the quantity demanded in this case increased more than the price.

Task 3. When the price of a mango falls from $5 to $4, does total revenue fall or rise? How do you know?

Revenue = Price x Quantity

Under the first scenario, revenue = $5 x 25 = $125

Under the second scenario, revenue = $4 x 50 = $200

So revenue increased by $75.

Task 4. When the price of a mango falls from $3 to $2, does total revenue fall or rise?

First scenario = $3 x 75 = $225

Second scenario = $2 x 100 = 200

So revenue actually falls by $25.