The demand curve for haircuts at Terry’s Hair Design is P=20-0.20Q
Where Q is the number of cuts per week and P is the price of a haircut. Terry is considering raising her price above the current price of $15.00. Terry is unwilling to raise price if the price hike will cause revenues to fall.
a. Should Terry raise the price of haircuts above$15.00? Why or why not?
b. Suppose demand for Terry’s haircuts increases to P=40 – 0.40Q. At a price of 15, should Terry raise the price of her haircuts? Why or why not?
To determine whether Terry should raise the price of haircuts, we need to analyze the impact on revenues first.
a. To analyze the impact on revenues, we need to find the current revenue and the potential revenue after the price hike.
The current price is $15, so we can substitute this value into the demand equation to find the current quantity demanded (Q):
P = 20 - 0.20Q
15 = 20 - 0.20Q
0.20Q = 20 - 15
0.20Q = 5
Q = 5 / 0.20
Q = 25
So the current quantity demanded (Q) is 25 haircuts per week.
To find the current revenue, we multiply the price by the quantity:
Current Revenue = Price * Quantity
Current Revenue = $15 * 25
Current Revenue = $375
Now let's analyze the potential revenue after the price hike. Let's assume Terry raises the price to $x. We can substitute this value into the demand equation:
P = 20 - 0.20Q
x = 20 - 0.20Q
To determine whether the price hike would cause the revenues to fall or not, we need to calculate the new quantity (Q) at the new price (x).
Given the demand equation, we can rearrange it to solve for Q:
Q = (20 - x) / 0.20
Now let's calculate the new quantity demanded for different price levels:
For x = $15 (current price):
Q = (20 - 15) / 0.20
Q = 5 / 0.20
Q = 25
For x = $15 + $1 (hypothetical price hike):
Q = (20 - 16) / 0.20
Q = 4 / 0.20
Q = 20
For x = $20:
Q = (20 - 20) / 0.20
Q = 0 / 0.20
Q = 0
Now, let's calculate the potential revenue at each price level:
For x = $15 (current price):
Potential Revenue = x * Q
Potential Revenue = $15 * 25
Potential Revenue = $375
For x = $15 + $1 (hypothetical price hike):
Potential Revenue = x * Q
Potential Revenue = $16 * 20
Potential Revenue = $320
For x = $20:
Potential Revenue = x * Q
Potential Revenue = $20 * 0
Potential Revenue = $0
Now, let's compare the potential revenue with the current revenue:
For x = $15 (current price):
Potential Revenue ($375) is the same as Current Revenue ($375).
For x = $15 + $1 (hypothetical price hike):
Potential Revenue ($320) is lower than Current Revenue ($375).
For x = $20:
Potential Revenue ($0) is lower than Current Revenue ($375).
Therefore, Terry should not raise the price of haircuts above $15 because it would result in a decrease in revenues.
b. Now let's consider the new demand equation where P = 40 - 0.40Q
Using the same process as above, we can analyze the impact on revenues at a price of $15:
Q = (40 - 15) / 0.40
Q = 25 / 0.40
Q = 62.5
For x = $15:
Potential Revenue = x * Q
Potential Revenue = $15 * 62.5
Potential Revenue = $937.50
Comparing the potential revenue ($937.50) with the current revenue ($375), it is evident that the potential revenue is significantly higher. Therefore, Terry should consider raising the price as it would lead to an increase in revenues.