The demand curve for haircuts at Terry Bernard'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 condering raising her price above the current price of $15. Terry is unwilling to raise price if the price hike will cause revenues to fall. Should Terry raise the price of haircuts above $15 Why or why not? 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?"

Question

The demand curve for haircuts at Terry Bernard'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 condering raising her price above the current price of $15. Terry is unwilling to raise price if the price hike will cause revenues to fall. Should Terry raise the price of haircuts above $15 Why or why not? 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?"

Answer 1

The demand curve for haircuts at Terry Bernard'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. Terry is unwilling to raise price if price hike will cause revenues to fall. Should Terry raise the price of haircuts above $15? Why or why not?

Answer 2

Increase in price will increase revenue if demand is inelastic . Hence , if demand is inelastic , He should increase the price .

Answer 3

To determine whether Terry should raise the price of haircuts above $15, we need to analyze the impact on revenues.

1. Demand curve: P = 20 - 0.20Q

To find the quantity demanded at the current price of $15, we substitute P = 15 into the equation:

15 = 20 - 0.20Q
0.20Q = 20 - 15
0.20Q = 5
Q = 5 / 0.20
Q = 25

So currently, Terry sells 25 haircuts per week at a price of $15.

Now, let's calculate the total revenue (TR) at the current price:

TR = P * Q
TR = 15 * 25
TR = $375

If Terry were to raise the price above $15, the demand equation becomes:

P = 20 - 0.20Q

However, Terry is unwilling to raise price if it causes revenues to fall. Since Terry's current revenue is $375, raising the price should result in a higher revenue. Therefore, Terry should consider raising the price above $15.

Now, let's consider the scenario where the demand increases to P = 40 - 0.40Q.

Using the same approach as above, we find that the quantity demanded at a price of $15 is:

15 = 40 - 0.40Q
0.40Q = 40 - 15
0.40Q = 25
Q = 25 / 0.40
Q = 62.5

So currently, Terry sells 62.5 haircuts per week at a price of $15.

The current revenue at $15 is:

TR = P * Q
TR = 15 * 62.5
TR = $937.5

Again, Terry should only consider raising the price if it leads to higher revenue. Since the current revenue is already $937.5, there is no need to raise the price at $15.

Answer 4

To determine whether Terry should raise the price of haircuts above $15, we need to analyze the impact of a price hike on revenues.

First, let's use the demand curve equation P = 20 - 0.20Q to calculate the current quantity demanded at a price of $15.

$15 = 20 - 0.20Q

0.20Q = 5

Q = 25

So, currently, Terry sells 25 haircuts per week.

Now, let's consider two scenarios:

Scenario 1: Price increases above $15 using the current demand curve (P = 20 - 0.20Q)

If Terry raises the price above $15, it means the new price (let's call it P') will be greater than $15. However, to determine whether raising the price will cause revenues to fall, we need to compare the new revenue (P' × Q) with the current revenue ($15 × 25).

Let's assume P' = $X, where X is the new price. Therefore, the new revenue can be calculated as X × Q.

New revenue = (20 - 0.20Q) × Q

By substituting Q = 25 (the current quantity) into the equation above, we can evaluate the new revenue:

New revenue = (20 - 0.20 × 25) × 25 = (20 - 5) × 25 = 15 × 25 = $375

Now, if the new revenue ($375) is greater than the current revenue ($15 × 25 = $375), then Terry should raise the price. However, if the new revenue is less than or equal to the current revenue, Terry should not raise the price.

In this case, since the new revenue is equal to the current revenue ($375 = $375), Terry should not raise the price of haircuts above $15.

Scenario 2: Price remains at $15, but the demand curve changes (P = 40 - 0.40Q)

Using the new demand curve equation, we can evaluate the quantity demanded (Q) at a price of $15.

$15 = 40 - 0.40Q

0.40Q = 40 - 15

0.40Q = 25

Q = 62.5

Since the quantity cannot be fractional (and we assume a whole number of haircuts), Terry can still sell 62 haircuts per week.

In this case, Terry should not raise the price of haircuts above $15 because the current revenue ($15 × 62 = $930) is higher than the new revenue (P' × Q) from a price above $15.

So, to summarize:
- With the current demand curve, Terry should not raise the price above $15.
- If the demand curve changes to P = 40 - 0.40Q, Terry should still not raise the price above $15.