Question

The demand curve for haircuts at Terry Bernard’s Hair Design is Q = 100 – 5P 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 the price hike will cause revenues to fall. a. Should Terry raise the price of haircuts above $15? Why or why not? b. Suppose demand for Terry’s haircuts increases to Q = 100 – 2.5P. At a price of $15, should Terry raise the price of her haircuts? Why or why not?

Answer 1

(a)

Substitute p in demand function

$Q=100-5p\\=100-5(15)\\=100-75\\=25$

Price elasticity of demand$=\frac{\Delta Q}{\Delta p}$

$=\frac{25}{15}=1.67$

The price elasticity of demand is elastic. For elastic demand total revenue and price have negative relationship. An increase an price lowers the total revenue so Terry should not raise the price.

(b)

Here we calculate the marginal revenue at the price of $15 to determine whether Terry should raise the price or not

$Q=100-2.5p\\2.5p=100-Q\\Q=40-0.4Q$

Revenue will be calculated as

$= P\times Q\\ = P \times (100 - 2.5P) \\ = 100P - 2.5 P^{2}$

$MR = 100 - 5P$

At a price of $15, $MR = 100 - 5(15) = 25$ ,

Terry should raise the price above $15 to increase revenues as marginal revenue is positive.