Question

A local pizzeria sells 500 large pepperoni pizzas per week at a price of $20 each. Suppose the owner of the pizzeria tells you that the price elasticity of demand for his pizza is -4, and he asks you for advice. He wants to know two things. First, how many pizzas will he sell if he cuts his price by 10%? Second, how will his revenue be affected?

Answer 1

Answer: (1) 700 pizzas

(2) Its revenue increases by $2600.

Step-by-step explanation:

Given that,

price elasticity of demand for his pizza = -4

Percentage change in price = 10%

Initial Quantity,
`Q_(0)` = 500 Pizzas

Elasticity of demand =
`(Percentage\ change\ in\ quantity )/(Percentage\ change\ in\ price )`

-4 =
`(Percentage\ change\ in\ quantity )/(0.1 )`

`\frac{Percentage\ change\ in\ quantity }` = -4 × 0.1

`(Q_(1)-Q_(0))/(Q_(0))` = 0.4

`(Q_(1)-500)/(500)` = 0.4

∴
`Q_(1)` = 700

Initial price,
`P_(0)` = $20

Changed price,
`P_(1)` = $18

Revenue at t = 0

`P_(0) Q_(0)` = 500 × 20 =$10000

Revenue at t = 1

`P_(1) Q_(1)` = 700 × 18 = $12600

Therefore, from the above calculations it was seen that his revenue increases by ($12600 - $10000)= $2600 and its sales increases to 700.