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.

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 = $\frac{Percentage\ change\ in\ quantity }{Percentage\ change\ in\ price }$

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

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

$\frac{Q_{1}-Q_{0}}{Q_{0}}$ = 0.4

$\frac{Q_{1}-500}{500}$ = 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.