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 -2, 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?
If he cuts his price by 10%, his sales will increase to     pizzas, and his total revenue will increase to $   .

Answer 1

Let
z----------------- > Price Elasticity
x----------------- > % Change in Quantity
y----------------- > % Change in Price

we Know that

Price Elasticity = (% Change in Quantity) / (% Change in Price)----> z=x/y

z=-2
y=-10%
x= ?
z=x/y---------------- > x=z*y=(-2)*(-10)=20 %
% Change in Quantity=20%
Part A) how many pizzas will he sell if he cuts his price by 10%?
He will sell (500 +20 %)----------> 500*1.2=600 pizzas per week

the answer part A is 600 pizzas per week

Part B) how will his revenue be affected?
initial revenue per week
500 pizzas*$20 =$10000

final revenue per week
(500 pizzas+20%) *($20-10%)=600 pizzas*$18=$10800
$10800-$10000=$800

the answer part B is
His revenue will increase  $800 per week