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

Cutting the pizza price by 10% increases the quantity sold by 20% due to the price elasticity of -2. The pizzeria would thus sell 600 pizzas instead of 500, increasing total revenue from $10,000 to $10,800 as the demand for his pizzas is quite elastic.

Step-by-step explanation:

The price elasticity of demand is a measure of how the quantity demanded of a good responds to a change in the price of that good. With an elasticity of -2, the pizzeria's owner is operating in an elastic demand market. A 10% price reduction will lead to a 20% increase in the quantity demanded, because the percentage change in quantity demanded is the price elasticity multiplied by the percentage change in price.

If the owner currently sells 500 pizzas at $20 each and reduces the price by 10%, to $18 (which is 90% of $20), he will then sell 600 pizzas (500 * 1.20), because the 10% drop in price leads to a 20% increase in sales (10% * -2).

The total revenue after the price cut is the new quantity sold times the new price, so $18 * 600 = $10,800, which is higher than the initial revenue of $20 * 500 = $10,000. Hence, his total revenue will increase.

Answer 2

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