A ski rental store raised
the price of rental skis from $12
to $14
per day. Correspondingly, sales fell
from 2 comma 500
rentals to 1 comma 800
rentals per month.
Using average values to calculate percentage changes, the absolute value of the price elasticity of demand is enter your response here
.
(Enter your response rounded to two decimal places.)
Part 2
In this case, demand is
▼a. elastic
b. indeterminate
c. indeterminate
The absolute value of the price elasticity of demand is 1.35.
In this case, demand is elastic.
To calculate the absolute value of the price elasticity of demand, you can use the following formula:
Price Elasticity of Demand = ((Q2 - Q1) / ((Q1 + Q2) / 2)) / ((P2 - P1) / ((P1 + P2) / 2))
In this formula, Q1 represents the initial quantity (2,500 rentals), Q2 represents the final quantity (1,800 rentals), P1 represents the initial price ($12), and P2 represents the final price ($14).
Plug in the values into the formula:
Price Elasticity of Demand = ((1,800 - 2,500) / ((2,500 + 1,800) / 2)) / (($14 - $12) / (($12 + $14) / 2))
Price Elasticity of Demand = ((-700) / (4,300 / 2)) / (($2) / ($26 / 2))
Price Elasticity of Demand = ((-700) / (2,150 )) / (($2 )/ ($13 ))
Price Elasticity of Demand = -700 / 430 / 2 / 2
Price Elasticity of Demand = -0.813
After rounding to two decimal places, the absolute value of the price elasticity of demand is 0.81.
For Part 2 of the question, to determine if demand is elastic, inelastic, or indeterminate, we need to compare the absolute value of the price elasticity of demand to 1.
Since the absolute value of the price elasticity of demand is less than 1 (0.81 < 1), the demand in this case is considered to be inelastic.
To calculate the absolute value of the price elasticity of demand, we can use the formula:
% change in quantity demanded / % change in price
First, let's calculate the % change in quantity demanded:
% change in quantity demanded = (new quantity - old quantity) / old quantity x 100
% change in quantity demanded = (1,800 - 2,500) / 2,500 x 100
% change in quantity demanded = -700 / 2,500 x 100
% change in quantity demanded = -28%
Next, let's calculate the % change in price:
% change in price = (new price - old price) / old price x 100
% change in price = (14 - 12) / 12 x 100
% change in price = 2 / 12 x 100
% change in price = 16.67%
Now, let's calculate the absolute value of the price elasticity of demand:
Price elasticity of demand = |-28% / 16.67%|
Price elasticity of demand = 1.68
Therefore, the absolute value of the price elasticity of demand is 1.68.
For Part 2, since the absolute value of the price elasticity of demand is greater than 1, demand is considered to be elastic.