Calculation questions about price elasticity of demand

1. How do you calculate price elasticity of demand?
Price elasticity of demand is calculated using the formula:

Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)

2. If the price of a product increases by 10% and the quantity demanded decreases by 5%, what is the price elasticity of demand?
Using the formula:

Price Elasticity of Demand = (-5%) / (10%) = -0.5

Therefore, the price elasticity of demand is -0.5.

3. If the price of a product decreases by 20% and the quantity demanded increases by 15%, what is the price elasticity of demand?
Using the formula:

Price Elasticity of Demand = (15%) / (-20%) = -0.75

Therefore, the price elasticity of demand is -0.75.

Question 1:

A store sells apples. When the price of apples increases from $1 to $1.2, the quantity demanded decreases from 100 apples to 80 apples. Calculate the price elasticity of demand using the midpoint method.

Solution:

Price elasticity of demand (Ed) = (% change in quantity demanded) / (% change in price)

Ed = ((80 - 100) / (80 + 100)) / ((1.2 - 1) / (1.2 + 1))
Ed = (-20 / 180) / (0.2 / 2.2)
Ed = -1.11

Question 2:

The elasticity of demand for a product is -0.8. If the price of the product increases by 5%, calculate the expected percentage decrease in quantity demanded.

Solution:

Price elasticity of demand (Ed) = % change in quantity demanded / % change in price

-0.8 = % change in quantity demanded / 5

% change in quantity demanded = -0.8 - 5
% change in quantity demanded = -4%

Question 3:

A company sells a product and observes the following data:

Price | Quantity Demanded
------- | --------
$10 | 1,000 units
$15 | 700 units

Calculate the total revenue at each price and determine whether demand is elastic, inelastic, or unitary elastic.

Solution:

Price $10:
Total revenue = Price - Quantity demanded
Total revenue = $10 - 1,000 units
Total revenue = $10,000

Price $15:
Total revenue = $15 - 700 units
Total revenue = $10,500

Price elasticity of demand (Ed) = (% change in quantity demanded) / (% change in price)

Ed = ((700 - 1,000) / (700 + 1,000)) / ((15 - 10) / (15 + 10))
Ed = (-300 / 1,700) / (5 / 25)
Ed = -0.58

Since Ed < 1, demand is inelastic.