1. Suppose that as the price of Y falls from $3.00 to $1.00 the quantity of Y demanded increases from 10 to 18. Compute the price elasticity of demand. Is the demand elastic or inelastic?
To compute the price elasticity of demand, you need to use the formula:
Price Elasticity of Demand = ((Percentage Change in Quantity Demanded) / (Percentage Change in Price))
Step 1: Calculate the percentage change in quantity demanded.
Percentage Change in Quantity Demanded = ((New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded) * 100
Initial Quantity Demanded = 10
New Quantity Demanded = 18
Percentage Change in Quantity Demanded = ((18 - 10) / 10) * 100 = 80%
Step 2: Calculate the percentage change in price.
Percentage Change in Price = ((New Price - Initial Price) / Initial Price) * 100
Initial Price = $3.00
New Price = $1.00
Percentage Change in Price = (($1.00 - $3.00) / $3.00) * 100 = -66.67%
Step 3: Compute the price elasticity of demand.
Price Elasticity of Demand = (80% / -66.67%) ≈ -1.20
Now let's determine if the demand is elastic or inelastic:
- If the absolute value of the price elasticity of demand is greater than 1, the demand is considered elastic.
- If the absolute value of the price elasticity of demand is less than 1, the demand is considered inelastic.
- If the absolute value of the price elasticity of demand is equal to 1, the demand is considered unitary elastic.
In this case, since the price elasticity of demand is -1.20 (greater than 1), the demand is elastic.