Question

We're looking at the market for cat food. When the price is $10, the quantity sold is 1000 bags. When the price drops 10%, the quantity sold increases 30%.

Calculate the price elasticity of demand. (Answer in format X.XX, round to the nearest hundredth.)

I know the formula is (% change in quantity demanded)/(% change in price), but I'm not sure what my first step should be.

Answer 1

The first step is to calculate the new price and the new quantity sold after their respective changes.

1. Calculate the new price:
Since the price dropped by 10%, this means the new price is 90% of the original price.
New price = 0.9 * $10 = $9

2. Calculate the new quantity sold:
Since the quantity sold increased by 30%, this means the new quantity is 130% of the original quantity.
New quantity = 1.3 * 1,000 = 1,300 bags

3. Now, use the price elasticity of demand formula:
% change in quantity demanded = (New quantity - Original quantity) / Original quantity
= (1,300 - 1,000) / 1,000 = 0.3 or 30% (as a decimal, 0.3)

% change in price = (New price - Original price) / Original price
= ($9 - $10) / $10 = -$1 / $10 = -0.1 or -10% (as a decimal, -0.1)

Price elasticity of demand = (% change in quantity demanded) / (% change in price)
= 0.3 / -0.1 = -3.00

The price elasticity of demand is -3.00.