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.
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.
The first step is to calculate the percentage change in quantity demanded and the percentage change in price.
To find the percentage change in quantity demanded, we can use the formula: ((New Quantity - Old Quantity) / Old Quantity) * 100
The new quantity in this case is 1000 bags + 30% of 1000 bags, which equals 1000 + (30/100) * 1000 = 1000 + 300 = 1300 bags.
Using the formula for the percentage change in quantity demanded, we have ((1300 - 1000) / 1000) * 100 = (300 / 1000) * 100 = 30%
Now, let's calculate the percentage change in price. We know that the price decreases by 10%, so the new price is 10 - (10/100) * 10 = 10 - 1 = $9.
Using the formula for the percentage change in price, we have ((9 - 10) / 10) * 100 = (-1 / 10) * 100 = -10%.
Now that we have the percentage change in quantity demanded (30%) and the percentage change in price (-10%), we can calculate the price elasticity of demand using the formula: (30% / -10%).
To calculate the price elasticity of demand, you need to determine the percentage change in quantity demanded and the percentage change in price. Here are the steps you can follow:
1. Calculate the percentage change in price:
- Start by finding the change in price: $10 - ($10 * 0.10) = $10 - $1 = $9.
- Then, calculate the percentage change in price: ($9 / $10) * 100% = 90%.
2. Calculate the percentage change in quantity demanded:
- Begin by finding the change in quantity demanded: 1000 bags * 0.30 = 300 bags.
- Next, calculate the percentage change in quantity demanded: (300 bags / 1000 bags) * 100% = 30%.
3. Finally, apply the formula for the price elasticity of demand:
Price Elasticity of Demand = (% change in quantity demanded) / (% change in price).
- Substitute the calculated values: Price Elasticity of Demand = 30% / 90%.
- Convert the percentages to decimals: Price Elasticity of Demand = 0.30 / 0.90 = 0.3333.
Therefore, the price elasticity of demand for cat food is approximately 0.33 (rounded to the nearest hundredth).