Travis's Cross-Price Elasticity Calculation

How to calculate Travis's cross-price elasticity?

Travis is doing his grocery shopping. Watermelon has increased in price from $1 per melon to $5 per melon. At the same time, Travis now purchases 13 kiwi, when he used to only purchase 6. Calculate his cross-price elasticity.

Calculation and Explanation

Travis's cross-price elasticity is 7/24.

To calculate the percentage change in quantity, we use the formula:

Percentage change in quantity = (New quantity - Old quantity) / Old quantity * 100%

In this case, the old quantity of kiwi Travis purchased was 6, and the new quantity is 13. Plugging these values into the formula, we have:

Percentage change in quantity = (13 - 6) / 6 * 100%

Now, let's calculate the percentage change in the price of watermelon:

Percentage change in price = (New price - Old price) / Old price * 100%

The old price of watermelon was $1 per melon, and the new price is $5 per melon. Plugging these values into the formula, we have:

Percentage change in price = ($5 - $1) / $1 * 100%

Now, we can calculate the cross-price elasticity using the formula:

Cross-price elasticity = (Percentage change in the quantity of kiwi) / (Percentage change in the price of watermelon)

Substituting the values we calculated earlier, we have:

Cross-price elasticity = (7 / 6 * 100%) / ($4 / $1 * 100%)

Cross-price elasticity = (7 / 6) / (4 / 1)

Cross-price elasticity = 7 / 6 * 1 / 4

Cross-price elasticity = 7 / 24