Gymitime and WeightWorld both offer gym memberships. Suppose Gymilime lowered the price of its membership by \( \mathbf{1 5 \%} \), As a result, WeightWorld experienced a \( 28 \% \) decline in the quantity demanded of their gym memberships. What is the of the cross-price elasticity between the two gym memberships? Include a negative sign if applicable, and round your answer to two decimal places. I

To calculate the cross-price elasticity of demand, you can use the formula: \[ E_{xy} = \frac{\text{Percentage change in quantity demanded of WeightWorld}}{\text{Percentage change in price of Gymitime}} \] 1. The percentage change in quantity demanded of WeightWorld is \(-28\%\) (as the demand decreased). 2. The percentage change in price of Gymitime is \(-15\%\) (as the price lowered). Now, plugging the values into the formula gives us: \[ E_{xy} = \frac{-28\%}{-15\%} = \frac{28}{15} \approx 1.87 \] Thus, the cross-price elasticity is approximately \(1.87\), indicating that the two memberships are substitutes. Now, it’s time to celebrate this newfound knowledge! Understanding how businesses impact each other's demand through pricing gives you insight into the competitive landscape. It's like a dance where each partner's move influences the other's! If you're curious about learning more about elasticity and its broader implications in economics, there are tons of resources available. Books like "Principles of Economics" by Gregory Mankiw offer great insights into elasticity along with other foundational concepts that will boost your economic fluency!