Final answer:
Cross-price elasticity of demand for two gym memberships measures how the price change of one affects the demand for the other. If the gym memberships are substitutes, the cross-price elasticity will be positive; if they are complements, it will be negative. Calculate it using the percentage changes in demand and price.
Step-by-step explanation:
For gym memberships, if one gym increases its prices, it affects the demand for memberships at another gym. If these gyms are substitutes, the cross-price elasticity will be positive, meaning that an increase in the price of one gym's membership will likely increase the demand for the other gym's membership. Conversely, if they are complements, which is unlikely in this case, the cross-price elasticity would be negative.
To calculate the cross-price elasticity of demand, you would use the formula: Cross-price elasticity = (% change in quantity demanded of good A) / (% change in price of good B). If a gym membership price increases by 10% and as a result, the demand for another gym's membership increases by 5%, the cross-price elasticity would be 0.5, indicating a positive relationship between the two goods as substitutes.