Final answer:
The absolute value of the own price elasticity of sneakers is 0.4, indicating an inelastic demand, as the percentage change in quantity demanded is less than the percentage change in price.
Step-by-step explanation:
If the quantity demanded for sneakers falls by 10 percent when the price increases 25 percent, the own price elasticity of sneakers can be calculated using the formula for price elasticity of demand:
Elasticity = (Percentage change in quantity demanded) / (Percentage change in price)
Therefore, Elasticity = (-10%) / (25%) = -0.4. This indicates an inelastic demand, since the absolute value of the elasticity is less than 1. Price elasticities of demand are usually represented as positive numbers, so we take the absolute value to find that the own price elasticity of sneakers is 0.4.
It is important to note that since quantity demanded and price have an inverse relationship along the demand curve, price elasticities of demand are negative. However, when discussing elasticity, we typically refer to the absolute value to denote the strength of the responsiveness.