Final answer:
Positive and negative signs in cross elasticity of demand indicate the type of relationship between goods: positive for substitutes and negative for complements. In elasticity of demand for one product, sign is less relevant as it indicates the magnitude of the response in quantity demanded to price changes.
Step-by-step explanation:
The reason why positive and negative signs matter when calculating cross elasticity of demand, but not elasticity of demand for one product is rooted in the relationships between goods. Cross-price elasticity of demand measures the percentage change in the quantity demanded of one good (Good A) in response to a change in the price of another good (Good B).
If Good A and Good B are substitutes, like coffee and tea, an increase in the price of Good B will lead to an increase in the quantity demanded for Good A, resulting in a positive cross-price elasticity. Conversely, if Good B is a complement to Good A, like coffee and sugar, the same price increase for Good B would lead to a decrease in the quantity demanded for Good A, therefore the cross-price elasticity would be negative.
When we are looking at the elasticity of demand for a single product, we are primarily concerned with the magnitude of the percentage change in quantity demanded in response to a percentage change in the price of the product itself without considering the impact of other goods, which is why the sign is usually omitted and understood to be negative.