Question

The price elasticity of demand uses the absolute value because it is sometimes negative or always negative

.The income and cross elasticities of demand do not use the absolute value because they can be negative only, positive only or positive or negative

The income elasticity of demand is positive for a normal or inferior good and negative for an inferior or normal good.

The​ cross-price elasticity of demand is positive for complementary or substitute goods and negative for complementary or substitute goods.

Answer 1

According to law of demand if price increases, quantity demanded decreases and vice versa. Therefore price elasticity takes absolute value because it is always negative.

The sign of income elasticity determines whether a good is normal or inferior. The sign of cross price elasticity determines whether a good is substitute or complementary. Therefore it doesn't use absolute value because they can be positive or negative.

The income elasticity of demand is positive for a normal good and negative for an inferior good.

If cross price elasticity positive, then the goods are complements because demand for one decreases with increase in price of another. If cross price elasticity is negative then, the goods are substitute good.