Understanding Demand Elasticity

The question asks about the relationship between two products when the "gross elasticity of demand" is negative. While "gross elasticity" isn't a standard term, in the context of product relationships and the given options, it strongly implies cross elasticity of demand. This measures how the quantity demanded of one good changes in response to a price change in another good.

Defining Cross Elasticity of Demand

Cross elasticity of demand ($E_{XY}$) is calculated as the percentage change in the quantity demanded of good X divided by the percentage change in the price of good Y. The formula is:

$ E_{XY} = \frac{\% \Delta Q_X}{\% \Delta P_Y} $

The sign of the cross elasticity coefficient tells us about the relationship between the two goods:

• Positive ($E_{XY} > 0$): Indicates that the goods are substitutes. When the price of good Y increases, the demand for good X increases, as consumers switch to the relatively cheaper good X.
• Negative ($E_{XY} < 0$): Indicates that the goods are complements. When the price of good Y increases, the demand for good X decreases, as consumers buy less of both goods together.
• Zero or Near Zero ($E_{XY} \approx 0$): Indicates that the goods are unrelated. A price change in good Y has no significant impact on the demand for good X.

Interpreting Negative Elasticity

The question states that the elasticity is negative. Based on the definition of cross elasticity of demand:

1. A negative sign means that as the price of one good (say, good Y) increases, the quantity demanded of the other good (good X) decreases.
2. This inverse relationship occurs when the two goods are typically consumed together.
3. Therefore, goods with a negative cross elasticity of demand are considered complementary products.

Examples of complementary goods include printers and ink cartridges, or cars and gasoline. If the price of ink cartridges goes up, people might buy fewer printers, or vice versa.

Given that the elasticity is negative, the two products are definitely complementary.