If two goods are economic complements, which statement about their cross price elasticity of demand is correct?

Introduction / Context:
In microeconomics, goods can be related to each other as substitutes, complements, or independent goods. The nature of this relationship can be measured using cross price elasticity of demand, which shows how the quantity demanded of one good responds when the price of another good changes. This question focuses on complementary goods and asks which statement correctly describes their cross price elasticity of demand.

Given Data / Assumptions:

• Two goods are described as complements, meaning they tend to be used together, like tea and sugar or printers and ink cartridges.
• Cross price elasticity of demand measures the percentage change in quantity demanded of one good divided by the percentage change in price of the other good.
• The options include statements about the sign of cross price elasticity and about how demand for one good responds to changes in the price of the other.
• Standard economic definitions are assumed, without considering extreme or unusual special cases.

Concept / Approach:
For complementary goods, an increase in the price of one good makes the combined use of both goods more expensive, so consumers tend to reduce consumption of both. Therefore, when the price of one complement rises, the quantity demanded of the other complement tends to fall. This implies that the cross price elasticity of demand for complements is negative, because the price of one good and the quantity demanded of the other move in opposite directions. In contrast, substitutes have positive cross price elasticity, and independent goods have cross price elasticity near zero.

Step-by-Step Solution:
Step 1: Recall the definition of complementary goods as goods that are consumed together, such as cars and fuel or bread and butter.Step 2: Understand that if the price of one complement increases, the combined cost of using both goods rises, so consumers usually reduce the quantity demanded of both goods.Step 3: Define cross price elasticity of demand as the percentage change in quantity demanded of good X divided by the percentage change in price of good Y.Step 4: For complements, when the price of good Y increases, the quantity demanded of good X decreases, meaning the numerator and denominator have opposite signs.Step 5: Therefore, the ratio is negative, and cross price elasticity of demand between complements is negative.Step 6: Compare this conclusion with the options and select the statement which says that cross price elasticity is negative.

Verification / Alternative check:
Standard microeconomics textbooks present a table summarising relationships between goods: substitutes have positive cross price elasticity, complements have negative cross price elasticity, and independent goods have near zero cross price elasticity. Examples of complements such as tea and sugar consistently show that higher prices for one reduce demand for the other, confirming the negative sign. Graphical analysis also illustrates that the demand curve for one good shifts leftward when the price of its complement rises, which is consistent with a negative cross price elasticity.

Why Other Options Are Wrong:
Option a states that cross price elasticity is positive, which describes substitutes, not complements. Option b claims that an increase in the price of one good increases demand for the other, which again describes substitutes. Option d suggests that complements must always be consumed in fixed proportions, which is only true for perfect complements and not for all complementary goods in general. Option e claims that changes in the price of one good have no effect on demand for the other, which would indicate independent goods rather than complements.

Common Pitfalls:
Students sometimes memorise relationships between substitutes and complements but confuse which sign of cross price elasticity applies to which type. A useful memory aid is that substitutes move in the same direction, so higher price of one increases demand for the other and cross price elasticity is positive. Complements move in opposite directions, so higher price of one reduces demand for the other and cross price elasticity is negative. Remembering this rule helps avoid mixing up the sign.

Final Answer:
If two goods are complements, the cross price elasticity of demand between them is negative.