Consider the pair of goods X and Y. It is observed that when price of Y falls the demand for X rises. Which one of the following options would you choose regarding the nature of these goods ?
They are complementary goods
Cross price elasticity: \(E_{XY} = \frac{\Delta Q_X / Q_X}{\Delta P_Y / P_Y}\)
Given: \(P_Y\) falls \((\Delta P_Y < 0)\) and \(Q_X\) rises \((\Delta Q_X > 0)\), so \(E_{XY} < 0\).
A negative cross price elasticity means the two goods are used together: a cheaper Y leads to more Y bought, and with it more X demanded (for example, cars and petrol).
Substitutes would show \(E_{XY} > 0\) (a cheaper Y would reduce the demand for X); giffen and inferior goods describe the own price or income response of a single good, not the link between two goods.
Hence, They are complementary goods.
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