Q.A rise in the price of petrol reduces the quantity of cars demanded. Petrol and cars are best described as:
Cross elasticity of demand, , tells us the relationship between two commodities from its SIGN. Here, X = cars and Y = petrol: a rise in the price of petrol () causes the quantity of cars demanded to FALL (), so is negative.
Option (a) Substitutes would require a POSITIVE cross elasticity (quantity of X rising when price of Y rises) — INCORRECT, since here quantity of cars FALLS.
Option (b) Complements is exactly the case of a negative cross elasticity — two goods used TOGETHER, so that a price rise in one (making the joint use of both costlier) reduces demand for the other. Petrol and cars are a textbook example of complementary goods — CORRECT.
Option (c) Independent goods would require cross elasticity to be ZERO (no response at all) — INCORRECT, since demand for cars clearly did respond.
Option (d) Inferior goods is a classification under INCOME elasticity, not cross elasticity, and describes a single good's own response to a change in income, not a relationship between two different goods — INCORRECT, and the wrong concept entirely for this question.
(b) Complements — petrol and cars are jointly demanded, so a rise in petrol's price lowers the quantity of cars demanded, giving a negative cross elasticity of demand.
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