Cross elasticity of demand
The key concept to understand the relationship between substitutes and complements is cross elasticity of demand. This is a measure of how the quantity demanded of one good responds to a change in the price of another good. It is calculated by dividing the percentage change in quantity demanded of one good by the percentage change in price of another good.
Cross elasticity of demand can be positive, negative, or zero. A positive cross elasticity of demand means that the goods are substitutes. When the price of one good increases, the quantity demanded of the other good increases, and vice versa. For example, if the price of tea increases, the quantity demanded of coffee increases, as some consumers switch from tea to coffee.
A negative cross elasticity of demand means that the goods are complements. When the price of one good increases, the quantity demanded of the other good decreases, and vice versa. For example, if the price of bread increases, the quantity demanded of butter decreases, as some consumers buy less bread and butter.
A zero cross elasticity of demand means that the goods are independent. The price of one good does not affect the quantity demanded of the other good. For example, the price of milk does not affect the quantity demanded of pens.