cross elasticity of demand

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Can anyone please explain why
"the goods between which the cross elasticity is negative is *not* always complementary"
why it is not always complementary?
Replies (2)
make the question more crystal clear

With the consumption behavior being related, the change in the price of a related good leads to a change in the demand of another good. Related goods are of two kinds, i.e. substitutes and complementary goods. In case the two goods are not related, the Coefficient of Cross Elasticity is zero.

In case the two goods are substitutes for each other like tea and coffee, the cross price elasticity will be positive, i.e. if the price of coffee increases, the demand for tea increases. On the other hand, in case the goods are complementary in nature like pen and ink, then the cross elasticity will be negative, i.e. demand for ink will decrease if prices of pen increase or vice-versa.

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