# How does the cross-price elasticity of a substitute good differ from that of a complementary good?

Oct 22, 2015

Cross elasticity of a substitute good is positive.
Cross elasticity of a complementary good is negative.

#### Explanation:

Cross elasticity of a substitute good is positive.
If Good-x and Good-y are substitutes. If we construct a a cross demand curve for good-x with reference to the price of good-y, the cross demand curve of good-x will slope up ward. It means a positive relation. This is because when the price of good-y goes up, price of good-x remaining constant becomes cheap. It makes the consumer to buy more of good-x when the price of good-y rises. Hence elasticity also positive.

Cross elasticity of a complementary good is negative. In case of complementary good, one good has be consumed along with the other good. Again assume consumer consumes good-A and good-B. Both are complements. If the price of good-B goes up, consumer will buy less quantity of it. Naturally (even though the price of good-A remain constant) he will consume less of Good-A also. If you develop a cross demand schedule for good-A with respect to the price of good-B, it will show a negative relation. Hence elasticity is also negative,

You must understand in the calculation of cross elasticity of demand we very much take into account the sign also.