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# Cross-elasticity

The cross-elasticity is the relationship between the amount of demand for a commodity and the price of another good. Given two goods A and B, the value of the cross-elasticity is determined by the ratio between the percentage change in the amount of demand for good A and the percentage change in price of good B. The concept of cross-elasticity is, therefore, a change in the elasticity of the application of different goods.

In calculus you can calculate the cross-elasticity of demand by the derivative of the demand function Qa than the price P of good B. The elasticity allows to analyze the relationship between the two goods. The possible cases are as follows:

• Substitute goods. In case of positive cross-elasticity (ε> 0) the two goods are goods substitutes since an increase in the price of the goods B determines the increase in the amount of application of the good A, and vice versa. In other words, when the price of goods gets too high (eg butter), the consumer replaces it with a good substitute (eg margarine).
• Complementary goods. In case of cross-elasticity negative (ε <0) the two goods are complementary goods since an increase in the price of the goods B determines the reduction of the amount of the good A, and vice versa. In other words, when the price of goods gets too high (eg gasoline) the consumer reduce his demand for the complementary good (eg your car).
• Independent goods. In case of no cross-elasticity (ε = 0) between the two goods there is no relationship of interdependence. In the latter case, when the price of good B changes, it does not affect the quantity demanded of good A.

In conclusion, the cross-elasticity is the relationship between the percentage change in quantity demanded and the percentage change in price of another good. The cross price elasticity is particularly useful in the classification of merchandise goods in various sectors and industries in competition analysis and market a business.

Cross-elasticity of supply. The elasticity can be used both on the demand side and supply side. In the latter case, the cross-elasticity of supply is the relationship between the quantity supplied of a good and the price of another good.

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