Cross elasticity of demand refers to a change in the quantity demanded of product A as s result of a change in the product B. When demand for a product changes due to a change in the price of another related commodity we have cross elasticity of demand. The formula for cross elasticity is,

We have stated the elasticity formula in terms of percentages but we can also state them in terms of “Proportion” of The Three kinds of elasticity it is price elasticity, which is of great significance in the determination of value. We shall deal with price elasticity of demand in greater detail.

Cross price of demand is defined as the percentage change in the quantity demanded of a good due to a change in the price of another good, other things remaining constant. Let two goods, Q_{1} and Q_{2} are available to the consumer with P_{1} and P_{2} as their respective prices. Then the cross price elasticity of demand of Q_{1} is the percentage change in the quantity demanded of Q_{1} due to one percent change in P_{2}. In general, if Q_{i }and Q_{j }are the two goods with respective prices as P_{i }and P_{j} then the cross price elasticity of demand of Q_{i} is defined as the percentage change in the quantity demanded of Q_{i} due to one percent change in P_{j}. In mathematical notation it is denoted as follows:

As price and quantity values cannot be in negative terms, the sign of the cross price elasticity is determined by the sign of the derivative ¶Q/¶P, If the value of the derivative is positive then will be positive and it will be positive and it will be negative, if the value of derivative is negative, other things remaining unchanged. When two goods are substitutes (i.e., both serve the same purpose and one can be used in the place of the other) then the increase in the price of one good decreases its own demand and increases the quantity demanded of the other good. In this case the cross price elasticity of demand is positive, the value of the derivative being positive. On the contrary, in the case of complimentary goods, (i.e. goods which are used jointly) the increase in the price of one good decrease the quantity demanded of both the goods. Here the value of the derivative, ¶Q_{i}/¶P_{j }is negative which in turn makes the value of e_{c} also negative. Consider three goods tea, coffee and sugar, where tea and coffee are substitutes and the combinations tea and sugar or coffee and sugar are complimentary goods. If the price of coffee increases then consumers then consumers will shift their preferences from coffee to tea thereby increasing the consumption of tea. In this case the value of the derivative, ¶Q_{i}/¶P_{j} is positive. On the other hand, considering the combination tea and sugar, if the price of tea increases then consumers will consume fewer amounts of both tea and sugar. So in the case of complimentary goods the value of the derivative, ¶Q_{i}/¶P_{j } as well as the cross price elasticity of demand e_{c }become negative.

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