**The below mentioned article provides study notes on cross elasticity of demand. **

E_{XY} = % change in quantity demanded for Y/% change in price X

E_{XY} = ∆Q_{Y}/Q_{Y}/∆P_{X}/P_{X} = ∆Q_{Y}/∆P_{X}. P_{X}/Q_{Y}

Cross elasticity may be positive or negative, depending on the relationship between the two commodities. If the commodities are substitutes, cross elasticity will be positive, i.e., a rise in the price of the first commodity will cause an increase in the demand for the other commodity.

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Fig. 2.57(a) shows the relationship between P_{X} and demand for substitute good, Y. If X and Y are substitutes then the quantity demanded for Y is directly related to the price of X. As P_{X} rises to P_{X1}, demand for Y rises from OY_{1} to OY_{2}.

If they are complements then quantity demanded for Y is inversely related to the price of X. In Fig. 2.57(b) demand curve has a negative slope. An increase in the price of X from P_{X} to P_{X1} leads to a fall in the demand for Y. Thus cross elasticity of demand has a negative value. Thus for substitute goods, cross elasticity of demand becomes positive and for complementary goods it is negative.

If goods X and Y are not related either way (say, good X is a calculator while good Y is a trouser) then the value of cross elasticity of demand becomes zero. Fig. 2.57(c) shows zero cross-elasticity of demand A rise or fall in the price of X does not result in a change in the demand for Y.