CROSS ELASTICITY OF DEMAND 
Definition: Cross elasticity (Exy) tells us the relationship between two products. it measures the sensitivity of quantity demand change of product X to a change in the price of product Y. Price elasticity formula: Exy = percentage change in Quantity demanded of X / percentage change in Price of Y.. If the percentage change is not given in a problem, it can be computed using the following formula: Percentage change in Qx = (Q1Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd of X, and Q2 = new Qd of X. Percentage change in Py = (P1P2) / [1/2 (P1 + P2)] where P1 = initial Price of Y, and P2 = New Price of Y. Putting the two above equations together: Exy = {(Q1Q2) / [1/2 (Q1+Q2)] } / {(P1P2) / [1/2 (P1 + P2)]}
Characteristics: Exy > 0, Qd of X and Price of Y are directly related. X and Y are substitutes. Exy approaches 0, Qd of X stays the same as the Price of Y changes. X and Y are not related. Exy < 0, Qd of X and Price of Y are inversely related. X and Y are complements.
Example: 1. If the price of Product A increased by 10%, the quantity demanded of B increases by 15 %. Then the coefficient for the cross elasticity of the A and B is : Exy = percentage change in Qx / percentage change in Py = (15%) / (10%) = 1.5 > 0, indicating A and B are substitutes. 2. If the price of Product A increased by 10%, the quantity demanded of B decreases by 15 %. Then the coefficient for the cross elasticity of the A and B is : Exy = percentage change in Qx / percentage change in Py = ( 15%) / (10%) =  1.5 < 0, indicating A and B are complements.
