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 = (Q1-Q2) / [1/2 (Q1+Q2)] where Q1 = initial Qd of X, and Q2 =  new Qd of X.

Percentage change in Py = (P1-P2) / [1/2 (P1 + P2)] where P1 = initial Price of Y, and P2 = New Price of Y.

Putting the two above equations together:

Exy = {(Q1-Q2) / [1/2 (Q1+Q2)] } / {(P1-P2) / [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 :