# Why two goods are of different types of Cross Elasticity if we swap them in formula?

I am using this formula for calculating Cross elasticity of demand:

$E_{XY}^D = \Large\frac{(Q_2^X - Q_1^X)(P_2^Y + P_1^Y)}{(Q_2^X + Q_1^X)(P_2^Y - P_1^Y)}$

• If $E_{XY}^D$ > 0 Then goods X and Y are substitutes.
• If $E_{XY}^D$ < 0 Then goods X and Y are complementary.
• If $E_{XY}^D$ = 0 Then goods X and Y are independent.

I have this data: P1 and P2 are prices; Q1 and Q2 are quantities.

Using above formula I have calculated cross elasticity $E_{XY}$ and $E_{YX}$ in Excel: I calculated Cross Elasticity for X and Y and the goods turned out to be Complementary goods, but when I swapped X and Y and calculated using the same formula the goods X and Y become Substitutes.

Why two goods belong to one type of cross elasticity, but if we swap X and Y and plug values into formula the goods turn out to be another type of Cross Elasticity. Can two goods be considered substitutes and complementary at the same time? Isn't it illogical?

Excel file with data and calculations available here: Dropbox

The cross elasticity of demand $E_{XY}^D$ is defined as the percent change in quantity demanded for X divided by the percent change in price of Y, holding the price of X fixed.