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If I try to calculate cross elasticity of demand (XED or CED) with individual demand quantity, it seems to break down since even small increase when the base number is small is a big increase in percentage. e.g. 1 to 2 is a 100% change.

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If you calculate XED you have two relative terms.

$XED=\frac{\Delta q_i}{q_i}\cdot \frac{p_j}{\Delta p_j}$

It is right that in your case $\frac{\Delta q_i}{q_i}=\frac{2-1}{1}=1$

Now it depends on the current price of good j and the change of the price how large XED is. From the relative change of the demand you cannot conlcude to the level of XED.

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