Essentially, all elasticities are computed the same way; though, depending on the level of the course, the specific computation may be a little more or less complex.
In general, all elasticities may be thought of as a ratio of
the percentage change in the quantity of interest (demand or supply
for us) and the percentage change in the variable that affects
that quantity (price, income, price of related goods, for example).
Because elasticities are ratios of percentages, they have no units,
they are simply numbers.
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