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Understanding the Relationship Between Total Revenue and Elasticity
Review: Total revenue is price times quantity demanded: TR = P x Q.
Review: Elastic demand indicates price sensitivity; inelastic demand indicates price
insensitivity.
When price changes, you can analyze the change in total revenue in terms of a price
effect and a quantity effect. Elasticity determines which effect is greater after a change
in price.
Begin this section by reviewing the formula for
total revenue: TR = P x Q.
The box on the left summarizes the
relationship between price changes, total
revenue, and elasticity:
1. With products that are price-sensitive, or
elastic, a percentage change in price means a
greater percentage change in quantity
demanded. Total revenue and price move
in opposite directions.
2. With products that are price-insensitive, or
inelastic, a percentage change in price
means a smaller percentage change in
quantity demanded. Total revenue and
price move in the same direction.
Using math shows that the relationships on
the left are true.
The mathematical relationship above is
analogous to the formula for finding a change
in total revenue when the price changes.
The formula in the lower part of the box on
the left says that the percentage change in
total revenue is equal to the percentage
change in price + the percentage change
in quantity demanded.
Assume that the change in price is an
increase. A price increase means that there
will be a decrease in quantity because the
demand curve is downward sloping.
By manipulating the equation, you can see
that the last term on the right is the formula
for elasticity.
If the elasticity is less than 1, as it is here,
then the product has inelastic demand.
The price effect is the increase in revenue
from selling the product at a higher price.
The quantity effect is the decrease in
revenue from the fall in quantity demanded
caused by the increase in price.
In this case, the price effect has dominated.
The increase in price has not caused a large
loss of customers. There has not been a large
decrease in quantity demanded, or a large
quantity effect. Therefore the increase in
total revenue from the price effect is greater
than the decrease in total revenue from the
quantity effect.
To summarize:
If the quantity effect dominates, then elasticity
is greater than 1 (demand is elastic), and
total revenue and price move in opposite
directions.
If the price effect dominates then elasticity is
less than 1 (demand is inelastic), and total
revenue and price move in the same
direction.