Revenue and Demand
curve is a tremendously useful illustration for those who can
read it. We have seen that the downward slope tells us that there is an
inverse relationship between price and quantity. One can also view the
demand curve as separating
a region in which sellers can operate from a region forbidden
to them. But there is more, especially when one considers what an area
on the graph represents.
If people will buy 100 units of a product when its price
is $10.00, as the picture below illustrates, total revenue for sellers
will be $1000. Simple geometry tells us that the area of the rectangle
formed under the demand curve in the picture is found by multiplying
the height of the rectangle by its width. Because the height is price
and the width is quantity, and since price multiplied by quantity is
total revenue, the area is total revenue. The fact that area on supply
and demand graphs measures total revenue (or total expenditure by
buyers, which is the same thing from another viewpoint) is a key idea
used repeatedly in microeconomics.
From the demand curve, we can obtain total revenue. From
total revenue, we can obtain another key concept: marginal
revenue. Marginal revenue is the additional revenue added by
an additional unit of output, or in terms of a formula:
Marginal Revenue = (Change in total revenue)
divided by (Change in sales)
According to the picture, people will not buy more than
100 units at a price of $10.00. To sell more, price must drop. Suppose
that to sell the 101st unit, the price must drop to $9.95. What will
the marginal revenue of the 101st unit be? Or, in other words, by how
much will total revenue increase when the 101st unit is sold?
There is a temptation to answer this question by
replying, "$9.95." A little arithmetic shows that this answer is
incorrect. Total revenue when 100 are sold is $1000. When 101 are sold,
total revenue is (101) x ($9.95) = $1004.95. The marginal revenue of
the 101st unit is only $4.95.
To see why the marginal revenue is less than price, one
must understand the importance of the downward-sloping demand curve. To
sell another unit, sellers must lower price on all units. They received
an extra $9.95 for the 101st unit, but they lost $.05 on the 100 that
they were previously selling. So the net increase in revenue was the
$9.95 minus the $5.00, or $4.95.
There is a another way to see why marginal revenue will
be less than price when a demand curve slopes downward. Price is
average revenue. If the firm sells 100 for $10.00, the average revenue
for each unit is $10.00. But as sellers sell more, the average revenue
(or price) drops, and this can only happen if the marginal revenue is
below price, pulling the average down.
The reasoning of why marginal will be below average if
average is dropping can perhaps be better seen in another example.
Suppose that the average age of 20 people in a room is 25 years, and
that another person enters the room. If the average age of the people
rises as a result, the extra person must be older than 25. If the
average age drops, the extra person must be younger than 25. If the
added person is exactly 25, then the average age will not change.
Whenever an average is rising, its marginal must be above the average,
and whenever an average is falling, its marginal must be below the
If one knows marginal revenue, one can tell what happens
to total revenue if sales change. If selling another unit increases
total revenue, the marginal revenue must be greater than zero. If
marginal revenue is less than zero, then selling another unit takes
away from total revenue. If marginal revenue is zero, than selling
another does not change total revenue. This relationship exists because
marginal revenue measures the slope of the total revenue curve.
The picture above illustrates the relationship between
total revenue and marginal revenue. The total revenue curve will be
zero when nothing is sold and zero again when a great deal is sold at a
zero price. Thus, it has the shape of an inverted U. The slope of any
curve is defined as the rise over the run. The rise for the total
revenue curve is the change in total revenue, and the run is the change
in output. Therefore,
Slope of Total Revenue Curve = (Change in total
revenue) / (Change in amount sold)
But this definition of slope is identical to the
definition of marginal revenue, which demonstrates that marginal
revenue is the slope of the total revenue curve.
Next we tie
marginal revenue to elasticity.