Examples and exercises on the marginal revenue function

Example

Suppose the demand curve is linear, given by P(y) = a  by (where a and b are constants). Then
TR(y) = yP(y) = ay  by2,
so
MR(y) = a  2by.
These functions are shown in the following figure.

Example

Suppose the demand curve is given by P(y) = a/y (where a is a constant). Then
TR(y) = yP(y) = a,
so MR(y) = 0. That is, the revenue obtained from selling an extra unit is zero: the price goes down enough to cancel out any gain.

Example

Suppose the demand curve is given by P(y) = a/y2 (where a is a constant). Then
TR(y) = yP(y) = a/y,
so
MR(y) = a/y2.
That is, the revenue obtained from selling an extra unit is negative: the price goes down enough to cause an increase in volume to lead to a decrease in revenue.
Copyright © 1997 by Martin J. Osborne