What does average revenue and marginal revenue mean?

Under imperfect competition both Average revenue and Marginal revenue fall downward. Marginal revenue lies below the Average revenue. When Average falls marginal revenue falls. This is the case with imperfect competition. On the other hand with average revenue is constant marginal revenue is also constant. This is the case with perfect competition. Average revenue is the
revenue per unit of commodity sold. It is equal to the total revenue divided by the total units sold. Average revenue diminishes with every increase in the total output sold.

Marginal revenue is the net addition to the total revenue when one more unit of commodity is sold. Marginal revenue falls with every additional units of output sold. Thus under imperfect competition both AR and MR curves fall and MR curve lies below AR curve.

Relationship between AR and MR curves:

Under imperfect competition AR and MR curves may be linear (straight line) or curve linear (bending line). When average revenue is downward sloping straight line its corresponding marginal revenue curve will be downward sloping straight line. On the other hand if the AR curve is in the form of a curve, the corresponding MR curve would become a curve. Thus the relation between AR and MR can be shown below with respect to their, being linear and curve-linear characteristics.

(i) When average revenue is a straight line, the corresponding marginal revenue will be a straight line too. If both AR and MR curve are straight line, MR curve will midway or halfway between AR curve and OY-axis. It means when both AR and MR are straight line and if a perpendicular is drawn parallel to OX-axis from a point on the AR curve to OY-axis, MR curve will cut this perpendicular at its middle point. In the figure given below is shown the relation between AR curve and MR curve.

In the above diagram, AR and MR curves are straight line; perpendicular is drawn parallel to OX-axis joining AR curve OY-axis at Q and P points. MR curve cuts halfway the distance at point R. Thus PR = PQ is to be proved. These are two olds of finding total revenue, (i) From AR and (ii) From MR Proof: Let a vertical straight line be drawn from point Q average revenue curve to the point M on the OX axis.

Alternative proof:

On the other hand if AR is not a straight line but a curve, the corresponding MR Curve becomes a curve. If AR Curve is convex to origin, MR curve is also convex to origin. Similarly if AR curve is concave to origin, MR curve will become so. When average revenue is convex to origin the MR Curve will cut the perpendicular line to the OY-axis left of the midpoint. On the other hand when AR curve is concave to the origin. MR curve cuts the perpendicular line to the right of the midpoint.