The relationship between AR and MR in monopoly

The relationship between the average and MR curves in monopoly is shown in diagram. Aa a monopolist’s demand curve slopes downward to the right (the market demand curve), an extra unit of output can only be sold by reducing the price at which all units of output are sold.

Total sales revenue increases by the area k in the diagram, but decreases by the area h. Areas k and h respectively show the revenue gain (namely the extra unit sold multiplied by its price) and the revenue lost resulting from the sale of an extra unit of output.

The revenue lost results from the fact that in order to sell one more unit of output, the price has to be reduced for all units of output, not just the extra unit sold. MR, which is the revenue gain minus the revenue loss (k − h), must be less than price or AR (area k).

Now in the top half (elastic section) of the AR curve, the area k is always larger than the area h, diagram illustrates. This means that MR is always positive under the top half of the AR curve.

However, the reverse is true under the bottom half of the demand curve. In this situation, demand is inelastic, with the result that the equivalent area k is always smaller than the equivalent area h. MR is now negative.

The final point to note is that provided the monopolist’s MR curve is linear (i.e. a straight line), the curve is twice as steep as the monopolist’s AR curve. MR falls to zero at the point where the MR curve cuts through the horizontal (output) axis of the diagram.