Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

CHAP. 9] PRICE AND OUTPUT UNDER PURE MONOPOLY 213
so as not to unduly complicate the table. The MR of $3 recorded at the sales level of 2.5 units is obtained from the change in
TR resulting from the increase in sales from 2 to 3 units; it will be needed later to show the equilibrium level of output for the
monopolist.
The D and MR schedules of Table 9.1 facing the monopolist are plotted in Fig. 9-1. Note that MR is positive as long as
the demand curve is elastic, is zero when e ¼ 1, and is negative when e , 1. This is because when D is elastic, a reduction in
the commodity price will cause TR to increase, so MR (which is given by DTR/DQ) is positive. When D has unitary elasticity,
a fall in price leaves TR unchanged, and so MR is zero. When D is inelastic, a reduction in price will result in a
reduction in TR, and so MR is negative.
9.2 THE MR CURVE AND ELASTICITY
The MR curve for any straight-line demand curve is a straight line which starts at the same point on the vertical
axis as the demand curve but falls at twice the rate as (i.e., it has twice the absolute slope of) the D curve.
Also, the MR at any level of sales is related to the price at the level of sales by the formula MR ¼ P(l 2 1/e),
where e stands for the absolute value of the coefficient of price elasticity of demand at that level of sales.
EXAMPLE 2. From point A to point B, the D curve of Fig. 9-1 falls by two units and has an absolute slope of 1. To locate
the MR corresponding to point B on the D curve, we drop four units from point A, or twice the drop from A to B, to get point
B 0 on the MR curve. Similarly, from A to C, the D curve falls by four units; thus, the MR corresponding to point C (i.e., point
C 0 ) is obtained by dropping another four units from point C (or 8 units from point A). A straight line from point A through
any one of such MR points (as B 0 or C 0 ) will give us the MR curve.
For the demand curve in Fig. 9-1, at point B,
therefore, MR ¼ $6 1
at point C,
e ¼ B 00 G
OB 00 ¼ 6 2 ¼ 3
1
3
e ¼ C 0 G
OC 0 ¼ 4 4 ¼ 1
therefore, MR ¼ $4 1
at point F,
therefore, MR ¼ $2 1
1
1=3
1
1
¼ $6 2 ¼ $4 ( point B 0 )
3
¼ $4(0) ¼ 0 ( point C 0 )
e ¼ F 0 G
OF 0 ¼ 2 6 ¼ 1 3
¼ $2( 2) ¼ $4 (not shown in the figure)
Note that in the case of perfect competition, e ¼ 1 (infinity). Therefore, MR ¼ P(l 2 1/1) ¼ P(l 2 0) ¼ P. Thus, the
marginal revenue curve and the demand curve of the perfectly competitive firm coincide.
9.3 SHORT-RUN EQUILIBRIUM UNDER PURE MONOPOLY: TOTAL APPROACH
The short-run equilibrium output of the monopolist is the output at which either total profits are maximized
or total losses minimized (provided TR . TVC; see Section 8.5).
EXAMPLE 3. In Table 9.2, TR [column (3)] minus STC [column (4)] gives total profits [column (5)]. Total profits are
maximized (at $3.75) and the monopolist is in short-run equilibrium when producing and selling 2.5 units of the commodity
per time period at the price of $5.50.