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

CHAP. 9] PRICE AND OUTPUT UNDER PURE MONOPOLY 215
EXAMPLE 4. The values in columns (1) through (5) of Table 9.3 come from Tables 9.1 and 9.2. The other values
in Table 9.3 are derived from the values given in columns (1), (2), (3), and (5). The monopolist maximizes total profits
(at $3.75) when producing and selling 2.5 units of output at the price of $5.50. At this level of output, MR ¼ SMC
(¼$3); MR is falling and SMC is rising (so that the negative slope of the MR curve is smaller than the positive slope of
the SMC curve). As long as MR . SMC, it pays for the monopolist to expand output and sales since doing so would
add more to TR than to STC (so profits rise). The opposite is true when MR , SMC (see Table 9.3). Thus total profits
are maximized where MR ¼ SMC.
(1)
P ($)
(2)
Q
(3)
TR ($)
(4)
MR ($)
Table 9.3
(5)
STC ($)
(6)
SMC ($)
(7)
SAC ($)
(8)
Profit/
Unit ($)
(9)
Total
Profit ($)
8.00 0 0 . . 6 . . . . . . 26.00
7.00 1 7.00 7 8 2 8.00 21.00 21.00
6.00 2 12.00 5 9 1 4.50 þ1.50 þ3.00
5.50 2.5 13.75 (3) 10 (3) 4.00 þ1.50 þ3.75
5.00 3 15.00 3 12 3 4.00 þ1.00 þ3.00
4.00 4 16.00 1 20 8 5.00 21.00 24.00
3.00 5 15.00 21 35 15 7.00 24.00 220.00
Fig. 9-3
The profit-maximizing or best level of output for this monopolist can also be viewed in Fig. 9-3 [obtained by plotting
the values of columns (1), (2), (4), (6), and (7) of Table 9.3].
In Fig. 9-3, the best, or optimum, level of output for the monopolist is given by the point where the SMC curve intersects
the MR curve from below (so that at the intersection point, the slope of the MR curve, which is always negative, is
smaller than the slope of the SMC curve, which is usually positive). At this best output level of 2.5 units, the monopolist
makes a profit of $1.50 per unit (the vertical distance between D and SAC at 2.5 units of output) and $3.75 in total (2.5 units
of output times the $1.50 profit per unit). Note that the best level of output is smaller than that associated with minimum SAC
and smaller than the output level at which P ¼ SMC.
9.5 LONG-RUN EQUILIBRIUM UNDER PURE MONOPOLY
In the long run, a monopolist will remain in business only if he or she can make a profit (or at least break
even) by producing the best level of output with the most appropriate scale of plant. The best level of output in
the long run is given by the point where the LMC curve intersects the MR curve from below. The most appropriate
scale of plant is the one whose SAC curve is tangent to the LAC curve at the best level of output.