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

222 PRICE AND OUTPUT UNDER PURE MONOPOLY [CHAP. 9
(c) From Fig. 9-9, we see that when P ¼ $10,
therefore MR ¼ $10 1
e ¼ 10
2 ¼ 5
1
5
¼ $10 4
¼ $8
5
When P ¼ $6; e ¼ 6 6 ¼ 1
therefore MR ¼ $6(1 1) ¼ $0
When P ¼ $2, e ¼ 2 10 ¼ 0:2
therefore MR ¼ $2 1
1
0:2
¼ $2(1 5) ¼ $8
Note that when TR is maximum (in this problem, $36), e ¼ 1 and MR ¼ $0.
9.5 (a) Sketch the curvilinear demand curve given by the points in Table 9.7. Derive geometrically the MR
curve by drawing tangents to the given D curve at various points and then proceeding in exactly the
same way as with a straight-line D curve. (b) What is the justification for this procedure?
Table 9.7
P ($) 11 8 5 4
Q 1 2 6 10
(a) In Fig. 9-10, the MR corresponding to point A on the curvilinear D curve is given by point A 0 . To get point A 0 ,
we draw a tangent to the D curve at point A, extend this tangent to the price axis, and treat this tangent as a
straight-line D curve. Since this (straight-line) tangent falls by three units from the point where it crosses the
price axis to point A, we get point A 0 by dropping three units directly below point A. We get the MR corresponding
to points B and C on the curvilinear D curve in exactly the same way. This will give us points B 0
and C 0 . By joining points A 0 , B 0 , and C 0 we get the MR curve shown in Fig. 9-10.‘
(b)
Fig. 9-10
The justification for this procedure is as follows. If we treat the tangent to the curvilinear D curve as a straightline
D curve, then at the point of tangency these two D curves will have the same e and will indicate the same