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

158 COSTS OF PRODUCTION [CHAP. 7
7.6 From the TVC curve of Problem 7.2, derive the AVC curve geometrically and explain its shape.
See Fig. 7-9. AVC equals TVC divided by output. For example, at point D on the TVC curve, TVC equal $60.
Thus, AVC equals $60 divided by 1, or $60. This is equal to the slope of ray OD and is plotted as point D 0 on the
AVC curve. At point E on the TVC curve, the AVC is given by the slope of ray OG. This equals $26.50 ($105/4)
and is plotted as point E 0 on the AVC curve. At point F on the TVC curve, AVC equals the slope of ray OF which is
$35 ($210/6). This gives point F 0 on the AVC curve. Other points on the AVC curve could be similarly obtained.
Note that the slope of a ray from the origin to the TVC curve falls up to point E (where the ray from the origin is
tangent to the TVC curve) and rises thereafter. Thus, the AVC curve falls up to point E 0 and rises afterward.
Fig. 7-8
Fig. 7-9
7.7 From the TC curve of Problem 7.2, derive the AC curve geometrically and explain its shape.
See Fig. 7-10. The AC at points H, J, and N on the TC curve is given respectively by the slope of rays OH, OM,
and ON. These are equal to $70, $52, and $55, respectively and are plotted as points H 0 , J 0 , and N 0 on the AC curve.
The AC at other points on the TC curve could be similarly obtained. Note that the slope of a ray from the origin to
the TC curve falls up to point J (where the ray from the origin is tangent to the TC curve) and rises thereafter. Thus,
the AC curve falls up to point J 0 and rises thereafter.
7.8 From the TC and TVC curves of Problem 7.2, derive the MC curve geometrically and explain its shape.
See Fig. 7-11. The slope of the TC and TVC curves is exactly the same at every output level. Thus, MC is given
by the slope of either the TC or the TVC curve. The slope of the TC curve and the TVC curve (i.e., the MC) at point
D is $32. (The value of $32 is obtained from measuring the slope of the tangent to the TC curve at point D. That is,
moving from D to R we rise $40 and we move to the right by 1.25 units; thus the slope of DR equals 40/1.25 or $32.)
This gives point D 0 on the MC curve. Point S is the point of inflection on the TC and TVC curves. At this point, the
slope of the TC and TVC curves is at its lowest value. That value gives us the lowest point (i.e., point S 0 ) on the MC