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732 MATHEMATICAL APPENDIX

$140 Total cost (C)

120
ΔQ = 1 Tangent line
100 at point B.
B Slope = $28/unit
C, cost (dollars) 80 Tangent line A
ΔC = 21
at point E.
60
Slope = $12/unit
48
E Tangent line
40 at point A.
Slope = $15/unit
20

0 1 2 3 4 5 6 7
Q, quantity (units)
(a)

$50 Marginal cost (MC)

40 Average cost (AC)
FIGURE A.2 Relating Total,
Average, and Marginal Cost
Graphically 30 MC = 28
Panel (a) shows the total cost of C, cost (dollars per unit) AC = 24
producing any specified amount
AC = 15
of output. The units on the ver- 20 MC = 15
tical axis of the top graph are
monetary (dollars). The bottom AC = 16
graph shows the marginal and MC = 12
average cost curves corresponding 10
to the total cost curve in the top
graph. The units on the vertical
axis of the bottom graph are
dollars per unit. In panel (b), the 0 1 2 3 4 5 6 7
value of the marginal cost at each Q, quantity (units)
quantity is the same as the slope (b)
of the total cost in panel (a).

A.2 WHAT IS A “MARGIN”? Consider once again Table A.1, which shows the
total cost based on equation (A.4). The dependent vari-
Decision makers are often interested in the marginal value of able is total cost, and the independent variable is the
a dependent variable. The marginal value measures the change quantity produced. The table shows two ways of measur-
in a dependent variable associated with a one-unit change in an ing the marginal cost. Column three illustrates the first
independent variable. The marginal cost therefore measures way by showing how the total cost changes when one
the rate of change of cost, that is, C/ Q. A decision maker more unit is produced. The column is labeled “Arc”
may be interested in the marginal cost because it tells her how Marginal Cost because it measures the change in total
much more it will cost to produce one more unit. cost over an arc, or region, over which the quantity