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LECTURE 16
COST FUNCTIONS (CONTINUED)
Let us review cost functions to this point.
Columns (1), (2), and (3) from
Table 151 are empirical relationships between key operating variables:
Different levels of output of our firm (ounces of gold produced per week); total
fixed cost per week for each level of output; and total variable cost per week
for each level of output, respectively.
Column (4), total cost per week for
each level of output is merely the sum of Column (2) and Column (3)
TC = TFC + TVC
Equation 161
Where TC is total cost at each level of output; TFC is total fixed cost at each
level of output; and TVC is total variable cost at each level of output.
Column (5) is average fixed cost, discussed in Lecture 15, and defined as
AFC = (TFC) / (Q)
Equation 162
Where AFC is average fixed cost per ounce at each level of output; TFC is
total fixed cost at each level of output; and Q is the level of output measured
in ounces of gold (all variables
per week
).
Remember, a graph of Equation
161 for any firm is always a
rectangular hyperbola
, such as Figure 154.
Column (6) is average variable cost, introduced in Lecture 15, and defined as
AVC = (TVC) / (Q)
Equation 163
Where AVC is average variable cost per ounce at each level of output; TVC is
total variable cost at each level of output; and Q is the level of output
measured in ounces of gold (all variables
per week
).
Column (7) is average total cost, introduced in Lecture 15, and defined as
ATC = (TC) / (Q)
Equation 164
Where ATC is average total cost per ounce at each level of output; TC is the
total cost of each level of output; and Q is the level of output measured in
ounces of gold (all variables
per week
).
Note, again, that ATC can be
calculated two different ways.
The first is Equation 164.
The second is
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View Full Document ATC = AFC + AVC
Equation 165
Where ATC, AFC, and AVC are all defined above.
The proof of this follows
from the creation of Column (4), where TC = TFC + TVC (Equation 161
above).
Since TC = TFC + TVC;
it follows that (TC) / (Q) = (TFC) / (Q) + (TVC) / (Q)
which is Equation 165.
(We simply divided Equation 161 through by Q.)
Column (8) is the
allimportant
variable, marginal cost.
1
Marginal cost is the
change
in column (5) divided by the change in column (1).
Marginal cost
answers the question, "How much does total cost increase each time we
increase output by one ounce of gold per week?"
MC = (
∆
TC) / (
∆
Q)
Equation 16
6
Where MC is the marginal cost of each unit of output produced;
defined as
∆
TC, the change in total cost, given a oneunit change in the level of output,
∆
Q.
Since fixed costs never change in the short run, all increases in total cost that
arise from producing ever more and more units of output per week must
result from the increase in total variable costs incurred when we increase the
level of output.
Hence, marginal cost can also be defined as the change in
total variable cost given a oneunit increase in output, or, the change in
column (3) divided by the change in column (1).
2
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This note was uploaded on 03/23/2011 for the course ECN 212 taught by Professor Nancy during the Spring '07 term at ASU.
 Spring '07
 nancy

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