Chapter 21
NAME
Cost Curves
Introduction.
Here you continue to work on cost functions. Total cost
can be divided into fixed cost, the part that doesn’t change as output
changes, and variable cost. To get the average (total) cost, average fixed
cost, and average variable cost, just divide the appropriate cost function
by
y
, the level of output. The marginal cost function is the derivative of
the total cost function with respect to output—or the rate of increase in
cost as output increases, if you don’t know calculus.
Remember that the marginal cost curve intersects both the average
cost curve and the average variable cost curve at their minimum points.
So to find the minimum point on the average cost curve, you simply set
marginal cost equal to average cost and similarly for the minimum of
average variable cost.
Example:
A firm has the total cost function
C
(
y
) = 100 + 10
y
. Let us
find the equations for its various cost curves. Total fixed costs are 100, so
the equation of the average fixed cost curve is 100
/y
. Total variable costs
are 10
y
, so average variable costs are 10
y/y
= 10 for all
y
. Marginal cost
is 10 for all
y
. Average total costs are (100 + 10
y
)
/y
= 10 + 10
/y
. Notice
that for this firm, average total cost decreases as
y
increases. Notice also
that marginal cost is less than average total cost for all
y
.
21.1 (0)
Mr. Otto Carr, owner of Otto’s Autos, sells cars. Otto buys
autos for $
c
each and has no other costs.
(a)
What is his total cost if he sells 10 cars?
10
c
.
What if he sells 20
cars?
20
c
.
Write down the equation for Otto’s total costs assuming
he sells
y
cars:
TC
(
y
) =
cy
.
(b)
What is Otto’s average cost function?
AC
(
y
) =
c
.
For every
additional auto Otto sells, by how much do his costs increase?
c
.
Write down Otto’s marginal cost function:
MC
(
y
) =
c
.
(c)
In the graph below draw Otto’s average and marginal cost curves if
c
= 20.
266
COST CURVES
(Ch.
21)
0
10
20
30
40
10
20
30
40
AC, MC
Red line
AC=MC=20
Output
(d)
Suppose Otto has to pay $
b
a year to produce obnoxious television
commercials.
Otto’s total cost curve is now
TC
(
y
) =
cy
+
b
, his
average cost curve is now
AC
(
y
) =
c
+
b/y
, and his marginal cost
curve is
MC
(
y
) =
c
.
(e)
If
b
= $100, use red ink to draw Otto’s average cost curve on the
graph above.
21.2 (0)
Otto’s brother, Dent Carr, is in the auto repair business. Dent
recently had little else to do and decided to calculate his cost conditions.
He found that the total cost of repairing
s
cars is
TC
(
s
) = 2
s
2
+ 10. But
Dent’s attention was diverted to other things
. . .
and that’s where you
come in. Please complete the following:
Dent’s Total Variable Costs:
2
s
2
.
Total Fixed Costs:
10
.
Average Variable Costs:
2
s
.
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 Spring '10
 JOSEPHPETRY
 Mr. Otto Carr

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