Lesson 9 – Marginal Functions in Economics
1
Lesson 9
Marginal Functions in Economics
Marginal Cost
Suppose a business owner is operating a plant that manufactures a certain product at a
known level.
Sometimes the business owner will want to know how much it costs to
produce one more unit of this product.
The cost of producing this additional item is
called the marginal cost
.
Example 1:
Suppose the total cost in dollars per week by ABC Corporation for
producing its bestselling product is given by
.
4
.
0
3000
000
,
10
)
(
2
x
x
x
C

+
=
Find the
actual cost of producing the 101
st
item.
The cost of producing the 101
st
item can be found by computing the average rate of
change, that is by computing
100
101
)
100
(
)
101
(


C
C
.
Note that
x
h
x
x
C
h
x
C
C
C

+

+
=


)
(
)
(
)
(
100
101
)
100
(
)
101
(
where
x
= 100 and
h
= 1.
The right hand side of this equation is the formula for average rate of change of the cost
function.
This will give us the actual cost of producing the next item.
However, it is
often inconvenient to use.
For this reason, marginal cost is usually approximated by
the instantaneous rate of change of the total cost function evaluated at the specific
point of interest.
That is to say, we’ll find the derivative and substitute in our point
of interest.
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2
Example 2:
Suppose the total cost in dollars per week by ABC Corporation for
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 Fall '08
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 business owner, ABC Corporation

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