Class
Meeting
#13
Marginal
Apalvsis
-Marginal
means
incremental change.
-Mathematical
equations
maybe used
to
model economic situations
and
mariy
important
decisions
are rnade
at
the
margin
How a untt change
in one
variable
effects
the change
in the
other.
*Margiual
analysis
attempts to study
the
rate
of
change of cost,
revenue, and
profit
functions.
*The
r4afeinA!
chanqe
in
a
function
at a
particular
value
is
defined to be
the
slqpp oflthe
lange:rt
line to the
graph
of the
function at that
value.
So,
Exarqple:
y:
50+3x
is
the
equation
of a
line with
slope 3. An
increase
of
I
in x
results in
an
increase of
3
in
y.
We
say the
marginal change in
y
at x:l
is 3.
Since the derivative
dyldx
=
3 is
constant,
the
marginal
change
is
y
is
always
3, regardless
ofthe
value
of
x.
Example:
If f[x)
:
0.5x2
+100
defines a
function.
f
'(x)
:
x.
Note
that the
marginal
change
in
f
changes
depending
on
the
value
ofx, since the
derivative
is
variable.
i.e., f
'111=T,f
'(2)-2.
Mareinal
Cost
-Let
C
=
total
cost
of
producing
x
units
of
an item. Then
C{x)
would
be the total cost function.
-Marginal
Cost
-
C
'(x)
and measures the
rate
of change
in
cost
per
unit
change
in
production
at a
gtven
output
level.
(this
approximates the
extra cost
of
producing
one additional
unit).
Example: Let C(x)=5,000*4x3.
Find
the margrnal cost
at
100 units.
(this
approximates the
cost
of the iOi
unit)
