Dr. Steven Waters
Econ 380
Page 1 of 5
Lecture 13
Costs II
… ye have eaten up the vineyard;
the spoil of the poor is in your houses.
What mean ye that ye beat my people to pieces,
and grind the faces of the poor?
Isaiah 3:1415
The Economics Outline
1.
Changing Input Prices
2.
LongRun Cost Functions
3.
ShortRun Cost Functions
The Mathematics Outline
1.
Homogeneity
2.
Algebra & Calculus
Cost Functions and Homogeneity
The total cost function is
homogeneous of degree one in input prices
.
Consider what
happens when input prices both increase by the same proportion,
t
.
Initial Total Cost function:
wL
vK
TC
+
=
Increase by proportion,
t
:
TC
t
wL
vK
t
L
tw
K
tv
⋅
=
+
=
+
)
(
)
(
)
(
Thinking about the cost minimizing bundle combination, the slope of the isoquant at the
cost minimizing point is 
w/v
even after the proportional increase in
v
and
w
.
Hence, the
same amount of
K
and
L
will minimize costs but costs will just be at a higher level.
Because the total cost function is homogeneous of degree one in all input prices, the
Average Cost function and the Marginal Cost function will also be homogeneous of
degree one in input prices.
To see this, consider the following:
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 Spring '11
 Stevens
 Economics, tc, total cost function

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