A Cost Function
Marginal and Average Cost
Qu a n tit y
MC
0
1
2
3
4
5
AC
0
1
2
3
4
5
Av e ra g e
Co s t
11
14
24
36
52
75
Average Cost
In c re m e n ta l
Co s t o r
Ma rg in a l Co st
Qu a n tity
0
1
2
3
4
5
12
Marginal and Average Cost
0
1
2
3
4
5
To ta l
Co s t
11
14
24
36
52
75
Av e ra g e
Co st
NA
14
12
12
13
15
Marginal and Average Cost
To ta l
Co st
11
14
24
36
52
75
Av e ra g e
Co s t
In c re m e n ta l
Co s t o r
Ma rg in a l Co st
NA
14
12
12
13
15
Marginal and Average Cost
Marginal Cost
Qu a n tity
In c re m e n ta l
Co s t o r
Ma rg in a l Co s t
Marginal and Average Cost
Average Cost
To ta l
Co st
Av e ra g e
Co st
11
14
24
36
52
75
Lectures in Microeconomics-Charles W. Upton
Qu a n tity
To ta l
Co s t
Marginal Cost
In c re m e n ta l
Co s t o r
Ma rg in a l Co s t
10
Qu a n tity
0
1
2
3
4
5
To ta l
Co s t
11
14
24
36
52
75
Av e ra g e
Co st
NA
14
12
12
13
15
In c re m e n ta l
Co s t o r
Ma rg in a l Co s t
3
10
12
16
23
Marginal and Average Cost
1
A Key Proposition
A Key Proposition
• If MC < AC, AC is falling
• If MC < AC, AC is falling
• If MC = AC, AC is constant
Marginal and Average Cost
Marginal and Average Cost
A Key Proposition
A Key Proposition
• If MC < AC, AC is falling
• If MC = AC, AC is constant
• If MC > AC, AC is rising
• If MC < AC, AC is falling
• If MC = AC, AC is constant
• If MC > AC, AC is rising
• Intuitively, the only way AC can be
rising is if the incremental units cost
more than the average.
Marginal and Average Cost
Marginal and Average Cost
The Proposition Illustrated
Qu a n tity
0
1
2
3
4
5
To ta l
Co st
11
14
24
36
52
75
Av e ra g e
Co s t
NA
14
12
12
13
15
Marginal and Average Cost
In c re m e n ta l
Co s t o r
Ma rg in a l Co s t
3
10
12
16
23
MC<AC; AC Falling
Qu a n tity
0
1
2
3
4
5
To ta l
Co s t
11
14
24
36
52
75
Av e ra ge
Co st
NA
14
12
12
13
15
In c re m e n tal
Co st o r
Ma rg in a l Cos t
3
10
12
16
23
Marginal and Average Cost
2
MC>AC; AC Rising
Qu a n t ity
0
1
2
3
4
5
To ta l
Co s t
11
14
24
36
52
75
Av e ra g e
Co s t
MC=AC; AC Constant
In c re m e n ta l
Co s t o r
Ma rg in a l Co s t
NA
14
12
12
13
15
3
10
12
16
23
Marginal and Average Cost
Qu a n tity
0
1
2
3
4
5
To ta l
Co s t
Av e ra g e
Co s t
11
14
24
36
52
75
In c re m e n ta l
Co st o r
Ma rg in a l Co st
NA
14
12
12
13
15
Marginal and Average Cost
The Graph
The Graph
MC
MC
AC
Marginal and Average Cost
The Mathematics
C (q)
AC =
q
Marginal and Average Cost
3
10
12
16
23
AC
Marginal and Average Cost
The Mathematics
AC =
C (q )
q
 1
dAC dC  1 
  − C (q ) 2 
=
dq
dq  q 
q 
Marginal and Average Cost
3
The Mathematics
AC =
C (q)
q
 1
dAC dC  1 
  − C (q) 2 
=
dq
dq  q 
q 
dAC  1  dC C (q) 

=  
−
dQ  q  dq
q 
Marginal and Average Cost
The Mathematics
dAC  1  dC C (q) 

=  
−
dQ  q  dq
q 
dAC  1 
=  ( MC − AC )
dQ  q 
Marginal and Average Cost
The Mathematics
dAC  1  dC C (q ) 

=  
−
dQ  q  dq
q 
Marginal and Average Cost
The Mathematics
dAC  1 
=  ( MC − AC )
dQ  q 
If MC > AC, AC is rising;
MC < AC, AC is falling
Marginal and Average Cost
The General Relation
MC
The U-Shaped AC Curve
MC
AC
Marginal and Average Cost
AC
Marginal and Average Cost
4
The U-Shaped AC Curve
MC
This is an empirical
AC
statement, not a general
requirement
Lets defer the question of
why this relation until later.
Marginal and Average Cost
End
©2004 Charles
W. Upton
Marginal and Average Cost
5