Cost Curves
Average Costs
Marginal Costs
Long run and Short
Run
Cost Function
In our example, the short-run cost function
was:
 70  5
3

+ 3,000
c( y ) = 
y
1
 (3,000 )3 
Variable costs
cv ( y )
Fixed costs
F
Cost Curve
c( y )
c ( y ), cv ( y ), F
cv ( y )
F
3,000
0
y
Average Cost Function
The short run average cost function:
2


c( y )
70
3,000
3
y +
AC ( y ) =
=
1
y
y
 (3,000)3 
Average variable cost Average fixed cost
AVC ( y )
AFC ( y )
Average Fixed Cost Curve
AFC ( y )
3,000
AFC ( y ) =
y
0
y
Average Variable Cost Curve
AVC ( y )
 70  2
3

AVC ( y ) = 
y
1
 (3000)3 
AVC ( y )
0
y
Why is AVC Increasing in y?
Production function and AVC:
 70  1 −1
0.6
0.2
0.6

y = (3,000) ( xl ) 
→ AVC ( y ) = 
y
1
 (3000 )3 
Productions function features decreasing
returns to scale wrt xl
Average Cost Curve
AC ( y )
AC ( y )
124
0
 70  2 3,000
3

+
AC ( y ) = 
y
1
y
 (3000 )3 
60
y
Marginal Cost Function
The short run cost function:
∂c ( y ) ∂cv ( y )
MC ( y ) =
=
∂y
∂y
The short run marginal cost function:
2


5
70
3

MC ( y ) = 
y
1
3  (3,000)3 


Marginal and Average Variable
Cost Curves
5  70  3
y
MC ( y ) = 
1
3  (3,000 )3 


2
AVC ( y ),
MC ( y )
MC ( y )
 70  2
y3
AVC ( y ) = 
1
 (3000 )3 
AVC ( y )
0
y
Marginal and Average Cost
Curves
MC ( y )
AC ( y )
AC ( y ),
AVC ( y ),
MC ( y )
AVC ( y )
124
0
60
y
Variable Costs and the Marginal
Cost Curve
5  70  3
y
MC ( y ) = 
1
3  (3,000)3 


2
MC ( y )
MC ( y )
cv ( y1 )
0
y1
y
Long Run
In the long run there are no fixed factors of
production
Firm can freely adjust inputs
Production costs are lower in the long run
Long and Short Run Cost Curves
cS ( y )
c ( y ), c ( y )
S
L
cL (y )
3,000
0
91
y
Long and Short Run Average
Cost Curves
AC S ( y )
AC ( y )
AC L ( y )
128
124
0
60
91
y
Long and Short Run Marginal
Cost Curves
MC S ( y )
MC ( y )
MC L ( y )
0
91
y
Long and Short Run Cost
Functions
1
4
 3 4
c ( y ) = 70 
y
 70  3
L
5
4
 1  5
S
3

c ( y ) = 70 
y
+ 3,000
1
 (3,000 )3 

