Transcript Behaviours Of Cost Curves

Behaviours Of
Cost Curves
Derivation And Properties of
Short Run Total, Average
And Marginal Cost Curves
How Does Total Cost Change ?
• It is actually a phenomenon in real world
that as a firm increases its output, its
productivity first rises faster and later rises
much slower or even decreases.
• So, if unit factor costs are kept constant,
the total cost first rise relatively slower
than the total output, but later rise much
faster.
Why Does This Happen ?
• In CE & AL level, such phenomenon is
explained in short run by the Law of
Diminishing (Marginal) Returns.
• In long run, it is caused by the dominance
of economies of scale in early production
and diseconomies of scale later on.
Law of Diminishing Returns
• This law states that when we continuously
add variable factors to fixed factors, the
total product (output) of a firm will first
rise more than proportionally and then less
than proportionally, or even decrease.
• Alternatively, we say that the marginal
product will eventually diminish.
An Illustration
• Suppose a farmer has a piece of cultivated
land and now wants to hire more workers
to work on the farm.
• Then he discovers that the farm’s output
changes as follow:
Output Table
No. Of
Land Total Output of
Workers (100m2) Vegetable (kg)
1
1
30
2
1
70
3
1
120
4
1
160
5
1
190
Output Table
No. Of
Land Total Output of
Workers (100m2) Vegetable (kg)
1
1
30
2
1
70
3
1
120
4
1
160
5
1
190
Variable
factor
Fixed
factor
Total
product
rises
faster
Total
product
rises
slower
Output Table
No. Of
Land
Total
Marginal
Workers (100m2) Product (kg) Product (kg)
1
1
30
30
2
1
70
40
3
1
120
50
4
1
160
40
5
1
190
30
Marginal product falls when
the third worker is added.
Plotting Short Run Costs Curves
• If factor costs are constant, e.g., the wage
of hiring one more worker is no different
from those hired before, total variable cost
rises proportionally.
• But due to the Law of Diminishing
(Marginal) Returns, total product rises
faster at first and slower later.
Cost ($)
Variable cost rises
proportionally.
TVC
TP(Q)
TP rises faster at first but slower at the end.
Adding Fixed Cost
• Fixed cost must occur as the production
begins and will not change with total
product.
• In short run, the total cost of production
includes both fixed and variable cost.
Cost ($)
TC and TVC are parallel
because the vertical
distance is fixed, that is
the same as the fixed
cost.
TC
TVC
TVC plus TFC
will be TC.
TFC
TP(Q)
Total fixed cost is a horizontal line
as it will not change with TP.
Cost ($)
TVC
TVC1
= AVC1
TP1
= tan Ø
TVC1
Ø
TP1
As tan Ø increases
when Ø is larger,
AVC is also larger.
TP(Q)
Cost ($)
TVC
Angle Ø decreases
first and then rises.
So does the AVC.
Q1
Q2
Q3
TP(Q)
Cost ($)
AVC also falls at the beginning
but rises later on.
AVC
Q1
Q2
Q3
TP(Q)
Cost ($)
TC
At same Q, angle Ø for
TC is greater than TVC.
Q1
TVC
Q3
TP(Q)
Cost ($)
Thus, at same Q, ATC
is higher than AVC.
ATC
AVC
Q1
Q2
Q3
TP(Q)
Cost ($)
But for fixed cost, its average
tends to fall as the total output
increases.
TFC
= AFC
TP
As only TP, not TFC, will
increase, the average
must be falling.
TFC
Q1
Q3
TP(Q)
Cost ($)
ATC and AVC are closing to
each other because AFC is
falling all the way.
ATC
AVC
AFC
AVC plus
AFC will be
ATC
Q1
Q2
Q3
TP(Q)
Cost ($)
The line from origin
forms the lowest angel
with TVC if it touches
TVC, but not
intersecting it.
Ø’
This tangency
point means at
Q’, we have the
lowest AVC.
Ø
Q’
Ø > Ø’
TVC
TP(Q)
Cost ($)
TC
The line from origin will
touch TC at a higher Q
than the TVC.
Q’ Q”
TVC
TP(Q)
Cost ($)
ATC reaches minimum
at a larger Q than the
minimum AVC.
ATC
AVC
AFC
Q’ Q”
TP(Q)
Cost ($)
At the range Q’ to Q”,
AVC is rising but AFC is
falling.
ATC
When AVC rises faster,
ATC will rise.
AVC
When AFC falls faster,
ATC still falls
AFC
Q’
Q”
TP(Q)
Cost ($)
Marginal cost =
Ø”
Change in Total cost
Change in Total Product
The tangency line will
overlap the curve segment if
the segment is very small.
This is a tangency
line touching TVC.
TVC
Q1
TP(Q)
Cost ($)
TVC
MC < AVC
Q1
MC = AVC
Q2
MC > AVC
Q3
TP(Q)
Cost ($)
AVC
MC
MC
MC < AVC
MC > AVC
MC = AVC
Q1
Q2
AVC
Q3
TP(Q)
Cost ($)
MC falls and rises
faster than the AVC.
MC
When MC is smaller
than AVC, AVC falls.
MC cuts AVC’s
minimum.
AVC
Q1
TP(Q)
Q2
Q3
When MC is larger
than AVC, AVC falls.
Cost ($)
Slopes are equal
for the same Q.
TC
TVC
TP(Q)
Q1
Q2
So, only one MC for both TC and TVC,
since they are parallel.
Cost ($)
TC
MC also cuts TC’s
minimum.
Q’ Q”
TVC
TP(Q)
Cost ($)
Assembly of all short
run cost curves
MC
ATC
AVC
AFC
MC cuts both ATC and
AVC at their minimum.
Q’ Q”
TP(Q)