Download Firm / Production Costs 7 Cost Concepts (Short-run)

06.11.2016
Firm / Production Costs
7 Cost Concepts (Short-run)
1.
2.
3.
4.
5.
6.
7.
Total Fixed Cost
Total Variable Cost
Total Cost
Average Fixed Cost
Average Variable Cost
Average Total Cost
Marginal Cost
(TFC)
(TVC)
(TC=TVC+TFC)
(AFC=TFC/Q)
(AVC=TVC/Q)
(AC=AFC+AVC)
(MC= ∆AVC/∆Q
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Fixed and Variable Costs
• Costs of production may be divided into
fixed costs and variable costs.
• Fixed costs are those costs that do not
vary with the quantity of output
produced.
• Variable costs are those costs that do
vary with the quantity of output
produced.
Formula of Total Cost
• Total Costs (TC)
– Total Fixed Costs (TFC)
– Total Variable Costs (TVC)
– Total Costs (TC)
TC = TFC + TVC
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Total Fixed Cost (TFC)
• Total fixed cost (TFC) is more commonly
referred to as "sunk cost" or "overhead
cost."
• Total fixed cost is the cost associated with
the fixed input.
– Examples: include the payment or rent for
land, buildings and machinery.
– The fixed cost is independent of the level of
output produced.
– Graphically, depicted as a horizontal line
Since TFC is constant,
its graph is a horizontal line.
Price
TFC
Quantity
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Total variable cost (TVC)
• Total variable cost (TVC) refers to the cost that
changes as the amount of output produced is
changed.
• Total variable cost is the cost associated with the
variable input.
– Examples: purchases of raw materials, payments to
workers, electricity bills, fuel and power costs.
– Total variable cost increases as the amount of output
increases.
• If no output is produced, then total variable cost is zero;
• the larger the output, the greater the total variable cost.
The TVC curve is upward sloping.
Price
TVC
It is often drawn like a
flipped over S, first getting
flatter & flatter,
& then steeper & steeper.
This shape reflects the
increasing & then
decreasing marginal returns
we discussed in the section
on production.
Quantity
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Total cost (TC)
• Total cost (TC) is the sum of total fixed cost
and total variable cost
TC=TFC+TVC
– As the level of output increases, total cost of the
firm also increases.
Price
TC
(Total Cost)
TVC
(Total Variable Cost)
TFC
(Total Fixed Cost)
Q
0
“TOTAL” COST CURVES
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Total Cost
Price
TC
TC = TFC + TVC
The TC curve looks
like the TVC curve,
but it is shifted up,
by the amount of
TFC.
TFC
Quantity
Average Costs
• Different types of average cost (ATC, AVC, and AFC) are
irrelevant to earning the greatest possible level of profit
– Common error—sometimes made even by business managers—is to
use average cost in place of marginal cost in making decisions
• Problems with this approach
– ATC includes many costs that are fixed in short-run—including cost of all fixed
inputs such as factory and equipment and design staff
– ATC changes as output increases
• Correct approach is to use the marginal cost and to consider
increases in output one unit at a time
– Average cost doesn’t help at all; it only confuses the issue
• Average cost should not be used in place of marginal cost as a
basis for decisions
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Average Costs
• Average Costs
– Average costs can be determined by dividing the firm’s
costs by the quantity of output it produces.
– The average cost is the cost of each typical unit of
product.
• Average Costs
– Average Fixed Costs (AFC)
– Average Variable Costs (AVC)
– Average Total Costs (ATC)
ATC = AFC + AVC
AVERAGE COSTS
AFC 
Fixed cost FC

Quantity
Q
AVC 
Variable cost VC

Quantity
Q
ATC 
Total cost TC

Quantity
Q
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Costs (dollars)
06.11.2016
• The AFC curve slopes
downward & gets
closer & closer to the
horizontal axis.
AFC
Quantity
Costs (dollars)
Average Variable Cost
AVC
Quantity
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Costs (dollars)
06.11.2016
ATC
AVC
AFC
Quantity
Average Total Cost Curve and Its Shape
• The average total-cost curve is U-shaped.
• At very low levels of output average total cost is
high because fixed cost is spread over only a
few units.
• Average total cost declines as output increases.
• Average total cost starts rising because average
variable cost rises substantially.
• The bottom of the U-shaped ATC curve occurs
at the quantity that minimizes average total
cost. This quantity is sometimes called the
efficient scale of the firm.
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• Average fixed cost (AFC) decreases as output
increases.
• The average variable cost curve (AVC) is Ushaped.
• The average total cost curve (ATC) is also Ushaped.
Average Total Cost
Price
ATC
AVC
Like AVC, ATC is
U-shaped, but it
reaches its minimum
after AVC reaches its
minimum.
This is because
ATC = AVC +AFC & AFC
continues to fall & pulls
down ATC.
Quantity
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Marginal Costs
• Marginal Cost
– Marginal cost (MC) measures the increase in
total cost that arises from an extra unit of
production.
– Marginal cost helps answer the following
question:
• How much does it cost to produce an additional
unit of output?
Formula of Marginal Cost
• Marginal Cost
= Change in Total Cost/Change in Quantity
= Change in Variable Cost/Change in
Quantity
MC 
(change in total cost) TC

(change in quantity)
Q
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Marginal Cost Curve and Its Shape
• Marginal cost rises with the amount of
output produced.
– This reflects the property of diminishing
marginal product.
While MC is U-shaped, it is often drawn so it
extends up higher on the right side.
$
MC
Quantity
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The MC must intersect the ATC at its minimum & the
AVC curve at its minimum.
MC
$
ATC
AVC
Quantity
Total Costs of Production
Quantity
Total
Fixed
Cost
Total
Variable
Cost
Total
Cost
Average
Cost
MC
AC
130
30
130
50
150
20
75
60
160
10
53.3
100
65
165
5
41.25
5
100
75
175
10
35
6
100
95
195
20
32.5
7
100
125
225
30
32.14
8
100
165
265
40
33.12
L
TFC
TVC
0
100
0
1
100
30
2
100
3
100
4
TC
Marginal
Cost
100 -
-
9
100
215
315
50
35
10
100
275
375
60
37.5
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1400
TC
1200
1000
TVC
800
600
400
TFC
200
0
0
2
4
6
8
180
160
140
120
100
80
60
40
20
0
10
12
MC
AC
AVC
0
2
4
6
8
10
12
• Average fixed cost declines steadily over the range of
production.
• Average variable cost declines at first but starts to
increase after 4 units.
• Average total cost also declines at first but starts to
increase after 4 units.
• Marginal cost declines and then starts to increase
once the third unit of output is produced.
• When MC < AVC, AVC is falling.
• When MC > AVC, AVC is rising.
• When MC = AVC, AVC is at its minimum.
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Relationship between MC and ATC
• Relationship between Marginal Cost and
Average Total Cost
– Whenever marginal cost is less than average total cost
MC < ATC average total cost is falling.
– Whenever marginal cost is greater than average total cost
MC > ATC, average total cost is rising.
– The marginal-cost curve crosses the average-total-cost
curve at the efficient scale.
• Efficient scale is the quantity that minimizes average
total cost.
P
TVC
Inflection
point
0
q1
(Total Variable Cost)
MC
Q
AVC
q1
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The Marginal Cost curve passes
through the minimum point of
the AVC curve.
P
MC (Marginal Cost)
It is also U-shaped. First it
decreases, reaches a minimum
and then increases.
AVC
(Average Variable Cost)
Minimum AVC
0
q1
Q
MC
P
AC
AVC
AFC
0
q1
Q
The “PER UNIT” COST CURVES
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Example 1.
• Produce 3 units at an average cost of £1 per
unit. Total cost: £3
• Increase production by 1 unit. The cost of
the additional unit is 0.6 £ – this is the MC
• Total cost = £3.6, total output = 4 units.
• Average cost = £0.9 per unit.
• If MC was £1.4, total cost = £4.4
• Average cost = £1.1 per unit.
Example 2.
• Produce 1,500 tonnes of wheat at an
average cost of £50 per tonne.
• Total cost: £75,000
• Increase production by 1 tonne, but the
cost of the additional tonne is 80 £ – this is
the marginal cost
• Total cost = £75,080, total output =1,501 t
• Average cost = £50.02
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The Short Run Cost Function
• A change in input
prices will shift the
cost curves.
– If fixed input costs are
reduced then ATC will
shift downward. AVC
and MC will remain
unaffected.
The Short Run Cost Function
• A change in input
prices will shift the
cost curves.
– If variable input
costs are reduced
then MC, AVC, and
AC will all shift
downward.
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Costs in the Short Run and in the Long
Run
• For many firms, the division of total costs
between fixed and variable costs depends
on the time horizon being considered.
– In the short run, some costs are fixed.
– In the long run, fixed costs become variable
costs.
Short-Run Cost Curves and Long-Run
Cost Curves
• Because many costs are fixed in the short
run but variable in the long run, a firm’s
long-run cost curves differ from its shortrun cost curves.
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Economic Time & Production Costs
• Law of Diminishing Returns
– As additional units of a variable factor are added
to a fixed factor, beyond some point the
additional product from each additional unit of
the variable factor decreases.
• Long-Run Costs
– Long-Run Total Cost, Average Cost, & Marginal
Cost
• Total cost, per unit cost, and cost per additional unit
of output, respectively.
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Economic Time & Production Costs
Long-run total cost
is the total
expenditure for
each level of output
in the long run.
Long-run average
total cost equals
unit cost; and longrun marginal cost
measures the cost
of producing an
additional unit of
output.
The Long Run Cost Function
• In the long run, all inputs to a firm’s production
function may be changed.
• There are no fixed inputs and thus there are no
fixed costs.
• Decisions regarding long-run cost of operations
are considered to be part of the management’s
planning horizon.
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Scale of
Production
(Capacity Level)
A
B
C
D
E
F
Total Product
(Output/month)
10,000
20,000
30,000
40,000
50,000
60,000
Long-Run
Total Cost
(LRTC)
50,000
90,000
120,000
150,000
200,000
260,000
Long-Run
Marginal Cost
(LRMC)
5.00
4.00
3.00
3.00
5.00
6.00
Long-Run
Average Cost
(LRAC)
5.00
4.50
4.00
3.75
4.00
4.33
LRTC = LTC
LRMC = LMC
LRAC = LAC
7
LRMC
6
5
LRAC
4
3
2
1
0
0
10000
20000
30000
40000
50000
60000
70000
The long-run cost function exhibits the same pattern of behavior
as the short-run cost function.
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LTC
LTC
Long Run Total Cost
All inputs are variable in the long
run. There are no fixed costs.
Total Product
Q
LONG-RUN TOTAL COST CURVE
The LAC
• The LAC curve is curve that envelopes all
possible plant sizes. Also known as „planning
curve”.
• It traces the lowest average cost of producing
each level of output.
• It is U-shaped because of
– Economies of Scale
– Diseconomies of Scale
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Cost
SRATC1
At a relatively low output level, in the short run, the firm might
have SRATC1 curve as its short run average cost curve.
Quantity of output
Cost
SRATC2
At a slightly higher output level, in the short run, the firm might
have SRATC2 curve as its short run average cost curve.
Quantity of output
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Cost
SRATC3
At a still higher output level, in the short run, the firm might have
SRATC3 curve as its short run average cost curve.
Quantity of output
Cost
LRATC
SRATC1
SRATC2
SRATC5
SRATC3
SRATC4
In the long run, the firm can pick any appropriate plant size. At
each output level, the firm picks the plant that has the SRATC
curve with the lowest value.
Quantity of output
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06.11.2016
Cost
LRATC
SRATC1
SRATC2
SRATC5
SRATC3
SRATC4
So, the LRATC curve is made up of segments of the SRATC curves.
Quantity of output
In many industries, the number of possible
plant sizes is virtually unlimited.
Then the LRATC curve is made up of points of
tangential of the theoretically unlimited
number of SRATC curves.
Then the long run ATC curve is smooth.
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06.11.2016
Cost
LRATC
SRATC1
SRATC5
SRATC2
SRATC4
SRATC3
Quantity of output
Economic Time & Production Costs
• Phases of Long-Run Average Total Cost
– Economies of Scale
• Occurs when the increasing size of production in the
long run causes the per unit cost of production to fall.
– Diseconomies of Scale
• Occur when the increasing size of production in the
long run causes the per unit cost of production to
rise.
– Constant Returns to Scale
• Occur in the range of production levels in which longrun average total cost is constant.
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The downward-sloping section of
the Long Run ATC curve reflects
Economies of Scale.
Economies of Scale:
As plant size increases, there are factors which lead to
lower average costs of production.
•
•
•
Labor Specialization: Jobs can be subdivided and
workers performing very specialized tasks can
become very efficient at their jobs.
Managerial Specialization: Management can also
specialize in a larger firm (in areas such as
marketing, personnel, or finance).
Equipment that is technologically efficient but only
effectively utilized with a large volume of
production can be used.
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Possible Reasons for
Economies of Scale
• Specialization in the use of labor and capital
• Indivisible nature of many types of capital equipment
• Productive capacity of capital equipment rising faster
than purchase price
• Economies in maintaining inventory of replacement parts
and maintenance personnel
• Discounts from bulk purchases
• Lower cost of raising capital funds
• Spreading of promotional and research and development
costs
• Management efficiencies (line and staff)
The upward-sloping section of
the Long Run ATC curve reflects
Diseconomies of Scale.
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Diseconomies of Scale:
As plant size increases, there are factors which lead to
higher average costs of production.
•
•
Expansion of the management hierarchy leads to
problems of communication, coordination, and
bureaucracy (red tape), and the possibility that
decisions will be wrong. („The left hand doesn’t
seem to know what the right hand is doing.”) The
result is reduced efficiency.
In large facilities, workers may feel alienated and
discoraged to work as much as they should. Then
additional supervision may be required and that
adds to the costs.
Sometimes there is a segment of the
LR ATC curve which is horizontal.
In that section,
the LR ATC is constant, & there are
Constant Returns to Scale.
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Average Total Cost in the Short and Long Run
Average
Total
Cost
ATC in short
run with
small factory
ATC in short
run with
medium factory
ATC in short
run with
large factory
ATC in long run
$12,000
10,000
Economies
of
scale
0
Constant
returns to
scale
1,000 1,200
Diseconomies
of
scale
Quantity of
Cars per Day
$/TL
LRAC
Q
economies
of scale
constant returns
to scale
(neither economies
nor diseconomies)
diseconomies
of scale
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06.11.2016
•
Economic
Time & Production Costs
Phases of Long-Run Average Total Cost
– Economies of Scale
• Occurs when the increasing size of production in the long run
causes the decrease in unit cost of production.
• Economies of scale refers to the firm’s property whereby longrun average total cost falls as the quantity of output increases.
– Diseconomies of Scale
• Occur when the increasing size of production in the long run
causes the per increase in unit cost of production.
• Diseconomies of scale refers to the firm’s whereby long-run
average total cost rises as the quantity of output increases.
– Constant Returns to Scale
• Occur in the range of production levels in which long-run
average total cost is constant.
• Constant returns to scale refers to the property whereby longrun average total cost stays the same as the quantity of output
increases
LMC
COST
SMC2
SMC1
0
LAC
SAC2
SAC1
Q1
Q
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Long Run Average Cost and Long Run
Marginal Cost
• Long-run Average Cost (LAC) curve
– is U-shaped.
– the envelope of all the short-run average cost
curves;
– driven by economies and diseconomies of size.
• Long-run Marginal Cost (LMC) curve
– Also U-shaped;
– intersects LAC at LAC’s minimum point.
The Learning Curve
• A line showing the relationship between labor
cost and additional units of output.
• Downward slope of the learning curve indicates
that the additional cost per unit declines as the
level of output increases because workers
improve with practice.
• The reduction in cost from this particular source
of improvement is referred to as the learning
curve effect.
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• The learning curve effect is measured by the
percentage decrease in additional labor cost each
time the output doubles.
• Learning rate is given by the following formula:

AC 2 
 x 100
learning rate  1 
AC
1 

• This is the rate at which average cost falls as
cumulative output doubles.
unit
labor
cost
cumulative output
over time
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unit
labor
cost
C
B
A
LRACt
LRACt+1
Qt
Qt+1
cumulative output
over time
From C to B, learning effect
From B to A, economies of scale effect
The Learning Curve
• Measures the
percentage decrease in
additional labor cost
each time output
doubles.
– An “80 percent” learning
curve implies that the
labor costs associated
with the incremental
output will decrease to
80% of their previous
level.
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The Learning Curve
• A downward slope in the learning curve
indicates the presence of the learning curve
effect
– Why? Workers improve their productivity with
practice
• The learning curve effect shifts the SRAC
downward
Economies of Scope
• The reduction in a firm’s unit cost that results
from producing two or more goods jointly
rather than separately.
• Sharing certain aspects of the production
process, the firm is able to decrease its unit
cost.
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We’ve discussed economies & diseconomies of scale.
When a firm produces more than one product, it
may also experience
economies or diseconomies of scope.
Economies of scope exist when a single firm
producing multiple products jointly can produce
them more cheaply than if each product was
produced by a separate firm.
Economies of scope may occur because
1. Production of different products use
common inputs.
•
Example: Automobile & truck production
may use the same factory assembly line and
raw materials.
2. Production of one good results in production
of by-products that company also can sell.
•
Example: A cattle producer raises cattle
to sell for beef, but can also sell leather.
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A measure of economies of scope is
TC(Q1 )  TC(Q 2 ) – TC(Q1  Q 2 )
TC(Q1  Q 2 )
where TC(Q1) is the total cost of producing Q1 units
of product 1 only, TC(Q2) is the total cost of
producing Q2 units of product 2 only, & TC(Q1+Q2) is
the total cost of producing them jointly.
This measure indicates the savings of joint
production compared to separate production, as a
percentage of joint production.
Example 1: The total cost of producing Q1 units of
product 1 only is 50,000. The total cost of producing Q2
units of product 2 only is 90,000. The total cost of
producing them jointly is 120,000. Determine if there
economies or diseconomies of scope, and measure
them.
There are economies of scope, since joint production is less
costly than the sum of the separate productions.
TC(Q1 )  TC(Q 2 ) – TC(Q1  Q 2 )
TC(Q1  Q 2 )

20,000
50,000  90,000  120,000

120,000
120,000
 0.167
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Example 2: The total cost of producing Q1 units of
product 1 only is 50,000. The total cost of producing Q2
units of product 2 only is 90,000. The total cost of
producing them jointly is 150,000. Determine if there
economies or diseconomies of scope, and measure
them.
There are diseconomies of scope, since joint production is
more costly than the sum of the separate productions.
TC(Q1 )  TC(Q 2 ) – TC(Q1  Q 2 )
TC(Q1  Q 2 )

 10,000
50,000  90,000  150,000

150,000
150,000
 0.067
Example 3: The total cost of producing Q1 units of
product 1 only is 50,000. The total cost of producing Q2
units of product 2 only is 90,000. The total cost of
producing them jointly is 140,000. Determine if there
economies or diseconomies of scope, and measure
them.
There are neither economies nor diseconomies of scope, since
joint production costs the same amount as the sum of the
separate productions.
TC(Q1 )  TC(Q 2 ) – TC(Q1  Q 2 )
TC(Q1  Q 2 )

0
50,000  90,000  140,000

140,000
140,000
0
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06.11.2016
To review and extend knowledge
• MIT Open Courseware - freely available video
recordings of introductory level
microeconomics classes at MIT corresponding
to lecture 2 of our course
1. Introduction to producer theory (00:37:21)
• http://www.youtube.com/watch?v=A6FOBdtbcz4&list=
SP61533C166E8B0028&index=9
2. Productivity and costs (00:47:30)
• http://www.youtube.com/watch?v=Q4iKuKAjzK0&list=
SP61533C166E8B0028&index=10
40