Table 1: Farmer Joe’s Total Product Schedule
Corresponding label in the figure
13-2. Firm’s decision and cost
Fertilizer input
(tons)
Corn output
(bushels)
The only variable input
TP
A
0
1000
B
1
1250
C
2
1550
D
3
1900
E
4
2200
F
5
2450
G
6
2600
H
7
2650
I
8
2650
J
9
2600
© 2007 Thomson South-Western
Figure 1: Total Physical Product (TPP) of Farmer Joe
Production function
Total Phycial Product of Farmer Joe
Total output
(tons of corn)
3000
Corn output (tons)
2500
7
6
5
8
9
TP
4
2000
3
2
1500
1
1000
0
500
0
Quantity of Input (fertilizer)
0
0
1
2
3
4
5
6
7
8
9
Fertilizer input (tons)
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From the Production Function to the
Total-Cost Curve
• The relationship between the quantity a firm
can produce and its costs determines pricing
decisions.
• The total-cost curve shows this relationship
graphically.
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© 2007 Thomson South-Western
The cost schedules of farmer Joe
Output of corn
(bushels)
Fixed cost
($)
Variable cost
($)
Total cost
($)
(costs associated
with land,
machinery, etc.)
(cost of fertilizer)
sum of all costs
1000
2000
0
2000
1250
2000
1 X 300 = 300
2300
1550
2000
2 X 300 = 600
2600
1900
2000
3 X 300 = 900
2900
2200
2000
4 X 300 = 1200
3200
2450
2000
5 X 300 = 1500
3500
2600
2000
6 X 300 = 1800
3800
2650
2000
7 X 300 = 2100
4100
© 2007 Thomson South-Western
The cost schedules of farmer Joe
THE VARIOUS MEASURES OF
COST
Output of corn
(bushels)
• Costs of production may be divided into fixed
costs and variable costs.
– Fixed costs are the costs of fixed inputs. They do
not vary with the quantity of output produced.
– Variable costs are the costs of variable inputs.
They do vary with the quantity of output
produced.
Fixed cost
($)
Variable cost
($)
Total cost
($)
(costs associated
with land,
machinery, etc.)
(cost of fertilizer)
sum of all costs
1000
2000
0
2000
1250
2000
1 X 300 = 300
2300
1550
2000
2 X 300 = 600
2600
1900
2000
3 X 300 = 900
2900
2200
2000
4 X 300 = 1200
3200
2450
2000
5 X 300 = 1500
3500
2600
2000
6 X 300 = 1800
3800
2650
2000
7 X 300 = 2100
4100
© 2007 Thomson South-Western
© 2007 Thomson South-Western
Fixed and Variable Costs
Graphical illustration
• Total Costs
•
•
•
•
TC
Total Fixed Costs (TFC)
Total Variable Costs (TVC)
Total Costs (TC)
TC = TFC + TVC
$
VC
FC
0
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© 2007 Thomson South-Western
Properties of the cost curves
Shape of the TC
•
•
•
•
FC is a horizontal line
The vertical distance between TC and VC is
FC, a constant.
•
•
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Q of
output
The slope is positive
The slope is concave at beginning and convex
later
(concavity is the shape of a part of a dome,
and convexity is the shape of a part of a
bowl).
When it is concave, the slope becomes
increasingly flat, but when it is convex, the
slope becomes increasingly steeper.
© 2007 Thomson South-Western
Fixed and Variable Costs
Fixed and Variable Costs
• 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 Fixed Costs (AFC)
Average Variable Costs (AVC)
Average Total Costs (ATC)
ATC = AFC + AVC
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average total cost
marginal cost
Output of corn
(250 bushels per unit)
Total cost
($)
Marginal cost
($)
© 2007 Thomson South-Western
Average Costs and Marginal Costs
Average total cost
($)
AFC =
…
…
…
4 (1000 bushels)
2000
-
…
-
5 (1250 bushels)
2300
300
460
6 (1500 bushels)
2550
250
425
7 (1750 bushels)
2750
200
392
8 (2000 bushels)
2900
150
363
9 (2250 bushels)
3150
250
350
10 (2500 bushels)
3550
400
355
11 (2750 bushels)
4300
750
391
AVC =
Application of Average Total Cost
Concepts
Variable cost VC
=
Quantity
Q
ATC =
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Fixed cost FC
=
Quantity
Q
Total cost TC
=
Quantity
Q
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Marginal Cost
• Cost per square foot (in the building industry)
• Cost per air travel mile (in the airline industry)
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• Marginal cost (MC) measures the increase in
total cost that arises from an extra unit of
production.
• Marginal cost is the difference between two
successive total cost figures
• Marginal cost helps answer the following
question: How much does it cost to produce an
additional unit of output?
• Graphically, marginal cost is the slope of the
total cost curve.
© 2007 Thomson South-Western
TC
Marginal Cost
MC =
$
(change in total cost) ∆TC
=
(change in quantity)
∆Q
0
Q of
output
MC
0
Q of
output
© 2007 Thomson South-Western
© 2007 Thomson South-Western
Cost Curves and Their Shapes
Summary of costs
• Marginal cost eventually rises with the amount
of output produced.
• TC = TFC + TVC
• ATC = AFC + AVC
• MC
• This reflects the property of diminishing marginal
product.
© 2007 Thomson South-Western
© 2007 Thomson South-Western
Place marginal cost (MC) and average cost (ATC)
Application of Marginal Cost
together
• MC is the additional cost due to one more unit
produced
• A firm is comparing the additional revenue
brought by one more unit of good (e.g. a unit of
corns), called Marginal Revenue and MC of
this unit of good.
• If MC > MR, it does not pay for the firm to
produce the good.
• Optimal production rule: MC = MR
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MC
ATC
0
Q of
output
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Cost Curves and Their Shapes
Cost Curves and Their Shapes
• 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 eventually 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.
© 2007 Thomson South-Western
© 2007 Thomson South-Western
Cost Curves and Their Shapes
Cost Curves and Their Shapes
• Relationship between Marginal Cost and
Average Total Cost
• Relationship between Marginal Cost and
Average Total Cost
• Whenever marginal cost is less than average total
cost, average total cost is falling.
• Whenever marginal cost is greater than average
total cost, average total cost is rising.
• The marginal-cost curve crosses the average-totalcost curve at the efficient scale.
• Efficient scale is the quantity that minimizes average total
cost.
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Typical Cost Curves
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Figure 5 Cost Curves for a Typical Firm
• It is now time to examine the relationships that
exist between the different measures of cost.
Note how
MCdeclines
hits both
Marginal
Cost
at ATC
first and AVC
then at their
minimum
points.
increases
due
to diminishing marginal product.
Costs
AFC, a short-run concept, declines throughout.
$3.00
2.50
MC
2.00
1.50
ATC
AVC
1.00
0.50
0
2
4
6
8
10
12
AFC
14
Quantity of Output
© 2007 Thomson South-Western
© 2007 Thomson South-Western
Typical Cost Curves
COSTS IN THE SHORT RUN AND
IN THE LONG RUN
• Important Properties of Cost Curves
• Marginal cost eventually rises with the quantity of
output.
• The average-total-cost curve is U-shaped.
• The average-variable-cost curve is U-shaped.
• The marginal-cost curve crosses the average-totalcost curve at the minimum of average total cost.
• 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 inputs are fixed.
– In the long run, all inputs are variable, thus all are variable
inputs.
© 2007 Thomson South-Western
© 2007 Thomson South-Western
Economies and Diseconomies of Scale
COSTS IN THE SHORT RUN AND
IN THE LONG RUN
• Likewise, in the short run, some costs are
fixed.
• In the long run, all fixed costs become variable
costs.
• 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 short-run cost
curves.
If you double all inputs, when the resulting
output is
• more than doubled, it is increasing returns to
scale.
• less than doubled, it is decreasing returns to
scale.
• exactly doubled, it is constant returns to scale
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Economies and Diseconomies of Scale
• Increasing returns to scale also called
economies of scale
• Decreasing returns to scale also called
diseconomies of scale
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Difference between
Decreasing Returns to Scale
and
Diminishing marginal returns
• Returns to scale refers to changes in all inputs
• Diminishing marginal return refers to change in
only one input.
• It is possible for a technology to have
increasing returns to scale but diminishing
marginal returns.
© 2007 Thomson South-Western
© 2007 Thomson South-Western
Economies and Diseconomies of Scale
• Economies of scale: long-run average total cost
falls as the quantity of output increases.
• Diseconomies of scale: long-run average total
cost rises as the quantity of output increases.
• Constant returns to scale: long-run average
total cost stays the same as the quantity of
output increases.
Figure 6 Average Total Cost in the Short and Long Run
Average
Total
Cost
ATC in short
run with
small factory
ATC in short ATC in short
run with
run with
medium factory 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
© 2007 Thomson South-Western
© 2007 Thomson South-Western
Summary
• A firm’s costs often depend on the time
horizon being considered.
• In particular, many costs are fixed in the short
run but variable in the long run.
© 2007 Thomson South-Western