Production Costs and Firm Output

1
Lecture 13
2
Production Costs and Firm Output

• Introduction
• what are costs to a firm of producing a good?
• useful to distinguish between two decision-making
  periods short run and long run
• short run is a period of time during which at
  least one factor of production, usually the size
  of the firm's plant, cannot be varied
• long run is a time period sufficient to allow a
  firm to alter the size of its plant and all other
  factors of production

3
Costs in the Short Run

• We shall assume that a factory already exists so
  that acquisition costs are sunk and therefore
  irrelevant
• focus on operating and possession costs
• Possession costs
• independent of quantity produced
• in production setting, called fixed costs
• costs that do not vary with the quantity produced

4
Costs in the Short run

• average fixed cost (AFC)
• (total fixed cost/quantity produced)
• always decreasing with output
• fixed dollar amount divided by increasing
  quantities

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Costs in the Short Run

• Operating costs
• cost of operating firm and producing output
• includes depreciation, materials, labor, etc.
• called variable costs
• costs that vary with the quantity produced
• average variable cost (AVC)
• (total variable cost/quantity produced)
• usually "U" shaped
• initially adding more workers and machines allows
  economies of size and specialization so cost per
  unit produced falls with increases in output
• eventually, given some inputs are fixed (e.g.
  size of plant), over-utilization leads to high
  unit costs
• congestion, waiting for equipment,etc.

6
Costs in the Short Run

• further rationale for U-shaped AVC curve the
  law of diminishing returns
• as more units of a variable factor are applied to
  a fixed amount of other resources output will
  eventually increase by smaller amounts

7
Costs in the Short Run

• further rationale for U-shaped AVC curve the
  law of diminishing returns
• given constant cost of inputs, law of diminishing
  returns implies average cost of output is
  increasing
• suppose 1 worker produces 100 units in a day, 2
  workers produce 160 units in a day and "wage" is
  40 per worker per day
• AVC of 100 units (1x40)/100 40/100 0.40
• AVC of 160 units (2x40)/160 80/160 0.50
• as productivity of workers goes down, cost per
  unit of output increases

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Costs in the Short Run

• measure productivity of inputs by their marginal,
  average and total product
• marginal product DOUTPUT/ DINPUT (holding
  levels of all other inputs constant)
• average product OUTPUT/INPUT
• total product OUTPUT
• law of diminishing returns says that marginal
  product eventually declines as increase quantity
  of an input
• note total product is still increasing

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Costs in the Short Run

• total cost
• sum of fixed and variable cost
• TCTFCTVC
• ATCTC/Q TFC/Q TVC/Q ATC AVC

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Costs in the Short Run

• Marginal cost
• marginal cost of production is the opportunity
  cost of producing an additional unit
• MC DTC /DQ DTC for one unit

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Costs in the Short Run

• Average vs. marginal costs
• marginal and average costs are related
• MC DTC /DQ
• ATC TC/Q
• relationship between marginal and average costs
• if MC gt ATC, ATC increases
• if MC lt ATC, ATC decreases
• if MC ATC, ATC remains constant
• marginal cost curve cuts through the bottom of
  the ATC and AVC curves

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Average and Marginal Cost Curves

• To understand the relationship between the
  average and marginal curves, we calculate each
  of the average curves from the total curves
  and then introduce the marginal curve.

Costper unit
80

• The average fixed cost curve (AFC) is the
  total fixed cost (TFC) divided by the output
  level. It is high for a few units, and
  becomes small as output increases.

60
/


Outputper day
AFC
TFC
50
0
----
1
50.00
50
40
2
25.00
50
3
16.67
50
4
12.50
50
5
10.00
50
20
6
8.33
50
7
50
7.14
6.25
8
50
9
5.56
50
10
5.00
50
4
2
8
12
6
10
11
50
4.55
Output
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Average and Marginal Cost Curves
Costper unit

• The average variable cost curve (AVC) is the
  total variable cost (TVC) divided by the
  output level. It is higher either for a few
  or lot of units and has some minimal point
  between the two where, when graphed later,
  marginal costs (MC) will cross it.

80
60
/


Outputper day
AVC
TVC
0
----
0
1
15.00
15
40
2
12.50
25
3
11.33
34
4
10.50
42
5
10.40
52
20
6
10.67
64
7
11.29
79
AFC
12.25
98
8
9
13.56
122
10
15.20
152
2
4
6
8
10
12
11
18.36
202
Output
14
Average and Marginal Cost Curves

Costper unit
80

• Note that MC starts low and increases as
  output increases. It also crosses AVC at its
  minimum point.

60
/


TC
?TC
MC
? Output
50
15.00
15
1
65
40
10
10.00
1
75
9
9.00
1
84
8
8.00
1
92
10
10.00
1
102
AVC
12
12.00
1
20
114
15
15.00
1
129
19
19.00
AFC
1
148
24
24.00
1
172
30
1
30.00
202
2
4
6
8
10
12
1
50.00
50
252
Output
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Average and Marginal Cost Curves

• Lastly we graph the average total cost curve
  (ATC) as TC divided by the output.

Costper unit

• Note that when the output is low, ATC is high
  because AFC is very high. Also, ATC is high
  when output is large as MC becomes large when
  output is high.

80

• These two relationships explain why the ATC
  curve has its distinct U - shape.

• Note MC crosses ATC at its minimum.

60
/


Outputper day
TC
ATC
0
----
1
65.00
40
2
37.50
3
28.00
4
23.00
5
20.40
AVC
20
6
19.00
7
18.43
AFC
18.50
8
9
19.11
10
20.20
2
4
6
8
10
12
11
22.91
Output
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Costs in the Long Run

• short run average total cost curve showed minimum
  cost per unit of producing various levels of
  output for a given level of the fixed factor(s)
  (eg. plant size)

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Costs in the Long run

• long run average cost curve shows the minimum
  cost per unit of producing various levels of
  output given that the levels of all inputs are
  variable
• long run costs will always be less than or equal
  to short run costs since can always choose
  factory size you are "stuck" with in the short
  run
• have more flexibility in the long run

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Costs in the Long run

• long run average total cost curve is made up of
  points from different short run average total
  cost curves

Q
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Costs in the Long run

LRATC
SRATC
(factory size1000)
1
13
(factory size2000)
SRATC
2
(factory size
SRATC
3
4000)
Q
200

• cheapest way to produce 200 units is with a
  factory size of 1000
• ATCSRATCLR13 per unit

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Costs in the Long run

LRATC
SRATC
(factory size1000)
1
13
(factory size2000)
SRATC
11
2
(factory size
SRATC
3
4000)
8
Q
200
450

• given factory of size 1000, output that yields
  lowest cost per unit is 450 (min. ATC 11 per
  unit)
• called capacity of plant

• note that if want to produce 450 units, could
  achieve lower cost by using a bigger plant of
  size 2000
• ATCSRATCLR8 per unit

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Costs in the Long run

LRATC
SRATC
(factory size1000)
1
13
(factory size2000)
SRATC
11
2
(factory size
SRATC
3
4000)
8
5
Q
200
450
1000

• in long run, when one can choose any sized
  factory, cost per unit is lowest when produce 900
  units with a factory of size 4000
• cost per unit is minimized at 5 per unit

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Costs in the Long run

• firm size and long run average total cost
• expect that over some range, unit costs will fall
  with higher volume of output
• called economies of scale or increasing returns
  to scale
• economies cost savings
• scale size
• rationale
• mass production techniques
• assembly lines
• specialization
• can get single-skill workers cheaper and will
  become more proficient

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Costs in the long run

• firm size and long run average total cost
• expect that over some range, unit costs will fall
  with higher volume of output
• rationale
• learning by doing
• represented by downward sloping long run ATC curve

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Costs in the Long run

• firm size and long run average total cost
• constant returns to scale
• as increase volume of output, cost per unit is
  constant
• LRATC is horizontal

• diseconomies of scale
• increases in output leads to higher LRATC

LRATC
Q
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Costs in the Long run

• LRATC and efficient scale
• efficient level of output per factory is one
  where cost per unit is lowest
• minimum of LRATC
• if LRATC curves are U-shaped, only one output
  level per factory (and one size factory) will be
  efficient

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Different Types of LRATC

• The LRATC may be U-shaped, with segments that
  represent economies of scale and
  diseconomies of scale.

• The LRATC depicted has a downward sloping
  segment demon- strating Economies of
  Scale for that range of output, meaning that
  output expansion can reduce per unit cost up to
  level q.

• There is also a upward sloping segment,
  demonstrating Diseconomies of Scale meaning
  that a further expansion in plant size leads
  to higher levels of cost

• Competition will drive firms to produce output q
  that
• minimizes average cost.

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Costs in the Long run

• in previous example, competition and desire to
  maximize profit would lead each factory to be
  size 2500 and produce 1000 units of output

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Costs in the Long run

• if there are constant returns to scale over some
  range then factories of various sizes (and
  varying outputs) could survive

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Different Types of LRATC

• Below, the LRATC represented has a downward
  sloping segment
• demonstrating Economies of Scale up to output
  q1,

an upward sloping segment, demonstrating
diseconomies of scale beyond q2
and a flat segment showing Constant Returns to
Scale.

• Constant Returns to Scale suggests that the
  ideal plant size would be one of any size that
  delivers between q1 and q2. Increases in
  plant size from q1 to any point below or
  including q2 would not alter average cost.

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Costs in the Long run

• factory sizes from 800 (producing Q1 units of
  output) to size 1200 (producing Q2 units of
  output) are efficient and will survive

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Costs in the Long run

• if there are economies of scale throughout the
  relevant range of output, cost is minimized with
  a single large plant
• will end up with only one firm
• known as natural monopoly

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Different Types of LRATC

• Below, the LRATC represented has a downward
  sloping segment

demonstrating Economies of Scale for the entire
range of output, which implies that the most
efficient size plant available would be the
largest one possible.
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Example Major U.S. Brewers (1992)
Anheuser-Busch
Coors
Miller

• Tables above indicate that breweries as small as
  2.7 million beer barrels and as large as 18.0
  million beer barrels could produce with similar
  costs

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Example Major U.S. Brewers (1992)

LRATC
Q
2.7 MBB (Tampa, FL)
18.0 MBB (Golden, CO)

• Breweries as small as 2.7 million beer barrels
  and as large as 18.0 million beer barrels could
  produce with similar costs

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EndLecture 13