Unit V
Production Costs (Chapter 12)
In this chapter, look for the
answers to these questions:
 What is a production function? What is
marginal product? How are they related?
 What are the various costs, and how are
they related to each other and to output?
 How are costs different in the short run
vs. the long run?
 What are “economies of scale”?
Short Run and Long run
• The Short Run: Fixed Plant
– The short run is a time frame in which the
quantities of some resources are fixed.
– In the short run, a firm can usually change the
quantity of labor it uses but not the quantity of
capital.
• The Long Run: Variable Plant
– The long run is a time frame in which the
quantities of all resources can be changed.
– A sunk cost is irrelevant to the firm’s decisions.
Short Run Production
• To increase output with a fixed plant, a firm
must increase the quantity of labor it uses.
• We describe the relationship between
output and the quantity of labor by using
three related concepts:
– Total product
– Marginal product
– Average product
The Production Function
• A production function shows the
relationship between the quantity of
inputs used to produce a good, and the
quantity of output of that good.
• It can be represented by a table,
equation, or graph.
• Example:
– Farmer Jack grows wheat.
– He has 5 acres of land.
– He can hire as many workers as he wants.
The Production Function
• Total Product
– Total product (TP) is the total quantity of
a good produced in a given period.
– Total product is an output rate—the
number of units produced per unit of time.
– Total product increases as the quantity of
labor employed increases.
The Production Function
• The figure shows
the total product
and the total
product curve.
• Points A through H
on the curve
correspond to the
columns of the
table.
• The TP curve is like
the PPF: It
separates attainable
points and
unattainable points.
EXAMPLE: Farmer Jack’s Production
Function
3,000
Q (bushels
(no. of
workers) of wheat)
Quantity of output
L
2,500
0
0
1
1000
2
1800
3
2400
500
4
2800
0
5
3000
2,000
1,500
1,000
0
1
2
3
4
No. of workers
5
Marginal Product
• Marginal product is the change in total product
that results from a one-unit increase in the quantity
of labor employed.
– Marginal product tells us the contribution to total product
of adding one more worker.
– E.g., if Farmer Jack hires one more worker,
his output rises by the marginal product of labor.
– Notation:
∆ (delta) = “change in…”
– Examples:
∆Q = change in output, ∆L = change in labor
– Marginal product of labor (MPL) =
∆Q
∆L
Marginal Product
• The figure shows
total product and
marginal product.
• We can illustrate
marginal product
as the orange bars
that form steps
along the total
product curve.
• The height of each
step represents
marginal product.
Marginal Product
• The table
calculates
marginal product
and the orange
bars in part (b)
illustrate it.
• Notice that the
steeper the slope
of the TP curve,
the greater is
marginal product.
Marginal Product
• The total product
and marginal
product curves in
this figure
incorporate a
feature of all
production
processes:
– Increasing
marginal
returns initially
– Decreasing
marginal
returns
eventually
– Negative
marginal
returns
EXAMPLE: Total & Marginal
Product
L
Q
(no. of (bushels
workers) of wheat)
0
MPL
0
∆Q = 1000
∆L = 1
1
1000
∆L = 1
2
∆Q = 600
600
∆Q = 400
400
∆Q = 200
200
2800
∆L = 1
5
800
2400
∆L = 1
4
∆Q = 800
1800
∆L = 1
3
1000
3000
EXAMPLE: MPL = Slope of Prod
Function
Q
(no. of (bushels
workers) of wheat)
0
MPL
3,000
MPL
0
1000
1
1000
800
2
1800
600
3
2400
400
4
2800
200
5
3000
Quantity of output
L
equals the
slope of the
2,500
production function.
2,000
Notice that
MPL diminishes
1,500
as L increases.
1,000
This explains why
500 production
the
function
gets flatter
0
as L0 increases.
1
2
3
4
No. of workers
5
Why MPL Is Important
• Rational people think at the margin.
• When Farmer Jack hires an extra worker,
– his costs rise by the wage he pays the worker
– his output rises by MPL
• Comparing them helps Jack decide
whether he would benefit from hiring the
worker.
Increasing Marginal Returns
• Increasing marginal returns occur when
the marginal product of an additional worker
exceeds the marginal product of the previous
worker.
• Increasing marginal returns occur when a
small number of workers are employed and
arise from increased specialization and
division of labor in the production process.
Why MPL Diminishes
• Decreasing marginal returns occur when
the marginal product of an additional worker is
less than the marginal product of the previous
worker.
– E.g., Farmer Jack’s output rises by a smaller and
smaller amount for each additional worker. Why?
– If Jack increases workers but not land,
the average worker has less land to work with,
so will be less productive.
• In general, MPL diminishes as L rises
whether the fixed input is land or capital
(equipment, machines, etc.).
Why MPL Diminishes
• Decreasing marginal returns are so pervasive that
they qualify for the status of a law:
• The law of decreasing returns states that:
As a firm uses more of a variable input, with a given
quantity of fixed inputs, the marginal product of the
variable input eventually decreases.
SHORT-RUN PRODUCTION
The figure graphs the
average product against the
quantity of labor employed.
The average product curve is
AP.
When marginal product
exceeds average product,
average product is
increasing.
SHORT-RUN PRODUCTION
When marginal product is
less than average product,
average product is
decreasing.
When marginal product
equals average product,
average product is at its
maximum.
SHORT-RUN COST
• To produce more output in the short run, a
firm employs more labor, which means the
firm must increase its costs.
• We describe the relationship between
output and cost using three cost concepts:
– Total cost
– Marginal cost
– Average cost
SHORT-RUN COST
•
Total Cost
– A firm’s total cost (TC) is the cost of all the
factors of production the firm uses.
•
Total Cost divides into two parts:
– Fixed cost (FC) is the cost of a firm’s fixed
factors of production used by a firm—the cost of
land, capital, and entrepreneurship.
o Fixed costs don’t change as output changes.
SHORT-RUN COST
– Variable cost (VC) is the cost of the
variable factor of production used by a firm—
the cost of labor.
o To change its output in the short run, a firm must
change the quantity of labor it employs, so total
variable cost changes as output changes.
o Total cost is the sum of total fixed cost and total
variable cost. That is,
TC = FC + VC
SHORT-RUN COST
Fixed cost (FC) is
constant—it graphs as
a horizontal line.
Variable cost (VC)
increases as output
increases.
Total cost (TC) also
increases as output
increases.
SHORT-RUN COST
The vertical
distance
between the
total cost curve
and the total
variable cost
curve is total
fixed cost, as
illustrated by the
two arrows.
Marginal Cost
• Marginal Cost (MC)
is the increase in Total Cost from
producing one more unit:
∆TC
MC =
∆Q
Marginal cost tells us how total cost
changes as total product changes.
EXAMPLE: Marginal Cost
0
TC
MC
$100
$70
1
170
50
2
220
40
3
260
50
4
310
70
5
380
100
6
620
∆TC
MC =
∆Q
$100
Usually,
MC
rises
as
Q
rises,
due
$75
to diminishing marginal product.
$125
$50
Sometimes (as here), MC falls
$25
before rising.
$0
480
140
7
$200 Marginal Cost (MC)
Recall,
is $175
the change in total cost from
producing
one more unit:
$150
Costs
Q
(In other0 examples,
MC may be
1 2 3 4 5 6 7
constant.)
Q
SHORT-RUN COST
• Average Cost
– There are three average cost concepts:
– Average fixed cost (AFC) is total fixed
cost per unit of output.
– Average variable cost (AVC) is total
variable cost per unit of output.
– Average total cost (ATC) is total cost per
unit of output.
SHORT-RUN COST
•The average cost concepts are calculated from
the total cost concepts as follows:
TC = TFC + TVC
•Divide each total cost term by the quantity
produced, Q, to give
TC = TFC + TVC
Q
Q
Q
or,
ATC = AFC + AVC
A C T I V E L E A R N I N G 1:
Costs
Fill in the blank spaces of
this table.
Q
VC
0
1
10
2
30
TC
AFC
AVC
ATC
$50
n.a.
n.a.
n.a.
$10
$60.00
80
3
16.67
4
100
5
150
6
210
150
20
12.50
36.67
8.33
$10
30
37.50
30
260
MC
35
43.33
60
A C T I V E L E A R N I N G 1:
Answers
AFC = TC/Q
FC/Qbetween MC and TC
Use relationship
ATC
AVC
VC/Q
Q
VC
TC
AFC
AVC
ATC
First, deduce FC = $50 and use FC +
0
$0
$50
n.a.
n.a.
n.a.
VC = TC.
1
10
60
$50.00
$10
$60.00
2
30
80
25.00
15
40.00
3
60
110
16.67
20
36.67
4
100
150
12.50
25
37.50
5
150
200
10.00
30
40.00
6
210
260
8.33
35
43.33
MC
$10
20
30
40
50
60
EXAMPLE: Average Fixed Cost
FC
AFC
0
$100
n.a.
1
100
$100
2
100
50
3
100
33.33
4
100
25
5
100
20
6
100
16.67
7
100
14.29
$200
Average
fixed cost (AFC)
is$175
fixed cost divided by the
quantity
of output:
$150
Costs
Q
AFC
$125
= FC/Q
$100
Notice
$75 that AFC falls as Q rises:
The
firm is spreading its fixed
$50
costs over a larger and larger
$25
number of units.
$0
0
1
2
3
4
Q
5
6
7
EXAMPLE: Average Variable Cost
VC
AVC
0
$0
n.a.
1
70
$70
2
120
60
3
160
53.33
4
210
52.50
5
280
56.00
6
380
63.33
7
520
74.29
$200
Average
variable cost (AVC)
is$175
variable cost divided by the
quantity
of output:
$150
Costs
Q
AVC
$125
= VC/Q
$100
As$75
Q rises, AVC may fall initially.
In most cases, AVC will
$50
eventually rise as output rises.
$25
$0
0
1
2
3
4
Q
5
6
7
EXAMPLE: Average Total Cost
Q
TC
0 $100
ATC
AFC
AVC
n.a.
n.a.
n.a.
1
170
$170
$100
$70
2
220
110
50
60
3
260 86.67 33.33
53.33
4
310 77.50
25
52.50
5
380
76
20
56.00
6
480
80 16.67
63.33
7
620 88.57 14.29
74.29
Average total cost
(ATC) equals total
cost divided by the
quantity of output:
ATC = TC/Q
Also,
ATC = AFC + AVC
EXAMPLE: Average Total Cost
TC
0 $100
1
2
170
220
ATC
$200
Usually,
as in this example,
$175
the ATC curve is U-shaped.
n.a.
$150
$170
110
Costs
Q
$125
$100
3
260 86.67
4
310 77.50
$50
5
380
76
$25
6
480
80
$0
7
620 88.57
$75
0
1
2
3
4
Q
5
6
7
EXAMPLE: The Various Cost Curves
Together
$200
$175
ATC
AVC
AFC
MC
Costs
$150
$125
$100
$75
$50
$25
$0
0
1
2
3
4
Q
5
6
7
SHORT-RUN COST
The vertical distance
between these two curves
is equal to average fixed
cost, as illustrated by the
two arrows.
REMEMBER -- The
marginal cost curve (MC)
intersects the average
variable cost curve and the
average total cost curve at
their minimum points.
SHORT-RUN COST
• Why the Average Total Cost Curve Is
U-Shaped
– Average total cost, ATC, is the sum of average fixed
cost, AFC, and average variable cost, AVC.
–The shape of the ATC curve combines the shapes of
the AFC and AVC curves.
–The U shape of the average total cost curve arises
from the influence of two opposing forces:
o Spreading total fixed cost over a larger output
o Decreasing marginal returns
EXAMPLE: Why ATC Is Usually Ushaped
$200
As Q rises:
Eventually,
rising AVC
pulls ATC up.
$150
Costs
Initially,
falling AFC
pulls ATC down.
$175
$125
$100
$75
$50
$25
$0
0
1
2
3
4
Q
5
6
7
EXAMPLE: ATC and MC
When MC < ATC,
ATC is falling.
$175
$150
ATC is rising.
$125
Costs
When MC > ATC,
The MC curve
crosses the
ATC curve at
the ATC curve’s
minimum.
ATC
MC
$200
$100
$75
$50
$25
$0
0
1
2
3
4
Q
5
6
7
SHORT-RUN COST
• Cost Curves and Product Curves
– The technology that a firm uses determines its
costs.
– At low levels of employment and output, as the
firm hires more labor, marginal product and
average product rise, and marginal cost and
average variable cost fall.
– Then, at the point of maximum marginal
product, marginal cost is a minimum.
– As the firm hires more labor, marginal product
decreases and marginal cost increases.
SHORT-RUN COST
– But average product continues to rises,
and average variable cost continues to fall.
– Then, at the point of maximum average
product, average variable cost is a
minimum.
– As the firm hires even more labor, average
product decreases and average variable
cost increases.
SHORT-RUN COST
This figure illustrates the
relationship between the
product curves and cost curves.
A firm’s marginal cost curve is
linked to its marginal product
curve.
If marginal product rises, marginal
cost falls.
If marginal product is a maximum,
marginal cost is a minimum.
SHORT-RUN COST
A firm’s average variable cost
curve is linked to its average
product curve.
If average product rises, average
variable cost falls.
If average product is a maximum,
average variable cost is a
minimum.
SHORT-RUN COST
At small outputs,
MP and AP rise and
MC and AVC fall.
At intermediate outputs,
MP falls and MC rises and
AP rises and AVC falls.
At large outputs,
MP and AP fall and
MC and AVC rise.
SHORT-RUN COST
• Shifts in Cost Curves
Technology
– A technological change that increases
productivity shifts the total product curve
upward. It also shifts the marginal product
curve and the average product curve upward.
– With a better technology, the same inputs can
produce more output, so an advance in
technology lowers the average and marginal
costs and shifts the short-run cost curves
downward.
SHORT-RUN COST
Prices of Factors of Production
–An increase in the price of a factor of production
increases costs and shifts the cost curves.
–But how the curves shift depends on which
resource price changes.
An increase in rent or another component of fixed cost
–Shifts the fixed cost curves (TFC and AFC)
upward.
–Shifts the total cost curve (TC) upward.
–Leaves the variable cost curves (AVC and TVC)
and the marginal cost curve (MC) unchanged.
SHORT-RUN COST
• An increase in the wage rate or another
component of variable cost
– Shifts the variable curves (TVC and AVC)
upward.
– Shifts the marginal cost curve (MC) upward.
– Leaves the fixed cost curves (AFC and TFC)
unchanged.
LONG-RUN COST
• Plant Size and Cost
– When a firm changes its plant size, its cost of
producing a given output changes.
– Will the average total cost of producing a
gallon of smoothie fall, rise, or remain the
same?
– Each of these three outcomes arise because
when a firm changes the size of its plant, it
might experience:
o Economies of scale
o Diseconomies of scale
o Constant returns to scale
Economies of Scale
• Economies of scale exist if when a firm
increases its plant size and labor employed
by the same percentage, its output
increases by a larger percentage and
average total cost decreases.
– The main source of economies of scale is
greater specialization of both labor and capital.
Diseconomies of Scale
• Diseconomies of scale exist if when a
firm increases its plant size and labor
employed by the same percentage, its
output increases by a smaller percentage
and average total cost increases.
– Diseconomies of scale arise from the difficulty
of coordinating and controlling a large
enterprise.
– Eventually, management complexity brings
rising average total cost.
Constant Returns to Scale
• Constant returns to scale exist if when
a firm increases its plant size and labor
employed by the same percentage, its
output increases by the same percentage
and average total cost remains constant.
– Constant returns to scale occur when a firm is
able to replicate its existing production facility
including its management system.
LONG-RUN COST
•The Long-Run Average Cost Curve
–The long-run average cost curve shows
the lowest average cost at which it is
possible to produce each output when the
firm has had sufficient time to change both
its plant size and labor employed.
EXAMPLE: LRATC with 3 Factory Sizes
Firm can choose
from 3 factory
sizes: S, M, L.
Each size has its
own SRATC curve.
The firm can
change to a
different factory
size in the long
run, but not in the
short run.
Avg
Total
Cost
ATCS
ATCM
ATCL
Q
EXAMPLE: LRATC with 3 Factory Sizes
To produce less
than QA, firm will
choose size S
in the long run.
To produce
between QA
and QB, firm will
choose size M
in the long run.
To produce more
than QB, firm will
choose size L
in the long run.
Avg
Total
Cost
ATCS
ATCM
ATCL
LRATC
QA
QB
Q
A Typical LRATC Curve
In the real world,
factories come in
many sizes,
each with its own
SRATC curve.
ATC
LRATC
So a typical
LRATC curve
looks like this:
Q
How ATC Changes as
the Scale of Production Changes
Economies of
scale: ATC falls
as Q increases.
ATC
LRATC
Constant returns
to scale: ATC
stays the same
as Q increases.
Diseconomies of
scale: ATC rises
as Q increases.
Q
CONCLUSION
• Costs are critically important to many
business decisions, including
production, pricing, and hiring.
• This chapter has introduced the various
cost concepts.
• The following chapters will show how
firms use these concepts to maximize
profits in various market structures.
CHAPTER SUMMARY
 Implicit costs do not involve a cash outlay,
yet are just as important as explicit costs
to firms’ decisions.
 The production function shows the relationship
between output and inputs.
 The marginal product of labor is the increase in
output from a one-unit increase in labor,
holding other inputs constant. The marginal
products of other inputs are defined similarly.
 Marginal product usually diminishes as the
input increases. Thus, as output rises, the
production function becomes flatter, and the
total cost curve becomes steeper.
CHAPTER SUMMARY
 Variable costs vary with output; fixed costs do
not.
 Marginal cost is the increase in total cost from an
extra unit of production. The MC curve is usually
upward-sloping.
 Average variable cost is variable cost divided by
output.
 Average fixed cost is fixed cost divided by output.
AFC always falls as output increases.
 Average total cost (sometimes called “cost per
unit”) is total cost divided by the quantity of
output. The ATC curve is usually U-shaped.
CHAPTER SUMMARY
 The MC curve intersects the ATC curve
at minimum average total cost.
When MC < ATC, ATC falls as Q rises.
When MC > ATC, ATC rises as Q rises.
 In the long run, all costs are variable.
 Economies of scale: ATC falls as Q rises.
Diseconomies of scale: ATC rises as Q rises.
Constant returns to scale: ATC remains
constant as Q rises.