Overview
Overview
BA 210 Lesson III.1 Inputs and Costs
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Overview
Chapter 12 Inputs and Costs
Lesson III.1 Inputs and Costs
Total Product
Marginal Product
Total Cost and Marginal Cost
Diminishing Returns
Cost Relations
Short Run verses Long Run Costs
Summary
Review Questions
BA 210 Lesson III.1 Inputs and Costs
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Total Product
Total Product
BA 210 Lesson III.1 Inputs and Costs
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Total Product
Study Inputs and Costs to Minimize Costs. Everyone should:
• All firms in all market environments

Monopoly (1 firm with restricted entry)

Duopoly (2 firms with restricted entry)

Perfect Competition (many firms with free entry)
• Charities

Toys for Tots should minimize the cost of getting toys to tots
• They should often solicit cash over donated toys or labor. (Instead
of having 1000 people each buying 1 toy for $20, people could
each donate $20 and Toys for Tots could buy more than 1000 toys
for $20,000 by getting a quantity discount.)
• Donors

Perfectly altruistic people helping kids (not feeling warm and fuzzy)
should donate money rather than toys or labor, and so minimize their
own cost of giving. (see
http://faculty.pepperdine.edu/jburke2/giving.pdf)
BA 210 Lesson III.1 Inputs and Costs
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Total Product
• A production function is the relationship between the quantity
of inputs a firm uses and the quantity of output it produces.
• A fixed input is an input whose quantity is fixed for a period of
time and cannot be varied.
• A variable input is an input whose quantity the firm can vary at
any time.
• The short run is the time period in which at least one input is
fixed.
• The long run is the time period in which all inputs can be
varied.
• For example, a Subway shop cannot change its ovens within
24 hours, but it could with a year.
BA 210 Lesson III.1 Inputs and Costs
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Total Product
Short-Run vs. Long-Run Decisions
• Examples where some capital or labor is fixed in the short-run.
 Office space may not be adjustable in the short-run.
 Labor with contracts is not completely adjustable in the
short-run.
• It takes time to terminate labor.
• Unless stated otherwise in a homework or exam problem, just
consider the case where labor is variable in both the short-run
and long-run, and capital is fixed in the short-run but flexible
in the long-run.
BA 210 Lesson III.1 Inputs and Costs
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Total Product
• The total product curve shows how the quantity of output
depends on the quantity of the variable input, for a given
quantity of the fixed input.
BA 210 Lesson III.1 Inputs and Costs
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Marginal Product
Marginal Product
BA 210 Lesson III.1 Inputs and Costs
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Total Product, Marginal Product, Average Product
• Average Product of an Input: measures output produced per
unit of input. (It is a common measure of productivity, but it is
less useful than marginal product, explained later.)
• Marginal Product on an Input: change in total output
attributable to the last unit of an input.
• As we will see, Marginal Product is the essential measure of
input productivity for cost minimization.
BA 210 Lesson III.1 Inputs and Costs
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Marginal Product
Production Function and Total Product Curve for George and
Martha’s Farm
Quantity of wheat
(bushels)
Adding a 7th worker
leads to an increase in
output of only 7 bushels
Quantity Quantity MP of labor
of labor L of wheat Q MPL= DQ/ DL
(worker)
100
80
Adding a 2nd worker
leads to an increase in
output of 17 bushels
Total product, TP
60
40
20
0
1
2
3
4
5
6
7
(bushels) (bushels per worker)
0
0
1
19
2
36
3
51
4
64
5
75
6
84
7
91
8
96
19
17
15
13
11
9
7
5
8
Quantity of labor (workers)
BA 210 Lesson III.1 Inputs and Costs
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Marginal Product
Marginal Product of Labor Curve
Marginal product
of labor (bushels
per worker)
There are
diminishing returns
to labor.
19
17
15
13
11
9
7
5
Marginal product of labor, MPL
0
1
2
3
4
5
6
7
8
Quantity of labor (workers)
BA 210 Lesson III.1 Inputs and Costs
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Marginal Product
• There are diminishing returns to an input when an increase in
the quantity of that input, holding the levels of all other inputs
fixed, leads to a decline in the marginal product of that input.
BA 210 Lesson III.1 Inputs and Costs
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Marginal Product
Increasing, Diminishing and Negative Marginal Productivity
Q
Increasing
Marginal
Productivity
Diminishing
Marginal
Productivity
Negative
(and diminishing)
Marginal
Productivity
Total Product
MP
BA 210 Lesson III.1 Inputs and Costs
L
13
Total Cost and Marginal Cost
Total Cost and Marginal Cost
BA 210 Lesson III.1 Inputs and Costs
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Total Cost and Marginal Cost
• Types of Costs

Short-Run
• Fixed costs (FC) is a fixed amount owed for any positive output.
– If capital is fixed in the short-run, then FC equals the cost of
capital.
– For example, you lease a railroad car for $10,000 for a month,
FC = $10,000.
• Short-run total costs (TC)
• Short-run variable costs (VC). Defined by VC = TC – FC.

Long-Run
• All costs are variable.
• Zero fixed costs.
BA 210 Lesson III.1 Inputs and Costs
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Total Cost and Marginal Cost
C(Q): Minimum total cost of
producing alternative levels of
$
output:
C(Q) = VC(Q) + FC
C(Q) = VC + FC
VC(Q): Costs that vary with
output.
VC(Q)
FC: Costs if output is zero.
FC
0
BA 210 Lesson III.1 Inputs and Costs
Q
16
Total Cost and Marginal Cost
FC: Costs that do not change
as output changes.
Since fixed cost is forever lost $
after it has been paid, decision
makers should ignore fixed
costs to minimize costs.
• Being rational in your personal
life is a challenge. The extra
$120,000 I paid for my house in
2007 (compared with prices 1
year later) is like a sunk cost.
C(Q) = VC + FC
VC(Q)
FC
Q
BA 210 Lesson III.1 Inputs and Costs
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Total Cost and Marginal Cost
Marginal Cost MC = DC/DQ
• Marginal cost curves often
initially decrease with output Q
because of specialization of labor.
• Example: Workers at the Malibu
$
MC
subway work best when there are
several customers (Q midsize)
because the workers specialize.
• Marginal cost curves eventually
increase with output when inputs
crowd.
•Example: Workers at the Malibu
subway work become less productive
and costs increase if Q is so large that
workers are crowded.
• Unless a homework or exam
problem explicitly states otherwise,
draw the marginal cost curves Ushaped, as on the right.
Specialization
of Labor
BA 210 Lesson III.1 Inputs and Costs
Decreasing
productivity
of inputs
because of
diminishing
returns
Q
18
Total Cost and Marginal Cost
• The total cost curve becomes steeper as more output is produced
due to diminishing returns.
BA 210 Lesson III.1 Inputs and Costs
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Total Cost and Marginal Cost
Total Cost Curve for George and Martha’s Farm if labor cost
$200 each unit, and capital is fixed and costs $400 total.
$2,000
Total cost, TC
I
1,800
H
1,600
G
1,400
F
1,200
Total cost, TC
E
1,000
D
800
C
600
B
400
A
200
0
19
36
51
64
75
84
91 96
Quantity of wheat (bushels)
Point on
graph
A
B
C
D
E
F
G
H
I
Quantity of
labor L
(worker)
0
1
2
3
4
5
6
7
8
Quantity of
wheat Q
(bushels)
0
19
36
51
64
75
84
91
96
Variable
cost
(VC)
$O
200
400
600
800
1,000
1,200
1,400
1,600
Fixed Cost
(FC)
Total
cost
(TC = FC+VC)
$400
400
400
400
400
400
400
400
400
$ 400
600
800
1,000
1,200
1,400
1,600
1,800
2,000
BA 210 Lesson III.1 Inputs and Costs
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Diminishing Returns
Diminishing Returns
BA 210 Lesson III.1 Inputs and Costs
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Diminishing Returns
Costs at Selena’s Gourmet Salsas
BA 210 Lesson III.1 Inputs and Costs
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Diminishing Returns
Total Cost and Marginal Cost Curves for Selena’s Gourmet
Salsas
(a) Total Cost
Cost
8th case of salsa
increases total cost
by $180.
$1,400
(b) Marginal Cost
Cost of
case
TC
$250
MC
1,200
1,000
800
200
2nd case of salsa
increases total
cost by $36.
150
600
100
400
50
200
0
1
2
3
4
5
6
7
8
9
10
0
1
2
Quantity of salsa (cases)
BA 210 Lesson III.1 Inputs and Costs
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4
5
6
7
8
9
10
Quantity of salsa (cases)
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Diminishing Returns
Why is the Marginal Cost Curve Upward Sloping?
• Because there are diminishing returns to inputs in this example.
As output increases, the marginal product of the variable input
declines.
• This implies that more and more of the variable input must be
used to produce each additional unit of output as the amount of
output already produced rises.
• And since each unit of the variable input must be paid for, the
cost per additional unit of output also rises.
BA 210 Lesson III.1 Inputs and Costs
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Cost Relations
Cost Relations
BA 210 Lesson III.1 Inputs and Costs
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Cost Relations
Average Total Cost Curve
• Increasing output has two opposing effects on average total cost:

The spreading effect: the larger the output, the greater the
quantity of output over which fixed cost is spread, leading to
lower the average fixed cost.

The diminishing returns effect: the larger the output, the greater
the amount of variable input required to produce additional
units leading to higher average variable cost.
BA 210 Lesson III.1 Inputs and Costs
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Cost Relations
Average Costs for Selena’s Gourmet Salsas
BA 210 Lesson III.1 Inputs and Costs
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Cost Relations
Average Total Cost Curve for Selena’s Gourmet Salsas
Cost of
case
$140
Average total cost, ATC
Minimum
average
total cost
120
100
M
80
60
40
20
0
1
2
3
4
5
6
7
8
9
10
Quantity of salsa (cases)
Minimum-cost output
BA 210 Lesson III.1 Inputs and Costs
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Cost Relations
Average Total Cost
ATC = AVC + AFC
ATC(Q) = C(Q)/Q
$
Relation of MC and ATC:
• MC > ATC implies ATC is increasing
MC
ATC
• MC < ATC implies ATC is decreasing
(There is an analogy to your GPA:
If your next grade > GPA, your
GPA is increasing.)
Thus, ATC is decreasing until it
intersects MC, then it is increasing.
Q
BA 210 Lesson III.1 Inputs and Costs
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Cost Relations
Average Variable Cost
AVC = VC(Q)/Q
$
Relation of ATC and AVC:
ATC > AVC in the short-run, since
FC > 0.
MC
ATC
AVC
Relation of MC and AVC:
• MC > AVC implies AVC is
increasing
• MC < AVC implies AVC is
decreasing
Q
BA 210 Lesson III.1 Inputs and Costs
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Cost Relations
Summary
Average Total Cost
ATC = AVC + AFC
ATC = C(Q)/Q
$
MC
ATC
AVC
Average Variable Cost
AVC = VC(Q)/Q
Average Fixed Cost
AFC = FC/Q = ATC-AVC
Marginal Cost
MC = DC/DQ
AFC
Q
BA 210 Lesson III.1 Inputs and Costs
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Cost Relations
Recovering Fixed Cost
Q0(ATC-AVC)
$
= Q0 AFC
= Q0(FC/ Q0)
MC
ATC
AVC
= FC
ATC
AFC
Fixed Cost
AVC
Q0
BA 210 Lesson III.1 Inputs and Costs
Q
32
Cost Relations
Recovering Variable Cost
$
Q0AVC
MC
ATC
= Q0[VC(Q0)/ Q0]
AVC
= VC(Q0)
AVC
Variable Cost
Minimum of AVC
Q0
BA 210 Lesson III.1 Inputs and Costs
Q
33
Cost Relations
Recovering Total Cost
Q0ATC
$
MC
= Q0[C(Q0)/ Q0]
ATC
AVC
= C(Q0)
ATC
Minimum of ATC
Total Cost
Q0
BA 210 Lesson III.1 Inputs and Costs
Q
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Short Run verses Long Run Costs
Short Run verses Long Run Costs
BA 210 Lesson III.1 Inputs and Costs
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Short Run verses Long Run Costs
Short-Run versus Long-Run Costs
• In the short run, fixed cost is completely outside the control of a
firm. But all inputs are variable in the long run.
• The firm will choose its fixed input (fixed cost) in the long run
based on the level of output it expects to produce.
BA 210 Lesson III.1 Inputs and Costs
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Short Run verses Long Run Costs
Cost of
case
Choosing the
Level of
Fixed Cost
of Selena’s
Gourmet
Salsas:
$250
At low output levels, low
fixed cost yields lower
average total cost
At high output levels, high
fixed cost yields lower
average total cost
200
Low fixed cost
ATC1
150
100
ATC2
High fixed cost
50
0
1
2
3
4
5
Low fixed cost (FC = $108)
Quantity
of salsa
(salsa)
1
2
3
4
5
6
7
8
9
10
High
variable
cost
Total
cost
$12
48
108
192
300
432
588
768
972
1,200
$120
156
216
300
408
540
696
876
1,080
1,308
ATC of
case
ATC1
$120.00
78.00
72.00
75.00
81.60
90.00
99.43
109.50
120.00
130.80
6
7
8
9
10 Quantity of salsa (cases)
High fixed cost (FC = $216)
Low
variable
cost
$6
24
54
96
150
216
294
384
486
600
Total
cost
$222
240
270
312
366
432
510
600
702
816
ATC of
case
ATC2
$222.00
120.00
90.00
78.00
73.20
72.00
72.86
75.00
78.00
81.60
BA 210 Lesson III.1 Inputs and Costs
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Short Run verses Long Run Costs
The long-run average total cost curve shows the relationship between
output and average total cost when fixed cost has been chosen to
minimize average total cost for each level of output.
BA 210 Lesson III.1 Inputs and Costs
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Short Run verses Long Run Costs
Short-Run and Long-Run Average Total Cost Curves
If you anticipated producing quantity 3, you would have selected
the fixed costs (fixed inputs) in curve ATC3 so to minimize ATC
Cost of case
Constant
returns to
scale
Increasing returns to scale
ATC
Decreasing returns to scale
ATC ATC LRATC
6
9
3
B
Y
A
0
X
C
3
4
5
6
7
8
9
BA 210 Lesson III.1 Inputs and Costs
Quantity of salsa (cases)
39
Short Run verses Long Run Costs
Returns to Scale
• There are increasing returns to scale (economies of scale)
when long-run average total cost declines as output increases.
• There are decreasing returns to scale (diseconomies of scale)
when long-run average total cost increases as output increases.
• There are constant returns to scale when long-run average total
cost is constant as output increases.
BA 210 Lesson III.1 Inputs and Costs
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Summary
Summary
BA 210 Lesson III.1 Inputs and Costs
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Summary
1.
2.
3.
The relationship between inputs and output is a producer’s
production function. In the short run, the quantity of a fixed
input cannot be varied but the quantity of a variable input
can. In the long run, the quantities of all inputs can be varied.
For a given amount of the fixed input, the total product curve
shows how the quantity of output changes as the quantity of
the variable input changes.
There are diminishing returns to an input when its marginal
product declines as more of the input is used, holding the
quantity of all other inputs fixed.
Total cost is equal to the sum of fixed cost, which does not
depend on output, and variable cost, which does depend on
output.
BA 210 Lesson III.1 Inputs and Costs
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Summary
4.
5.
Average total cost, total cost divided by quantity of output, is
the cost of the average unit of output, and marginal cost is
the cost of one more unit produced. U-shaped average total
cost curves are typical, because average total cost consists of
two parts: average fixed cost, which falls when output
increases (the spreading effect), and average variable cost,
which rises with output (the diminishing returns effect).
When average total cost is U-shaped, the bottom of the U is
the level of output at which average total cost is minimized,
the point of minimum-cost output. This is also the point at
which the marginal cost curve crosses the average total cost
curve from below.
BA 210 Lesson III.1 Inputs and Costs
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Summary
6.
7.
In the long run, a producer can change its fixed input and its
level of fixed cost. The long-run average total cost curve
shows the relationship between output and average total cost
when fixed cost has been chosen to minimize average total
cost at each level of output.
As output increases, there are increasing returns to scale if
long-run average total cost declines; decreasing returns to
scale if it increases; and constant returns to scale if it remains
constant. Scale effects depend on the technology of
production.
BA 210 Lesson III.1 Inputs and Costs
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Review Questions
Review Questions
 You should try to answer some of the following questions
before the next class.
 You will not turn in your answers, but students may request
to discuss their answers to begin the next class.
 Your upcoming cumulative Final Exam will contain some
similar questions, so you should eventually consider every
review question before taking your exam.
BA 210 Lesson III.1 Inputs and Costs
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Review Questions
Follow the link
http://faculty.pepperdine.edu/jburke2/ba210/PowerP3/Set8Answers.pdf
for review questions for Lesson III.1
BA 210 Lesson III.1 Inputs and Costs
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BA 210
Introduction to Microeconomics
End of Lesson III.1
BA 210 Lesson III.1 Inputs and Costs
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