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Chapter 3
Balancing Costs and Benefits
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Last Chapter Review
During the last chapter, we looked at the
basic concepts concerning…
Demand
Supply
Equilibrium
Elasticity
3-2
Main Topics of Ch. 3:
Balancing Benefits and Costs
In chapter 1, one of the most basic
principles of economics was that “Tradeoffs are unavoidable”. In this chapter, we
look at the basics of how we juggle these
trade-offs to find the best choice.
We will look at…
Maximizing benefits less costs
Thinking on the margin
Marginal Benefit vs. Cost
Sunk costs and decision-making
3-3
Maximizing Net Benefit
Terms defined…
Net benefit: total benefit minus total cost
Total (economic) cost must include opportunity cost
Opportunity cost: the cost associated with
foregoing the opportunity to employ a resource
in its best alternative use
What is your opportunity cost to attend univ.?
Right decision is the choice with the greatest
difference between total benefit and total cost
3-4
Car Repair Example
You own an old car that you use for
delivering pizza, but now want to sell it.
You know that if some repairs are made,
the value of the car will increase.
The more time the mechanic spends
repairing the car, the more it will be worth.
Also, the more time the mechanic spends,
the more it will cost you.
3-5
Car Repair Example:
Benefit Schedule
The mechanic’s time
is available in onehour increments
Maximum repair time
is 6 hours
The more time the car
is repaired, the more
it is worth
Table 3.1: Benefits of Repairing Your
Car
Repair Time
(Hours)
Total Benefit
($)
0
0
1
615
2
1150
3
1600
4
1975
5
2270
6
2485
3-6
Car Repair Example: Cost Schedule
Table 3.2: Costs of Repairing Your Car
Repair
Time
(Hours)
Cost of Mechanic and
Parts
($)
Lost Wages from
Pizza Delivery Job
($)
Total
Cost
($)
0
0
0
0
1
140
10
150
2
355
25
380
3
645
45
690
4
1005
75
1080
5
1440
110
1550
6
1950
150
2100
The mechanics time costs you money.
Also, remember your opportunity cost with
your pizza job!
3-7
Car Repair Example:
Maximizing Net Benefit
How should you decide how many hours
is the “right” number to have your car
repaired?
Recall that every hour in the shop will
bring both benefits and costs
Choose the number of hours where
benefits exceed costs by the greatest
amount
3-8
Car Repair Example:
The Right Decision
Table 3.3: Total Benefit and Total Cost of
Repairing Your Car
Repair Time
(Hours)
Total Benefit
($)
Total Cost
($)
0
0
0
1
615
150
2
1150
380
3
1600
690
4
1975
1080
5
2270
1550
6
2485
2100
Net Benefit
($)
3-9
Car Repair Example:
The Right Decision
Table 3.3: Total Benefit and Total Cost of
Repairing Your Car
Repair Time
(Hours)
Total Benefit
($)
Total Cost
($)
Net Benefit
($)
0
0
0
0
1
615
150
465
2
1150
380
770
3
1600
690
910
4
1975
1080
895
5
2270
1550
720
6
2485
2100
385
3-10
Car Repair Example:
The Right Decision
Table 3.3: Total Benefit and Total Cost of
Repairing Your Car
Best
Choice
Repair Time
(Hours)
Total Benefit
($)
Total Cost
($)
Net Benefit
($)
0
0
0
0
1
615
150
465
2
1150
380
770
3
1600
690
910
4
1975
1080
895
5
2270
1550
720
6
2485
2100
385
3-11
Car Repair Example:
Graphical Approach
(Figure 3.1)
 Data from Table 3.3 are
shown in this graph
 Costs are in red; benefits
are in blue
 The best choice is where
benefits > costs and the
distance between them
is maximized
 This is at 3 hours, net
benefit = $910
Total
Benefit,
Total
Cost
($)
2400
2000
710
1600
910
1200
800
400
465
1
2
3
4
5
6
Repair
Hours
Best Choice
3-12
Maximizing Net Benefit:
Finely Divisible Actions
Many decisions involve actions that are
more finely divisible
E.g. mechanic’s time available by the
minute
In these cases, you can use benefit and
cost curves rather than points or a
schedule to make the best decision
Underlying principle is the same:
maximize net benefit
3-13
Car Repair Example:
Finely Divisible Benefit
(a): Total Benefit
Horizontal axis
measures hours of
mechanic’s time
Vertical axis
measures in dollars
the total increase in
your car’s value
B(H)=654H-40H2
Total Benefit
($)
B
2270
1602
614
0
1
2
3
4
5
6
Hours (H)
3-14
Car Repair Example:
Finely Divisible Cost
(b): Total Cost
Vertical axis
measures total cost
in dollars
Includes opportunity
cost
C(H)=110H+40H2
Total Cost
($)
C
1550
690
150
0
1
2
3
4
5
6
Hours (H)
3-15
Car Repair Example:
Finely Divisible Net Benefit
Best choice is 3.4
hours of repair,
maximizes net
benefit
Net benefit with finely
divisible choices is
greater than in
previous example;
more flexibility allows
you to do better
(c): Total Benefit versus Total
Cost
Total
Benefit
Total
Cost
($)
B
1761.20
924.80
C
836.40
0
1
2
3
Hours
(H)
4
5
6
3.4
3-16
Net Benefit Curve
(Figure 3.3)
Can also graph the
net benefit curve
Vertical axis shows
B-C, net benefit
Best choice is the
number of hours that
corresponds to the
highest point on the
curve, 3.4 hours
Net
Benefit
($)
924.80
B–C
0
1
2
3
Hours (H)
4
5
6
3.4
3-17
Thinking on the Margin
Thinking like an economist
Another approach to maximizing net
benefits
Capture the way that benefits and costs
change as the level of activity changes
just a little bit
For any action choice X, the marginal units
are the last DX units, where DX is the
smallest amount you can add or subtract.
Ie. the mechanic may charge by the hour, ½
hour or even by the minute.
3-18
Marginal Cost
The marginal cost of an action at an activity
level of X units is equal to the extra cost
incurred due to the marginal units, divided by
the number of marginal units
MC 
DC C ( X )  C ( X  DX )

DX
DX
3-19
Car Repair Example:
Marginal Cost
Marginal cost measures the additional
cost incurred from the marginal units (DH)
of repair time
If C(H) is the total cost of H hours of
repair work, the extra cost of the last DH
hours is DC = C(H) – C(H-DH)
To find marginal cost, divide this extra
cost by the number of extra hours of
repair time, DH
3-20
Car Repair Example:
Marginal Cost
So the marginal cost of an additional hour of
repair time is:
DC C ( H )  C ( H  DH )
MC 

DH
DH
Using the data from Table 3.2 (p65), if H= 3,
we see:
MC 
C (3)  C (3  1)
 690  380  310
1
3-21
Car Repair Example:
Marginal Cost Schedule
Table 3.5: Total Cost and Marginal
Cost of Repairing Your Car
Repair
Time
(Hours)
Total Cost
($)
Marginal Cost (MC)
($/hour)
0
0
-
1
150
150
2
380
230
3
690
310
4
1080
390
5
1550
470
6
2100
550
3-22
Marginal Benefit
The marginal benefit of an action at an
activity level of X units is equal to the extra
benefit produced due to the marginal units,
divided by the number of marginal units
MC 
DB B( X )  B( X  DX )

DX
DX
3-23
Car Repair Example:
Marginal Benefit
Marginal benefit measures the additional
benefit gained from the marginal units
(DH) of repair time
This parallels the definition and formula
for marginal cost
3-24
Car Repair Example:
Marginal Benefit
The marginal benefit of an additional hour of
repair time is:
DB B( H )  B( H  DH )
MC 

DH
DH
Using the data from Table 3.1 (p65) , if H= 3,
we see:
MC 
B(3)  B(3  1)
 1600  1150  450
1
3-25
Car Repair Example:
Marginal Benefit Schedule
Table 3.6: Total Benefit and Marginal Benefit
of Repairing Your Car
Repair Time
(Hours)
Total Benefit
($)
Marginal Benefit (MB)
($/hour)
0
0
-
1
615
615
2
1150
535
3
1600
450
4
1975
375
5
2270
295
6
2485
215
3-26
Marginal Analysis and Best
Choice
Comparing marginal benefits and marginal
costs can show whether an increase or
decrease in a level of an activity raises or
lowers the net benefit
Increase level if MB of doing so is greater
than MC; if MC of last increase was greater
than MB, decrease the level
At the best choice, a small change in
activity level can’t increase the net benefit
Get as close to MB=MC as possible
3-27
Marginal Analysis and Best
Choice
Table 3.7: Marginal Benefit and Marginal
Cost of Repairing Your Car
Best
Choice
Repair
Time
(Hours)
Marginal
Benefit (MB)
($/hour)
Marginal
Cost (MC)
($/hour)
0
-
-
1
615
>
150
2
535
>
230
3
450
>
310
4
375
<
390
5
295
<
470
6
215
<
550
No Marginal Improvement can be made. Why?
Under what situation could this be improved?
3-28
Marginal Analysis with
Finely Divisible Actions
Can conduct the same analysis if choices are
finely divisible by using marginal benefit and
marginal cost curves
Derive marginal benefit and marginal cost from
total benefit and total cost curves
Marginal benefit at H hours of repair time is
equal to the slope of the line drawn tangent to
the total benefit function at that point
Usually called simply the “slope of the total
benefit curve” at point D
3-29
Car Repair Example:
Finely Divisible Marginal Benefit
Let DH' = the smallest possible change in hours
of car repair
Adding the last DH‘ of repairs increases total
benefit from point F to point D in Figure 3.4 (on
the next slide), this equal to:
DB  B( H )  B( H  DH )
Recall that marginal benefit (slope) is DB' /DH'
Since the vertical axis measures hours of work
and the horizontal axis measures total benefit,
then marginal benefit equals “rise” over “run”
between points F and D.
3-30
Relationship between Total
Benefit and Marginal Benefit
(Figure 3.4)
Total Benefit
($)
Slope = MB
D
B( H )
Slope = MB =
DB' '
DB' / DH'
E
B( H  DH' ' )
DB'
Slope
= MB =
B( H  DH' )
F
H  DH '
DB' ' / DH' '
H  DH' '
H
Hours (H)
DH ' '
DH'
3-31
Relationship between Total
Benefit and Marginal Benefit
Tangents to the total benefit function at
three different numbers of hours (H = 1,
H = 3, H = 5)
Slope of each tangent equals the
marginal benefit at each number of hours
Figure (b) shows the MB curve: note how
the MB varies with the number of hours
Marginal benefit curve is described by
the function MB(H)= 654-80H
3-32
Relationship between Total
Benefit and Marginal Benefit
(Figure 3.5)
(b): Marginal Benefit
(a): Total Benefit
Slope = MB = 254
Total Benefit
($)
Marginal Benefit
($/hour)
Slope = MB = 414
654
2270
B
574
Slope = MB = 574
1602
414
MB
254
614
0
1
2
3
Hours (H)
4
5
6
0
1
2
3
4
5
6
Hours (H)
3-33
Relationship between Total Cost
and Marginal Cost
Parallels relationship between total benefit curve
and marginal benefit
When actions are finely divisible, the marginal
cost when choosing action X is equal to the
slope of the total cost curve at X
3-34
Relationship between Total Cost
and Marginal Cost
Tangents to the total cost curve at three
different numbers of hours (H = 1, H = 3,
H = 5)
Slope of each tangent equals the
marginal cost at each number of hours
Figure (b) shows the MC curve: note how
the MC varies with the number of hours
Marginal cost curve is described by the
function MC(H)= 110+80H
3-35
Relationship between Total Cost
and Marginal Cost
(Figure 3.6)
(a): Total Cost
(b): Marginal Cost
Marginal Cost
($/hour)
Total Cost
($)
C
MC
510
1550
350
Slope = MC = 510
Slope = MC = 190
690
190
110
Slope = MC = 350
150
0
1
2
3
Hours (H)
4
5
6
0
1
2
3
4
5
6
Hours (H)
3-36
Marginal Benefit Equals Marginal
Cost at a Best Choice
At the best choice of 3.4 hours, the No
Marginal Improvement Principle holds so
MB = MC
At any number of hours below 3.4, MB >
MC, so a small increase in repair time will
improve the net benefit
At any number of hours above 3.4, MC >
MB, so that a small decrease in repair
time will improve net benefit
3-37
Marginal Benefit Equals Marginal
Cost at a Best Choice (Figure 3.7)
Marginal
Benefit,
Marginal
Cost
($/hour)
654
MC
382
MB
110
0
1
2
Hours (H)
3
4
5
6
3.4
3-38
Slopes of Total Benefit and Total
Cost Curves at the Best Choice
MC = MB at the best choice of 3.4 hours
of repair
Therefore, the slopes of the total benefit
and total cost curves must be equal at
this point
Tangents to the total benefit and total
cost curves show this relationship
3-39
Slope of Total Benefit and Total
Cost Curves
(Figure 3.8)
Total
Benefit
Total
Cost
($)
B
924.80
0
1
2
3
Hours (H)
4
C
5
6
3.4
3-40
Marginal Anal. – 2 Steps to
Finding the Best Choice
Step 1: Identify any interior actions that
satisfy the No Marginal Improvement
Principle. MB=MC
Step 2: Compare the net benefits of the
best interior action to those from the
boundary actions. Best choice is the one
with the highest net benefit.
3-41
Marginal Anal. – Mechanic Ex.
Step 1: MB=MC
Marginal Benefit Eq. = MB(H)= 654-80H
Marginal Cost Eq. = MC(H)= 110+80H
654-80H=110+80H
H=3.4 ($924.80…remember…the total benefit
equation is 654H-40H² and the total cost equation is
110H-40H²)
Step 2: Compare to boundary #s
H=0 ($0)
H=6 ($385 ~ rounded to nearest $5)
Which is the best choice?
3-42
Sunk Costs and Decision Making
A sunk cost is a cost that the decision
maker has already incurred, or
A cost that is unavoidable regardless of
what the decision maker does.
Sunk cost examples….?
Sunk costs affect the total cost of a
decision
Sunk costs do not affect marginal costs
So sunk costs do not affect the best
choice
3-43
Car Repair Example: Best Choice
with a Sunk Cost
Figure 3.9 shows a cost-benefit
comparison for two possible cost
functions with sunk fixed costs: $500 and
$1100.
In both cases, the best choice is H = 3.4:
the level of sunk costs has no effect on
the best choice
Notice that the slopes of the two total
cost curves, and thus the marginal costs,
are the same
3-44
Best Choice with a Sunk Cost
(Figure 3.9)
C´
Total Benefit,
Total Cost
($)
B
-175.20
C
424.80
1100
500
0
1
2
3
Hours (H)
4
3.4
5
6
3-45
More Sunk Costs
Knowing what will happen before the
money is sunk can prevent you from
even spending the initial money.
Chunnel Example.
1987 est. cost = 3 B. Pounds
1987 est. revenue = 4 B.
1990 sunk cost = 2.5 B.
1990 est. addit. Cost = 2 B.
Finish or abandon project? Why?
3-46
Summary
Maximize benefits less cost
Best choice yields the highest net benefit of
all alternatives
Thinking on the Margin
Looking at marginal benefits can influence
decision making
No Marginal Improvement Principle…
Sunk Costs
The size of the sunk costs has no effect on
the best choice.
The act of sinking a cost can matter
3-47
Problem
“If the cost of repairing your car goes up,
you should do less of it.” Is this statement
correct? If you think the answer is yes,
explain why. If you think the answer is no,
give an example in which the best choice
is higher when the cost is higher.
3-48
Problems
“If the cost of repairing your car goes up, you
should do less of it.” If this statement correct?
If you think the answer is yes, explain why. If
you think the answer is no, give an example
in which the best choice is higher when the
cost is higher.
In the absence of any other changes (specifically
changes to benefits), this statement is correct.
The only way that a higher cost could inspire a
higher best choice would be if the benefits also
increase, and if the benefits increased by more
than the costs. (Note that if benefits and costs
both increase by the same amount, the best
choice should remain unchanged.)
3-49
Problems
Chunnel Example.
1987 est. cost = 3 B. Pounds
1987 est. revenue = 4 B.
1990 sunk cost = 2.5 B.
1990 est. addit. Cost = 2 B.
Finish or abandon project? Why?
How much could the additional costs add up
to before the Chunnel project would be
abandoned…why?
3-50
Problem
 How much could the additional costs add up to before
the Chunnel project would be abandoned…why?
 Once the investors expenses are incurred, they are sunk and no
longer relevant to a decision to continue or no.
 If the cost of quitting is ₤0, the benefit of abandoning the project is
also ₤0, since there would be no revenue earned.
 So, we need to compare the benefit to the cost of completing the
project.
 The benefit of completing the project is ₤4 million in revenue that they
expect to earn. If the cost of completing the project is ₤X million, then
the net benefit is ₤(4 – X) million.
 So long as X < 4, this net benefit would be positive, making it greater
than the net benefit of quitting. In other words, given that the initial
₤2.5 million is a sunk cost, investors will complete the project as long
as they can break even starting from the present.
3-51