Managerial Economics
eighth edition
Thomas
Maurice
Chapter 3
Marginal Analysis for
Optimal Decision Making
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Optimization
• An optimization problem involves
the specification of three things:
• Objective function to be maximized or
minimized
• Activities or choice variables that
determine the value of the objective
function
• Any constraints that may restrict the
values of the choice variables
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Choice Variables
• Choice variables determine the
value of the objective function
• Continuous variables
• Can choose from uninterrupted span
of variables
• Discrete variables
• Must choose from a span of variables
that is interrupted by gaps
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Net Benefit
• Net Benefit (NB)
• Difference between total benefit (TB)
and total cost (TC) for the activity
• NB = TB – TC
• Optimal level of the activity (A*) is
the level that maximizes net benefit
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Optimal Level of Activity
(Figure 3.1)
Total benefit and total cost (dollars)
T
C
4,000
G
•
F
D
•
•D’
3,000
B
•
2,310
•
TB
2,000
NB* = $1,225
C
•
1,085
1,000
• B’
•C’
0
200
A
350 = A*
600 700
1,000
Level of activity
Net benefit (dollars)
Panel A – Total benefit and total cost curves
M
1,225
1,000
Panel B – Net benefit curve
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•
•
600
0
5
•c’’
d’’
200
350 = A*
600
f’’
A
•
Level of activity
1,000
NB
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Marginal Benefit & Marginal Cost
• Marginal benefit (MB)
• Change in total benefit (TB) caused by
an incremental change in the level of
the activity
• Marginal cost (MC)
• Change in total cost (TC) caused by an
incremental change in the level of the
activity
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Marginal Benefit & Marginal Cost
Change in total benefit TB
MB 

Change in activity
A
Change in total cost TC
MC 

Change in activity
A
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Relating Marginals to Totals
• Marginal variables measure rates
of change in corresponding total
variables
• Marginal benefit & marginal cost are
also slopes of total benefit & total
cost curves, respectively
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Relating Marginals to Totals
(Figure 3.2)
Total benefit and total cost (dollars)
T
C
4,000
100
320
3,000
100
520
100
•B
•C
1,000
C’
•
•
•
TB
820
100
2,000
640
•D
D’•
F
G
•
B’
520
100
340
A
100
0
200
350 = A*
600
800
1,000
Level of activity
Marginal benefit and
marginal cost (dollars)
Panel A – Measuring slopes along TB and
TC
MC (= slope of TC)
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c (200, $6.40)
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5.20
4
•
•d’ (600, $8.20)
b
•
•c’ (200, $3.40)
d (600, $3.20)
•
2
MB (= slope of TB)
0
•
1,000
g
200
350 = A*
Panel B – Marginals give slopes of totals
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600
Level of activity
800
A
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Using Marginal Analysis to Find
Optimal Activity Levels
• If marginal benefit > marginal cost
• Activity should be increased to reach
highest net benefit
• If marginal cost > marginal benefit
• Activity should be decreased to reach
highest net benefit
• Optimal level of activity
• When no further increases in net benefit
are possible
• Occurs when MB = MC
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Using Marginal Analysis to Find A*
(Figure 3.3)
Net benefit (dollars)
MB = MC
MB > MC
100
300
•
c’’
MB < MC
M
•
100
•
d’’
500
A
0
200
350 = A*
600
800
NB
Level of activity
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1,000
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Unconstrained Maximization with
Discrete Choice Variables
• Increase activity if MB > MC
• Decrease activity if MB < MC
• Optimal level of activity
• Last level for which MB exceeds MC
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Irrelevance of Sunk, Fixed, &
Average Costs
• Sunk costs
• Previously paid & cannot be recovered
• Fixed costs
• Constant & must be paid no matter the level
of activity
• Average (or unit) costs
• Computed by dividing total cost by the
number of units of the activity
• These costs do not affect marginal cost
& are irrelevant for optimal decisions
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Constrained Optimization
• The ratio MB/P represents the
additional benefit per additional
dollar spent on the activity
• Ratios of marginal benefits to
prices of various activities are used
to allocate a fixed number of
dollars among activities
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Constrained Optimization
• To maximize or minimize an
objective function subject to a
constraint
• Ratios of the marginal benefit to price
must be equal for all activities
• Constraint must be met
MBA MBB
MBZ

 ... 
PA
PB
PZ
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