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summarize the key economic principles and concepts in each of the assigned chapters.

Chapter 3
Marginal Analysis for
Optimal Decisions
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
1-1
Learning Objectives
â– Define several key concepts and terminology related to
marginal analysis
â– Use marginal analysis to find optimal activity levels in
unconstrained maximization problems and explain why
sunk costs, fixed costs, and average costs are irrelevant
for decision making
â– Employ marginal analysis to find the optimal levels of
two or more activities in constrained maximization and
minimization problems
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-2
Optimization
â– A persons decision is optimal if it leads to
the best outcome under a given set of
circumstances. This is accomplished by
using Marginal Analysis.
â– A person needs to determine the benefit
of a changing activity and compare it with
the cost associated with the change in
activity.
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-3
Optimization
â– Tactical Decisions
â– Strategic Decisions
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manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-4
Optimization
â– An optimization problem involves the
specification of three things:
~ Objective function – what is to be maximized
or minimized (profit, satisfaction, value).
~ Activities or choice variables that determine
the value of the objective function â€“
production level for profits.
~ Any constraints that may restrict the values of
the choice variables â€“ such as cost.
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-5
Optimization
â– We have discrete and continuous choice
variables.
â– A Discrete Choice Variable can only take
on specific integer values.
â– A Continuous Choice Variable can take
on any value between two points.
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-6
Optimization
â– Maximization problem
~ An optimization problem that involves
maximizing the objective function
â– Minimization problem
~ An optimization problem that involves
minimizing the objective function
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-7
Optimization
â– Unconstrained optimization
~ An optimization problem in which the decision
maker can choose the level of activity from an
unrestricted set of values.
â– Constrained optimization
~ An optimization problem in which the decision
maker chooses values for the choice
variables from a restricted set of values (such
as total costs).
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-8
Choice Variables
â– Activities or choice variables determine
the value of the objective function
â– Discrete choice variables
~ Can only take specific integer values
â– Continuous choice variables
~ Can take any value between two end points
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-9
Marginal Analysis
â– Analytical technique for solving
optimization problems that involves
changing values of choice variables by
small amounts to see if the objective
function can be further improved
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-10
Net Benefit
â– Net Benefit (NB)
~ Difference between total benefit (TB) and total
cost (TC) for the activity
~ NB = TB â€“ TC
â– Optimal level of the activity (A*) is the
level that maximizes net benefit
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-11
Optimization
â– The optimal level of activity does not
generally result in the maximization of
benefits.
â– The optimal level of activity in an
unconstrained maximization problem
does not result in the minimization of total
costs.
â– Only marginal benefits and marginal costs
are relevant in the decision process.
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-12
Optimal Level of Activity
(Figure 3.1)
Total benefit and total cost (dollars)
TC
4,000
D
B
â€¢
2,310
F
â€¢
â€¢ Dâ€™
3,000
â€¢
â€¢
G
TB
2,000
NB* = \$1,225
C
â€¢
1,085
1,000
â€¢ Bâ€™
â€¢Câ€™
0
200
A
350 = A*
600
700
1,000
Level of activity
Net benefit (dollars)
Panel A â€“ Total benefit and total cost curves
M
1,225
1,000
â€¢câ€™â€™
â€¢
â€¢
600
0
dâ€™â€™
200
350 = A*
â€¢
600
Level of activity
A
fâ€™â€™
1,000
NB
Panel B â€“ Net benefit curve
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-13
Marginal Benefit & Marginal Cost
â– Marginal benefit (MB)
~ Change in total benefit (TB) caused by an
incremental change in the level of the activity
â– Marginal cost (MC)
~ Change in total cost (TC) caused by an
incremental change in the level of the activity
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-14
Marginal Benefit & Marginal Cost
Change in total benefit ï„TB
MB =
=
Change in activity
ï„A
Change in total benefit ï„TC
MC =
=
Change in activity
ï„A
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-15
Using Marginal Analysis to Find
Optimal Activity Levels
â– If marginal benefit > marginal cost
~ Activity should be increased to reach highest
net benefit
â– If marginal cost > marginal benefit
~ Activity should be decreased to reach highest
net benefit
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-16
Using Marginal Analysis to Find
Optimal Activity Levels
â– Optimal level of activity
~ When no further increases in net benefit are
possible
~ Occurs when MB = MC
Â© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
3-17
Unconstrained Maximization with
Discrete Choice Variables
â– Increase activity if MB > MC