Consumer behaviour from economics that is microeconomics

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1. Chapter 3: Marginal Analysis
for Optimal Decision
McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

2. 3-2
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

3. 3-3
Optimization
•Maximization problem
•An optimization problem that involves
maximizing the objective function
•Minimization problem
•An optimization problem that involves
minimizing the objective function

4. 3-4
Optimization
•Unconstrained optimization
•An optimization problem in which the decision
maker can choose the level of activity from an
unrestricted set of values
•Constrained optimization
•An optimization problem in which the decision
maker chooses values for the choice
variables from a restricted set of values

5. 3-5
Choice Variables
•Choice variables determine the value of
the objective function
•Continuous variables
•Discrete variables

6. 3-6
Choice Variables
•Continuous variables
•Can choose from uninterrupted span of
variables
•Discrete variables
•Must choose from a span of variables that is
interrupted by gaps

7. 3-7
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

8. 3-8
Optimal Level of Activity
(Figure 3.1)
NB
TB
TC
1,000
Level of activity
2,000
4,000
3,000
A
0 1,000600200
Total benefit and total cost (dollars)
Panel A – Total benefit and total cost curves
A
0 1,000600200
Level of activity
Net benefit (dollars)
Panel B – Net benefit curve
•
G
700
•
F
•
•
D’
D
•
•
C’
C
•
•
B
B’
2,310
1,085
NB* = $1,225
•
f’’
350 = A*
350 = A*
•
M
1,225
•
c’’
1,000
•
d’’
600

9. 3-9
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

10. 3-10
Marginal Benefit & Marginal CostTB
MB
A


==
Change in total benefit
Change in activity 

Change in total benefit
Change in activity
TC
MC
A
==

11. 3-11
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

12. 3-12
Relating Marginals to Totals
(Figure 3.2)
MC (= slope of TC)
MB (= slope of TB)
TB
TC
•
F
•
•
D’
D
•
•
C’
C
Level of activity
800
1,000
Level of activity
2,000
4,000
3,000
A
0 1,000600200
Total benefit and total cost (dollars)
Panel A – Measuring slopes along TB and TC
A
0 1,000600200
Marginal benefit and marginal cost (dollars)
Panel B – Marginals give slopes of totals
800
2
4
6
8
350 = A*
100
520
100
520
350 = A*
•
•
B
B’
b
•
•
G
•
g
100
320
100
820
•
•
d’ (600, $8.20)
d (600, $3.20)
100
640
100
340
•
•
c’ (200, $3.40)
c (200, $6.40)
5.20

13. 3-13
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

14. 3-14
Using Marginal Analysis to Find
Optimal Activity Levels
•Optimal level of activity
•When no further increases in net benefit are
possible
•Occurs when MB = MC

15. 3-15
Using Marginal Analysis to Find A*
(Figure 3.3)
NB
A
0 1,000600200
Level of activity
Net benefit (dollars)
800
•
c’’
•
d’’
100
300
100
500
350 = A*
MB = MC
MB > MC MB < MC
•
M

16. 3-16
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

17. 3-17
Irrelevance of Sunk, Fixed, and
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

18. 3-18
Irrelevance of Sunk, Fixed, and
Average Costs
•These costs do not affect marginal cost & are
irrelevant for optimal decisions

19. 3-19
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

20. 3-20
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...
A B Z
A B Z
MBMBMB
PP P
===