• Marginal cost (MC)
– Change in total cost (TC) caused by an incremental change in the level of the activity
3-5
Marginal Benefit & Marginal Cost
MB Change in total benefit TB
Optimization
• An optimization problem involves the specification of three things:
– Objective function to be maximized or minimized – Activities or choice variables that determine the
– Activity should be increased to reach highest net benefit
• If marginal cost > marginal benefit
– Activity should be decreased to reach highest net benefit
value of the objective function – Any constraints that may restrict the values of the
choice variables
3-1
Choice Variables
• Choice variables determine the value of the objective function
Level of activity
Panel A – Total benefit and total cost curves
G•
TB
A 1,000
(Figure
Net benefit (dollars)
1,225 1,000
600
0 Panel B – Net benefit curve
M
••
c’’ 200 350 = A*
• Optimal level of activity
– When no further increases in net benefit are possible – Occurs when MB = MC
4,000 3,000
TC
100 F
• 320 •D
100
•D’
820
G•
TB
2,000
• 520
100
B
100
• 640
1,000
C
•B’
520
•C’
100 340
100
A
0
200 350 = A*
600
800
1,000
Level of activity
Panel A – Measuring slopes along TB and TC
3-2
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
3-3
Optimal Level of Activity
3.1)
TC
Total benefit and total cost (dollars)
4,000
3,000 2,310
2,000 1,085
1,000
D
•
F•
•
B
D’
•
C•
NB* = $1,225
• B’
•
C’
0
200 350 = A*
600 700
Marginal benefit and marginal cost (dollars)
MC (= slope of TC)
8
c (200, $6.40)
•
d’ (600, $8.20)
6 5.20
• •b
4
•
c’ (200, $3.40)
d (600, $3.20)
•
2
MB (= slope of TB)
0
200 350 = A*
600
•g
800
1,000
A
Panel B – Marginals give slopes of totals
Level of activity
3-8
Using Marginal Analysis to Find Optimal Activity Levels
• If marginal benefit > marginal cost
• Continuous variables
– Can choose from uninterrupted span of variables
• Discrete variables
– Must choose from a span of variables that is interrupted by gaps
•d’’ •f’’
600
Level of activity
NB
1,000
A
3-4
Marginal Benefit & Marginal Cost
• Marginal benefit (MB)
– Change in total benefit (TB) caused by an incremental change in the level of the activity
Change in activity
A
MC Change in total cost TC Change in activity A
3-6
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
3-7
Relating Marginals to Totals
(Figure 3.2)
Total benefit and total cost (dபைடு நூலகம்llars)