Chapter One Homework
due tomorrow in lab
Numbers 10, 12 and 17
Managerial Economics &
Business Strategy
Chapter 1
The Fundamentals of Managerial
Economics
Net Benefits
• Net Benefits = Total Benefits - Total Costs
• Profits = Revenue - Costs
Marginal Benefit (MB)
• Change in total benefits arising from a change
in the control variable, Q:
B
MB 
Q
• Slope (first derivative) of the total benefit
curve.
Marginal Cost (MC)
• Change in total costs arising from a change in
the control variable, Q:
C
MC 
Q
• Slope (first derivative) of the total cost curve
Marginal Principle
• To maximize net benefits MB = MC.
• MB > MC means the last unit of the control
variable increased benefits more than it
increased costs.
• MB < MC means the last unit of the control
variable increased costs more than it
increased benefits.
• Can we do it??? Start with a control
variable that can only be used in WHOLE
units (discrete)
Control
Variable
Total
Benefits
Total
Costs
Net
Benefits
Q
B(Q)
C(Q)
N(Q)
0
0
0
1
90
10
2
170
30
3
240
60
4
300
100
5
350
150
6
390
210
7
420
280
8
440
360
9
450
450
10
450
550
Marginal Marginal
Benefits
Costs
MB(Q)
Marginal
Net
Benefits
MC(Q) MNB(Q)
Control
Variable
Total
Benefits
Total
Costs
Net
Benefits
Q
B(Q)
C(Q)
N(Q)
0
0
0
0
1
90
10
80
2
170
30
140
3
240
60
180
4
300
100
200
5
350
150
200
6
390
210
180
7
420
280
140
8
440
360
80
9
450
450
0
10
450
550
-100
Marginal Marginal
Benefits
Costs
MB(Q)
Marginal
Net
Benefits
MC(Q) MNB(Q)
Control
Variable
Total
Benefits
Total
Costs
Net
Benefits
Marginal Marginal
Benefits
Costs
Q
B(Q)
C(Q)
N(Q)
MB(Q)
0
0
0
0
---
1
90
10
80
90
2
170
30
140
80
3
240
60
180
70
4
300
100
200
60
5
350
150
200
50
6
390
210
180
40
7
420
280
140
30
8
440
360
80
20
9
450
450
0
10
10
450
550
-100
0
Marginal
Net
Benefits
MC(Q) MNB(Q)
Control
Variable
Total
Benefits
Total
Costs
Net
Benefits
Marginal Marginal
Benefits
Costs
Q
B(Q)
C(Q)
N(Q)
MB(Q)
0
0
0
0
---
---
1
90
10
80
90
10
2
170
30
140
80
20
3
240
60
180
70
30
4
300
100
200
60
40
5
350
150
200
50
50
6
390
210
180
40
60
7
420
280
140
30
70
8
440
360
80
20
80
9
450
450
0
10
90
10
450
550
-100
0
100
Marginal
Net
Benefits
MC(Q) MNB(Q)
Control
Variable
Total
Benefits
Total
Costs
Net
Benefits
Marginal Marginal
Benefits
Costs
Marginal
Net
Benefits
Q
B(Q)
C(Q)
N(Q)
MB(Q)
0
0
0
0
---
---
---
1
90
10
80
90
10
80
2
170
30
140
80
20
60
3
240
60
180
70
30
40
4
300
100
200
60
40
20
5
350
150
200
50
50
0
6
390
210
180
40
60
-20
7
420
280
140
30
70
-40
8
440
360
80
20
80
-60
9
450
450
0
10
90
-80
10
450
550
-100
0
100
-100
MC(Q) MNB(Q)
What if we can use fractional parts of
the control variable?
Total Benefits
& Total Costs
Costs
Slope =MB
Benefits
B
Slope = MC
C
Q*
Q
Let’s talk calculus…
• What is the MB?

300-12Y
• What is the MC?

8Y
B(Y )  300Y  6Y
C (Y )  4Y
• What is the profit max level of Y?



300-12Y = 8Y
300=20Y
Y=15
• What are the Net Benefits at this level
of Y?


NB = ((300*15)-(6*15^2))-(4*15^2)
NB = 2250
2
2
One more check….Is it a
maximum point??
• Second derivative of the Net Benefit
equation must be negative
• N(Y) = B(Y)-C(Y)
• First derivative

(300-12Y)-8Y
• Second derivative


B (Y )  300Y  6Y 2
C (Y )  4Y 2
-12-8= -20
Negative  Maximum
• Shows


N(Y) is concave
Slope of MB curve < slope of MC curve