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Chapter One Homework due tomorrow in lab Numbers 10, 12 and 17
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Chapter One Homeworkdue tomorrow in lab
Numbers 10, 12 and 17
Managerial Economics & Business Strategy
Chapter 1The 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:
• Slope (first derivative) of the total benefit curve.
Q
BMB
Marginal Cost (MC)
• Change in total costs arising from a change in the control variable, Q:
• Slope (first derivative) of the total cost curve
Q
CMC
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
Marginal Benefits
Marginal Costs
Marginal Net
Benefits
Q B(Q) C(Q) N(Q) MB(Q) MC(Q) MNB(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
Control Variable
Total Benefits
Total Costs
Net Benefits
Marginal Benefits
Marginal Costs
Marginal Net
Benefits
Q B(Q) C(Q) N(Q) MB(Q) MC(Q) MNB(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
Control Variable
Total Benefits
Total Costs
Net Benefits
Marginal Benefits
Marginal Costs
Marginal Net
Benefits
Q B(Q) C(Q) N(Q) MB(Q) MC(Q) MNB(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
Control Variable
Total Benefits
Total Costs
Net Benefits
Marginal Benefits
Marginal Costs
Marginal Net
Benefits
Q B(Q) C(Q) N(Q) MB(Q) MC(Q) MNB(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
Control Variable
Total Benefits
Total Costs
Net Benefits
Marginal Benefits
Marginal Costs
Marginal Net
Benefits
Q B(Q) C(Q) N(Q) MB(Q) MC(Q) MNB(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
What if we can use fractional parts of the control variable?
Q
Total Benefits & Total Costs
Benefits
Costs
Q*
B
CSlope = MC
Slope =MB
Let’s talk calculus…• What is the MB?
300-12Y
• What is the MC? 8Y
• 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
4)(
6300)(
YYC
YYYB
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 -12-8= -20 Negative Maximum
• Shows N(Y) is concave Slope of MB curve < slope of MC curve
2
2
4)(
6300)(
YYC
YYYB
