Managerial Economics &
Business Strategy
Calculus Review
Functions
• Will be dealing with equations of the form: y=f(x)
• Where f(x) is a function of X.
• f(xi) denotes the values of f(x) when x=xi
•
•
•
•
Example:
f(x)= 5+x2
f(0)=5+(0)2=5
f(2)=5+(2)2=9
Rates of Change
• When x changes from an original value x0 to a
new value x1, the change in X is denoted by
∆x=x1-x0.
• From this we can deduct that x1=x0+∆x.
• If y=f(x), the change in y per unit of change in
x can be represented as:
∆y f ( x1 ) − f ( x0 )
=
∆x
∆x
Marginal Analysis
Economics of Effective Management
Marginal Analysis Principle I
• Marginal principle
– To maximize net benefits, the manager should
increase the managerial control variable up to
the point where marginal benefits equal
marginal costs. This level of the managerial
control variable corresponds to the level at which
marginal net benefits are zero; nothing more can
be gained by further changes in that variable.
1-5
Table 1
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Control Variable
Total Benefits
Total Costs
Net Benefits
Marginal Benefit
Marginal Cost
Marginal Net Benefit
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
Copyright © 2014 by the McGraw-Hill
Companies, Inc. All rights reserved.
2-6
• MB=MC Max NB
• MB=0
Max TB
• Q=0(MC=0)
Min TC
Table 2
Control Variable Total Benefits
Total Cost
Net Benefits
Marginal Benefit
Marginal Cost
Marginal Net Benefit
Q
B(Q)
C(Q)
N(Q)
MB(Q)
MC(Q)
MNB(Q)
100
1200
950
250
210
60
150
101
1400
1020
380
200
70
130
102
1590
1100
490
190
80
110
103
1770
1190
580
180
90
90
104
1940
1290
650
170
100
70
105
2100
1400
700
160
110
50
106
2250
1520
730
150
120
30
107
2390
1650
740
140
130
10
108
2520
1790
730
130
140
-10
109
2640
1940
700
120
150
-30
110
2750
2100
650
110
160
-50
Table 2
• (1) Net benefits are maximized at Q = 107.
• (2) Marginal cost is slightly smaller than marginal
benefit (MC = 130 and MB = 140). This is due to the
discrete nature of the control variable.
Economics of Effective Management
Determining the Optimal Level of a Control Variable
Total benefits
Total costs
Maximum total benefits
𝐶𝐶 𝑄𝑄
Maximum net
benefits
0
𝐵𝐵 𝑄𝑄
Quantity
(Control Variable)
1-10
Economics of Effective Management
Determining the Optimal Level of a Control Variable II
Net benefits
Maximum
net benefits
Slope =𝑀𝑀𝑀𝑀𝑀𝑀(𝑄𝑄)
0
𝑁𝑁 𝑄𝑄 = 𝐵𝐵 𝑄𝑄 − 𝐶𝐶 𝑄𝑄 = 0
Quantity
(Control Variable)
1-11
Economics of Effective Management
Determining the Optimal Level of a Control Variable III
Marginal
benefits, costs
and net benefits
Maximum net
benefits
𝑀𝑀𝑀𝑀 𝑄𝑄
0
𝑀𝑀𝑀𝑀𝑀𝑀 𝑄𝑄
𝑀𝑀𝑀𝑀 𝑄𝑄
Quantity
(Control Variable)
1-12