DECISION CRITERIA CONSOLIDATION:
A THEORETICAL FOUNDATION OF PARETO PRINCIPLE TO
MICHAEL PORTER’S COMPETITIVE FORCES
Jason Chou-Hong Chen
Management Information Systems,
School of Business Administration, Gonzaga University
Spokane, WA 99258
(509) 323-3421
chen@gonzaga.edu
P. Pete Chong
Management Information Systems,
School of Business Administration, Gonzaga University
Spokane, WA 99258
(509) 323-3426
chong@gonzaga.edu
Ye-Sho Chen
Department of Information Systems and Decision Sciences
Ourso College of Business, Louisiana State University
Baton Rouge, LA 70803
(504) 388-2510
qmchen@unix1.sncc.lsu.edu
July 15, 1999
DECISION CRITERIA CONSOLIDATION:
A THEORETICAL FOUNDATION OF PARETO PRINCIPLE TO
MICHAEL PORTER’S COMPETITIVE FORCES
Abstract
Also known as the 80/20 rule, the Pareto Principle separates a class of significant few
from trivial many.
With this classification, Pareto Principle has managerial and strategic
implications in many disciplines.
Recent mathematical modeling of the Pareto Principle
identifies several important factors that cause such separation; they are the probability of new
entry (can be viewed as “entry barrier”) and the other is the recency of usage. However, the
probability of new entry determines the upperbound of the usage concentration, therefore it is
deemed to be the most important factor. Since Porter’s five competitive forces are all closely
related to the barrier of entry, based on these factors, it is apparent that the theoretical model of
Pareto Principle can be applied to be the theoretical foundation for Porter’s Five Competitive
Forces. Furthermore, we argue that, similar to that of microeconomics, the barrier of entry is the
most important factor that determines the market structure be it monopoly or pure competition.
Thus, the decision criteria in strategic planning can be greatly simplified to its effect on the
barrier of entry. Furthermore, we argue that the recency of usage (i.e., a product not recently in
use may be forgotten by customers thus reduce its future usage), though not emphasized in
Porter’s theory, should also be part of the strategy formation.
1.
Introduction
Business competitive strategy development is vital for the successes of both large
corporations and small businesses. In his well-known book on competitive strategy, Michael
Porter (1980) proposes a five-force model for business competition strategies: (1) bargaining
power of buyers, (2) bargaining power of suppliers, (3) rivalry among existing competitors, (4)
threat of new entrants, and (5) threat of substitute products or services.
---------------------------Insert Figure 1 Here
---------------------------Porter’s proposal is basically a strategy of making one’s product a monopoly in its class,
and making the company’s suppliers’ market a pure competition market. Conceptually, since
monopolies are price makers and pure competitions are price takers (Lipsey and Courant 1996),
a firm has better control over its revenues and expenses and can greatly increase the profit
margin (Carlton and Perloff 1994).
The four market structures of monopoly, oligopoly,
monopolistic competition, and pure competition are classified according to the number of
participant and the level of concentration in terms of business transactions; and their formation
has long been attributed to the level of barrier of entry. For example, monopoly is characterized
by having a high barrier of entry whereas pure competition requires “perfect information” and
open access to the market for all (Lipsey and Courant 1996). Thus, Porter’s competitive forces
can be probed further through studying the formation of market structures, which, in turn, rests
on the study of market concentrations.
The simplest way to describe a concentration pattern is to assign some quantitative
measurement to it. Vilfredo Pareto (1909) first reports that in Italy about 80% of wealth is in the
hands of about 20% of the population. Since then, many other sociological, economic, political,
and natural phenomena have been observed to follow the similar pattern. J. M. Juran claims
Pareto Principle page 2
credit for coining the term Pareto Principle (Sanders 1987), which is better known as the 80/20
Rule. The Pareto Principle has wide applications (see Table 1), but its importance lies in its
separation of the significant few from trivial many (Chen and Chong 1998, Chen et al. 1994,
1993).
For example, in the ABC inventory control, we concentrate our efforts on those
significant 10 to 20 percent of high-value items that typically account for 70-80 percent of the
total dollar value (Monks 1977).
---------------------------Insert Table 1 Here
---------------------------When the Pareto Principle is used to describe the firm-size distributions, we find that
while there are only a few very large firms, numerous small firms exist (80% of business assets
are in the top 20% of firms). Common sense tells us that when customers prefer a firm’s
products, this firm is more likely to grow, thus it implies that the firm size is determined by the
way customers allocate their resources among products, which in turn translates to business
assets. Therefore, the customers’ product usage pattern (we call it usage concentration in this
paper) determines the concentration of assets among firms, and consequently the firm-size
distribution and the market structure. Ijiri and Simon’s 1977 book, Skew Distribution and the
Sizes of Business Firms, collected many studies of business concentrations, and included in this
book is a theory that models how business concentrations are formed. Since Herbert Simon is
the center of this collective effort of many, in this paper we will refer to this theory as the
Simon’s Model. Simon’s original model has two assumptions: (1) there is a constant probability
of new entrants into the system, and (2) the more an item is used, the more likely it will be used
again.
Based on these two assumptions, Simon and Von Wormer (1963) also provide an
algorithm that successfully simulates this usage pattern.
Pareto Principle page 3
The purpose of this paper is to provide a theoretical foundation, in terms of Pareto
Principle, for Porter’s five competitive forces. Section 2 is a brief overview of the Pareto
Principle (or the 80/20 rule).
Section 3 describes the mathematical model for the Pareto
Principle by Chen et al. (1994, 1993), indicating that the probability of new entry is the primary
factor in determining the level of concentration. Section 4 discusses the assumptions used in
Simon’s two models on usage concentration, and the interpretation of the parameters in usage
analysis to make the connection between usage concentration and different market structures.
Section 5 shows how these findings can be used to simplify the decision criteria in strategic
planning and thus supports the validity of Porter’s approach that the main goal is to control the
barrier of new entrants – or the probability of new entry in Simon’s terms. Section 6 goes
beyond Porter’s five forces and describes the other significant factor of usage concentration in
Simon’s later model, i.e., the decay rate, and its implication to strategic planning. Finally,
Section 7 is the conclusion.
2.
Pareto Principle and Market Concentration
Recently a mathematical model (Chen et al. 1994, 1993) has been developed to describe
the behavior of the Pareto Principle. This model uses the slope and distance to fully describe the
usage concentration curve (we call it the Pareto Curve in this paper) demonstrated in the Pareto
Principle. It shows that the upper-bound of the usage concentration is determined by the slope
formed by the group of the least-used items (the trivial many). Furthermore, this slope is the
inverse of the usage per item – which can be the proxy for the probability of a new entrant to the
selection process. A simulation model based on Simon and Von Wormer’s algorithm has been
used to verify this mathematical model.
Pareto Principle page 4
As described in Section 1, the Pareto Principle has very wide applications across many
disciplines. We will follow that traditional study of the Pareto Principle and use Kendall’s
(1960) study on 1763 papers published on operations research (Table 2) to describe the Pareto
Curve.
---------------------------Insert Table 2 Here
---------------------------If we tabulate the number of authors who have published n papers and arrange this list in
ascending order of n, we would find that n does not run consecutively at places, especially when
n is large. We would also find that there are m different clusters of authors who publish the same
number of papers, and m  max{n}. To take into account the scatter of the larger values of n,
Chen and Leimkuhler (1987) introduced an index i = 1,2,...,m, for the m successive observations
of n and let ni denote the i-th nonzero value of n where ni < ni+1. Using this Index Approach, We
define
f(ni) = the number of authors with ni papers,
i1f (ni ) = total number of authors,
m
R =  n i f ( n i ) = total number of papers,
i1
T=
m
 = R/T = the number of published paper per author.
Note m is the maximum index, indicating that f(nm) is the number of authors who are the most
productive; and nm is the productivity of this cluster’s authors. Similar to Kendall’s data,
typically there is only one author in this cluster. Thus f(nm) is usually 1. For each index level,
let xi be the fraction of total authors and i the fraction of total papers, then
m
and

xi =
1
f (n k )
T k  m i 1
i =
1
n k f (n k ) .
R k  m i 1
(1)
m

(2)
Pareto Principle page 5
Plotting xi on the x-axis and i on the y-axis, and we obtain a Pareto Curve. Figure 2 shows the
Pareto Curve based on Kendall’s data. In more general terms, we can substitute the words
“item” or “company” for “author” and the words “usage” or “business” for “paper,” and the
curve shows the usage or market concentration.
---------------------------Insert Figure 2 Here
---------------------------Using notations above, if we define the curve formed by (xi,i), i = 1,2,...,m, to be Pareto
Curve, then the Pareto Principle (the 80/20 rule) states that there exists some i that (xi,i) = (0.20,
0.80). Table 2 shows that the top 22.7% of authors (84) published 77.4% of papers (1365). It is
clear that this Pareto Curve is more like 77/23 than 80/20. Using another example, Table 3 is the
transaction data collected from a state university library. It shows that there are 103 different
groups of usage (m = 103) ranging from 31,113 books being checked out once to 1 book being
checked out 619 times. The total number of books checked out was T = 61,606, and total
number of transactions was R = 154,703. Thus, the average number of times a book was
checked out was  = 2.511. Figure 3 is the Pareto Curve, plotting (xi,i), i = 1,2,...,m. Note that
the curve has a concentration of approximately 68/32, and not 80/20.
-----------------------------------------Insert Table 3 and Figure 3 Here
-----------------------------------------3.
Theoretical Foundation of the Pareto Principle
By arranging equations (1) and (2) stated in Section 2, Chen et al. obtained

i = xi i ,
(3)

where i is the usage per item at that particular point while  is the overall average.
Pareto Principle page 6
Chen et al. defined si and di to be the slope and distance, respectively, of the line segment
between (xi-1, i-1) and (xi, i), i = 1,2,...,m, and (x0,0) = (0,0), and they derived
n mi 1

1
( m 2  n 2mi 1 f 2 ( n mi 1 ) .
di =
R
si =
and
(4)
For now we will only discuss this slope si. First, let us look at the starting point, i.e.,
from the origin. Note that since the data are cumulated from the most productive ones first, this
segment contains the value of nm and f(nm) = 1 (the single most productive author). We
designate this slope s1. Since different data sets would have different m, there is no obvious
application at this point. The second observation is more important. The “terminal” segment
that leads to (100%, 100%) contains the data of “trivial many” (many authors with 1 paper each,
or n1 = 1), and we will designate its slope sm. Since at this point n1 has a unique value of 1, sm =
1/, or the inverse of the usage per item. For verification, in Kendall’s data sm = (1-0.885)/(10.451) = 0.21, which is the same as 1/ (1/4.77 = 0.21). In the Library example this slope is (10.79889)/(1-0.49497) = 0.398, which is the same as 1/ (1/2.511 = 0.398).
This inverse of average T/R may be viewed as the constant rate of success in a binomial
distribution when the population is large. In terms of usage, it is the probability that the next
items will be an item that has not been used before. In terms of market structure, it is the
probability that the next business transaction will involve a new company.
When this
“probability of new entry” is viewed from the other side, it is called “the entry barrier” – the
center of discussion in market structures. Geometrically, if this segment is extended to intersect
the y-axis, the y-intercept would indicate the greatest concentration available in this distribution,
Pareto Principle page 7
implying that this barrier of entry dictates the market concentration. The next section will tie this
probability of new entry to Simon’s model to examine the plausibility of the theory.
4.
Simon’s Models: the Entry Barrier and the Rate of Decay
The Basic Model and the Probability of New Entry
The work by Chen et al. only describes the properties of the Pareto curve; and we will
address the reason behind the formation of this usage concentration through Simon’s model. As
a result of studying firm sizes, Simon (1955) proposed that this selection process, be it for
business transaction or a word to write, is a stochastic process that can be separated into two
parts. He assumes that (1) there is a constant probability that the k-th selection will be a new
item (an item that has not been selected in the first k-1 selections), and (2) the probability that the
k-th selection that has been selected i times is proportional to its previous usage. Subsequently,
Simon and Von Wormer (1963) developed an algorithm that can generate distributions to
simulate the Pareto Curves.
Recall that the terminal slope sm equals to the inverse of the average usage. Using the
expected value of a binomial distribution, we can see that this slope is equal to the probability of
new entry indicated in Simon’s assumption 1. Chen et al. (1994) generated a series of Pareto
curves varying only the probability of new entry, ranging from 0.01 to 0.99. Figure 4 summaries
the results.
---------------------------Insert Figure 4 Here
---------------------------Figure 4 shows that the probability of new entry has inverse relationship with the level of
usage concentration. When the probability is 0.01 (very low), the usage concentration is very
Pareto Principle page 8
high (95% of usage are concentrated in about 1% of items), and when the probability of new
entry is high, the usage concentration disappears (50% of usage involve 50% of all items). We
may extend this observation to the market concentration. When the barrier of entry is high (low
probability of new entries) a highly concentrated market structure is formed (nearly monopoly),
whereas the lower entry barrier (high probability of new entry) spreads the usage more evenly
among participants – that is, forming a pure competition market.
Studies by Chen et al. (1994, 1993) show that the probability of new entry is the primary
factor that determines the usage concentration, just as economists have claimed all along. The
amount of trivial many determines how competitive a market may be, thus determines whether a
market is a monopoly or pure competition.
While this entry barrier has been cited as a
characteristic of the market structure in microeconomics, Simon’s model provides a model to
explain how the structure is formed.
The Autoregressive Model and the Decay Rate
The probability of usage of “old” items is assumed to be proportional to its previous
usage in Simon’s basic model. However, the rarely used items have a tendency of being
“forgotten.” In other words, the probability of the usage will decrease with time if a book has
not been checked out, or an author has not published lately. Popular library books can be
neglected for years to come once out of fashion. Ijiri and Simon (1977) refined the second
assumption of the Simon’s model to take this phenomenon into account. Thus, the probability of
an already-accessed information being used again decreases geometrically at a certain “decay
rate.”
While the terminal slope sm helps us assess the probability of new entry and draws out the
upperbound for concentration, the leading slope s1 also contributes to determine the level of
Pareto Principle page 9
concentration within bound. Base on Simon’s algorithm, Chen et al. (1994, 1993) find that s1 is
determined by the level of Simon’s decay rate. When the probability of new entry is held
constant, say at 0.20, varying this decay rate generate Pareto Curves like those in Figure 5. Note
that terminal slopes of all these curves are the same, though the length of segments may vary.
On the other hand, the initial slopes are different, and the curve with no decay has the highest
concentration.
It is logical that a higher decay rate reduces concentration because the
environment then allows the previously low-usage items not to be overwhelmed by items that
have their 15-minutes fame. On the other hand, unused items may lose their potential of being
used again rapidly, no matter how historically active it has been before. When there is no decay
at all, the results of autoregressive model are the same as the basic model.
Chen et al. further determine that while the changing decay rate affects the shape of the
usage concentration (thus changes the Pareto Curves), it does not affect the probability of new
entry. Therefore, these two rates can be assessed independently of each other. Unfortunately,
unlike the probability of new entry, there has not been an easy method to assess this decay rate.
---------------------------Insert Figure 5 Here
----------------------------
5.
The Role of the Entry Barrier in Porter’s Five Competitive Forces
Porter (1980) suggests that “the goal of competitive strategy for a business unit in an
industry is to find a position in the industry where the company can best defend itself against [the
five] competitive forces or can influence them in its favor.” Furthermore, “the crucial question in
determining profitability is whether firms can capture the value they create for buyers, or whether
Pareto Principle page 10
this value is competed away to others” (Porter 1985). The following is a brief description of these
five forces and their connections with the probability of new entry.

“Bargaining Power of Buyers” refers to the ability for customers to force down prices, reduce
product delivery cycle time, demand higher quality, and require better service. Porter identifies
seven factors, which suggest that whenever many alternatives available, customers have high
bargaining power. Thus, lower barrier of entry for new products (more alternatives, or high
probability of new entry) increases Bargaining Power of Buyers. Conversely, higher entry
barrier – which may result in higher concentration of market – leads to lower Bargaining Power
of Buyers.

“Bargaining Power of Suppliers” refers to the ability for suppliers to increase input material
prices, increase product delivery cycle time, and reduce the quality of goods supplied without
losing customers. Whenever alternative suppliers are available in an area, competition lowers
supplier power.
Thus, lower entry barrier for new suppliers (more alternatives, or high
probability of new entry) leads to lower Bargaining Power of Suppliers.

“Rivalry among Existing Competitors” is the degree to which companies respond to competitive
moves of other companies in the same industry, e.g., price cutting, new product introduction,
and advertising slugfests. This may be viewed as an extension of the Bargaining Power of
Suppliers. Though the focus here is the “degree” of the fierceness, with more suppliers,
competition tends to increase the fierceness of rivalry. We will discuss this force more in the
next section.

“Threat of New Entrants” is the number and quality of potential competitors that may enter the
industry. It is obvious that with higher barrier of entry, the number of new entry would reduce
and thus affect the bargaining power of customers and suppliers.
Pareto Principle page 11

“Threat of Substitute Products” refers to other products that can be used to satisfy the same
need. Since substitute products have the same effect as direct competition in taking business
away (therefore reduce the usage), the principle of entry barrier applies equally. In terms of
usage of a company’s product, the threat of substitute products should be treated the same as the
threat of new entrants.
Therefore, Michael Porter’s five forces can be summarized to a strategy that:

Reduces bargaining power of suppliers through finding alternative suppliers or substitute
goods, and

Reduces bargaining power of buyers through differentiating product to avoid direct
competition, or to build customer loyalty through having a product that is superior to other
competitors.
Following our analysis earlier, such strategy in effect is to (1) push supplier’s market
towards pure competition by creating more direct competition from other suppliers or indirect
competition from substitute goods, and (2) make one’s product a monopoly in its class (no
competition). Since our analysis of Pareto Principle in Section 4 shows theoretically that the
barrier of entry indeed is the primary factor that determines the market concentration, we may
narrow the decision criteria to just one: the effect of decision on the probability of new entry.
Strategies for controlling Entry Barrier and the benefit of e-commerce
The entry barrier can be the results of patents, startup costs, or availability of expertise.
The analysis of the Pareto Principle shows that this probability of new entry can be obtained by
dividing total item (company) by total usage (business), i.e., T/R. The higher barrier of entry
(i.e., low probability of new entry) may have either a low T or high R. To make one’s product a
monopoly, is to decrease the number of competitors either through patent or specialized services.
Pareto Principle page 12
On the other hand, a company can also flood the market with cheap or even free merchandize to
increase R. If competitors can not keep up, then the probability of new entry is effectively
lowered.
Though enjoy the de facto “monopoly,” the problem with a niche market is that the pie is
much smaller. Thanks to the internet, however, the niche market may broaden the customer base
and therefore obtain enough customers to reach the economies of scale. For larger companies,
the internet also enhances their ability to spread their product more rapidly to reduce
competitions.
In terms of making the supplier’s market a pure competition, the internet also increases
the ability for buyers to broaden the supplier base to increase competition among them. For
example, a customer may use several of internet sites (e.g., computershopper) to compare
computer equipment prices quickly. The decision is easy, especially when the product in mind is
a name brand and the price is the only differentiating factor. We can anticipate a rapid growth of
some buyer-seller matching program on the internet to help buyers to increase supplier base and
sellers to increase customer base.
6.
The Role of the Decay Rate in Porter’s Five Competitive Forces
In addition to Porter’s five forces that determine the terminal slope and therefore the
maximum usage concentration, Section 4 shows that within this constraint, the final usage
concentration is also determined by the “decay rate.”
One example in business for this rate of decay is customer loyalty to the product, or their
awareness of its existence. While in some industries customer loyalty is more stable, the high
tech industry has seen many rapid rise and fall of its “industry leaders.” Using the word
Pareto Principle page 13
processor market as an example, before Microsoft Word gained its dominance, the leaders have
moved from WordStar to WordPerfect, then to Word within a few years, thus the well-known
phrase “only the paranoid survives.” It seemed that some products simply disappeared once
were out of the limelight – all but forgotten like Mosaic or CompuServe.
It is important to recognize that while the probability of new entry is the corner stone of
Simon’s first assumption, decay rate plays an important role in the second assumption. In other
words, the proper interpretation requires the understanding that when the decay rate is
considered, we have already determined that the item to be used is not a new item. Therefore the
selection is limited to items that have been used before. Two of the Porter’s Five Forces describe
this property: “Rivalry among Existing Competitors” and “Threat of Substitute Products.” If any
of these forces is high, it would reduce the usage concentration, within the limit set up by the
probability of new entry, in the industry. In an industry where the rate of decay is high, the
smaller firms do have the opportunity to carve out a niche or wrestle a new technology to market
without being completely ignored. They may use their new product or services to temporarily
become a monopoly, and their product or services may serve as substitute products and take the
market share away from established leaders quickly.
Thus, it is necessary for the firm to continuously improve and market its products and
services. However, the urgency depends on the competition within the industry which may
affect the decay rate. It is important to note that the decay rate affect more on the share of the
pie rather than changing the pie size.
7.
Conclusion
Pareto Principle page 14
In this paper we expanded the findings of Chen et al. in the usage concentration modeling
to include the market concentration analysis, showing that indeed the entry barrier affects the
market structure. Based on this usage concentration model (the Pareto Principle), we use barrier
of entry as the connecting point to provide the theoretical foundation for the Porter’s Five
Competitive Forces. By recognizing the most important parameters, we can reduce the strategic
decisions to that of (1) controlling the probability of new entry and (2) controlling the decay rate.
While the former may determine the size of the pie, the latter determines the share of the pie.
We also provide several cases in e-commerce to illustrate this application of the Pareto Principle.
Since these two factors effectively determine the market structure, this theoretical
foundation will allow us to develop useful strategies that take unexpected forms. For example,
for a company to fend off rampant criticisms on the internet, a resourceful company may put out
many news releases to spin the situation. The benefit then could be many. While critics are busy
responding to these news releases, the consensus (i.e., the concentration of certain opinions) is
diluted. This can be seen easily in that the probability of new entry T/R is less than (T+c)/(R+c).
As the probability of entry increases, the usage concentration is lowered. Meanwhile, the name
of the company remains in the limelight to reduce the decay rate of customer royalty.
Furthermore, this ability to influence user’s mindshare can be a powerful barrier of entry for
competitors. Therefore, a strategy that creates a spin machine to influence the media or forms
alliance with news media becomes the stone that kills a flock of birds.
Pareto Principle page 15
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Pareto Principle page 16
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Pareto Principle page 17
Table 1: Phenomena that Exhibit Pareto Principle
Applications
Income Distribution
Marketing Decisions
Population Distribution
Firm Size Distribution
Library Resource Management
Academic Productivity
Software Menu Design
Database Management
Inventory Control
80% of the...
income/wealth
business
population
assets
transactions
paper published
usage
accesses
value
in 20% of the...
people
customer
cities
firms
holdings
authors
features used
data accessed
inventory
Pareto Principle page 18
Table 2: Kendall’s Data
--------------------------------------------------------------------------------------------------------------------i
ni
f(ni)
nif(ni) cum. nif(ni)
i
cum. f(ni) xi
(index*) (# paper) (# author)
--------------------------------------------------------------------------------------------------------------------26
242
1
242
242
0.137
1
0.003
25
114
1
114
356
0.202
2
0.005
24
102
1
102
458
0.260
3
0.008
23
95
1
95
553
0.314
4
0.011
22
58
1
58
611
0.347
5
0.014
21
49
1
49
660
0.374
6
0.016
20
34
1
34
694
0.394
7
0.019
19
22
2
44
738
0.419
9
0.024
18
21
2
42
780
0.442
11
0.030
17
20
2
40
820
0.465
13
0.035
16
18
1
18
838
0.475
14
0.038
15
16
4
64
902
0.512
18
0.049
14
15
2
30
932
0.529
20
0.054
13
14
1
14
946
0.537
21
0.057
12
12
2
24
970
0.550
23
0.062
11
11
5
55
1025
0.581
28
0.076
10
10
3
30
1055
0.598
31
0.084
9
9
4
36
1091
0.619
35
0.095
8
8
8
64
1155
0.655
43
0.116
7
7
8
56
1211
0.687
51
0.138
6
6
6
36
1247
0.707
57
0.154
5
5
10
50
1297
0.736
67
0.181
4
4
17
68
1365
0.774
84
0.227
3
3
29
87
1452
0.824
113
0.305
2
2
54
108
1560
0.885
167
0.451
1
1
203
203
1763
1.000
370
1.000
--------------------------------------------------------------------------------------------------------------------total
370
1763
 = 4.765
* To better show the Pareto Curve, the clusters are shown with the most productive authors at the
top of the list. Thus the index reflects the reversed order.
Pareto Principle page 19
Table 3: The Library Holding Usage Pattern
i
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
ni
f(ni)
i
ni
f(ni)
i
ni
f(ni)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
38
39
40
41
31113
12913
6829
3769
2240
1431
896
665
441
308
207
151
122
78
62
51
30
30
16
14
14
14
14
12
17
4
7
8
8
9
3
1
4
6
2
1
3
3
1
7
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
42
43
44
45
46
47
48
49
51
52
53
56
57
59
60
62
63
64
65
66
69
70
71
72
76
77
78
79
80
84
85
86
88
90
91
94
97
99
101
103
2
3
3
3
2
1
2
3
4
3
2
2
3
4
1
2
2
2
1
1
2
1
3
1
1
1
1
1
1
3
1
1
1
1
1
1
3
1
1
1
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
106
108
113
114
115
117
118
120
123
126
131
146
157
161
165
188
224
236
305
311
590
619
2
2
2
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
R = 154,703
T = 61,606
 = 2.5112
Pareto Principle page 20
Figure 1: Porter’s Five Competitive Forces
New
Market
Entrants
Substitute
Products
and Services
The
Firm
Suppliers
Traditional
Competitors
Customers
Pareto Principle page 21
Figure 2: The Pareto Curve for Kendall’s Data
100%
90%
80%
70%
% transactions
60%
50%
40%
30%
20%
10%
0%
0%
10%
20%
30%
40%
50%
% of items
60%
70%
80%
90%
100%
Pareto Principle page 22
Figure 3: The Pareto Curve for the Library Data
% of Total Transactions
100%
80%
60%
40%
20%
0%
0%
20%
40%
60%
% of Total Holdings
80%
100%
Pareto Principle page 23
Figure 4: Pareto Curves with Constant Probability of Entry
from top to down: 0.01, 0.10, 0.18, 0.20, 0.50, 0.70, and 0.99
Pareto Principle page 24
Figure 5: Pareto Curves with Constant Probability of Entry at 0.20
from top to down: low decay rate to high decay rate.
Pareto Principle page 25
Figure 4.1: Results for 80/20 Formulation, Constant 
Figure 5: Pareto Curves with Constant Probability of Entry at 0.20
from top to down: low decay rate to high decay rate.