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This is to certify that the
dissertation entitled

REAN INVESTIGATION OF THE INTERACTION OF
ADVERTISING, PRICING AND QUALITY ON SALES
RESPONSE

presented by
ERIC CHARLES JACKSON

has been accepted towards fulfillment
of the requirements for the

Ph.D degree in Department of Marketing and
Supply Chain Management

 

 

 

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6/2/ 0 4

Date

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6/01 cJCIRC/DateDuopes-sz

AN INVESTIGATION OF THE INTERACTION
OF ADVERTISING, PRICING AND QUALITY
ON SALES RESPONSE

By

Eric Charles Jackson

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy

Department of Marketing and Supply Chain Management

2004

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ABSTRACT

AN INVESTIGATION OF THE INTERACTION OF ADVERTISING, PRICING AND
QUALITY ON SALES RESPONSE

By

Eric Charles Jackson

Much information about product quality diffuses into the market place via consumer
to consumer communication and other mechanisms that are not directly connection to
predetermined corporate promotional policies. This fact raises questions about how the
information that has diffused into the market interacts with active corporate policies
attempting to communicate information to consumers. It also creates questions about how a
company might use the quality aspects of its products to take advantage of this diffusion
process to maximize its profitability. The NGM model was developed by Narasimhan, Ghosh
and Mendez (1993) to examine this question by considering how improving a product’s quality
profile might impact the total profits a company might realize over the life of a durable good.
The NGM model did this by using the product price as an optimal control variable and using
quality as a factor impacting purchasing as quality weighted goods diffuse into the marketplace.
This dissertation will extend the NGM model in three ways.

First, the original NGM model has no explicit competition for market share. In the
NGM model competition is implicit. The current work explicitly incorporates a second
product as competition to the first product in the marketplace. Second, the current work

disaggregates quality into two factors and examines how quality affects sales in two ways. The

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original NGM model examines quality as a single factor. In this work quality is considered
both in terms of improvements generated by a continuous quality improvement mechanism
and quality improvements made via a discontinuous mechanism, e.g. designed product
improvements such as new features. The third extension to the NGM model is to explicitly
incorporate the effect an advertising policy has on sales as well the impact that policy has on
information diffusion.

Practitioners are expected to be able to use the results from this dissertation to assess
policy decisions in two ways. First, they can compare and contrast their quality strategy with
existing competition in their market segment. They can also consider how a new entrant into
their market might impact their existing quality strategy. Second, they can consider different
levels of advertising expenditures within the context of quality information diffusion. This
information should suggest the best time periods to implement planned model changes and a

potentially more efficient use of advertising expenditures.

Copyright by
Eric Charles Jackson

2004

DEDICATION

To my parents Rita and Charles Jackson who made the daydream a possibility.

To my wife, Alison, and my children Danielle Ann and Christopher Louis, who made the

possibility an attempt.

To my committee who made the attempt a reality.

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ACKNOWLEDGMENTS

As always in a work of this nature there are too many people making significant contributions
to acknowledge each individually. All of the contributions from all people are greatly
appreciated and the work could not have been completed nor even attempted without their
help. However, beyond this there are some specific contributions that need to be highlighted.
Special thanks go to: Ram Narasimhan who showed patience well above and beyond the call
of duty, Ken Boyer whose faith and support were important beyond measure, Srinivas Talluri

whose sense of humor kept despair at bay and Anthony Ross whose enthusiasm kept

everything in perspective.

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TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table of Contents vii
List of tables ix
List of figures x
CHAPTER 1
Introduction 1
Product — Price Interactions 3
Product - Promotion Interaction 6
Competition 9
Research Motivation 9
Chapter 2
literature Review 15
Game Theory / Optimal Control Models 15
Advertising Literature 16
Advertising Literature Including Competition 20
Quality 21
Quality including Competition 23
Disaggregated Quality 24
Potential Contributions to the Literature 25
Chapter 3
Model Development 31
The NGM Model 31
Advertising 33
Competitive Advertising 35
Competitive Market Potential 38
Costs 41
Quality 42
The Complete Model 43
Experimental Design 48
Scenarios 1.0-1.4 50
Scenarios 2.0~2.8 54
Scenarios 3-3.4 58
Chapter 4
Simulation Results 61
Scenarios 61
Scenarios 1.0 to 1.3 61
Scenario 1.0 62

 

 

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Scenario 1.1 66
Scenario 1.2 68
Scenario 1.3 69
Scenario 1.4 69
Scenarios 2.0-2.8 72
Scenario 2.0 72
Scenarios 2.1~ 7 7 77
Scenarios 2.3-2.8 - . 80
Scenarios 3.0-3.4 85
Scenario 3.0 86
Scenarios 3.1 -3.2 90
Scenario 3.3 94
Scenario 3.4 95
Chapter 5

Conclusions and Contributions 97
Contributions 97
Quality influences on dynamic pricing in a duopoly 97
Advertising and Quality influences on dynamic pricing in a duopoly 100
Advertising and Discontinuous Quality influences in a duopoly 104
Strategic Implications 108
Concluding Remarks 114

Appendices .
Appendix 1 1 15
Appendix 2 131
Appendix 3 167
Bibliography 1 87

 

 

 

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LIST OF TABLES

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Number Page
Table 1- Scenario Development 13
Table 2— Literature Summary 27
Table 3— Scenarios 1 .0 to 1.4 52
Table 4— Scenarios 2 .0 to 2.8 55
Table 5— Scenarios 3 .0 to 3.4 59
Table 6— Sales increase due to Advertising 68
Table 7-— Relative profits Run 1-8 Scenario 2.0 76
Table 8— Relative profits Scenados 2.1 and 2.2 78
Table 9— Profitability differential from advertising 82
Table 10 Profitability differential from advertising 7 .. 83
Table 11 - Max and Min quality profit increases 84
Table 12- Advertising assistance. 84
Table 13— Profits Runs 1-8 Scenario 3 88
Table 14—Profits Continuous Improvement and Discontinuous Improvement ......................... 88
Table 15 -— Profit Difference from Advertising ..... 92
Table 16 — Difference Cont. Case vs. Discontinuous 93
Table 17 — Profit Advantage with 2 Discontinuous q Improvements 95
Table 18 — Advantage from Advertising Scenado 3.4 96

 

LIST OF FIGURES

Number .
Figure 1- Quality / Price Interaction

Figure 2 — Quality/ Promotion Interactions

Page

 

Figure 3 - VidalsWolfe Sales Response

17

 

33

 

Figure 4 Typical NGM Price Trajectories

Figure 6 —Run 1 Scenario 1.0

62

 

Figure 7—Run2 Scenario 1.0

63

 

63

 

Figure 8 -Run 3 Scenario 1.0

Figure 9 - Run 3 Scenario 1.0

64

 

 

Figure 10-Sales Run #1

Figure 11 — Quality Profiles Scenario 1.4

66

70

 

Figure 12 — Quality Trajectories Runs 1-8

73

 

73

 

Figure 13— Sales Competitor 1, e207

Figure 14 - Sales Competitor 2, e=O.7

74

 

Figure 15 - Sales Competitor 1, e=1.3

74

 

75

 

Figure 16 - Sales Competitor 2, e=1.3

Figure 17 — Quality Competitors 1 and 2

79

 

Figure 18 - Discontinuous Quality

86

 

89

 

Figure 19 — Sales Discontinuous Quality

Figure 20— Sales Continuous Quality

90

 

Figure 21 - Profit Advantage when Price elasticity is higher

98

 

 

Figure ‘

 

 

99

 

Figure 22 — Profit Advantage Inelastic Demand

Figure 23 — Advertising Impact Supporting Quality (Elastic Demand)

 

 

Figure 24 — Advertising Impact Supporting Quality Inelastic Demand

 

Figure 25 — Counter Advertising Elastic Demand

Figure 26 — Counter Advertising Inelastic Demand

 

 

Figure 27 -— Discontinuous Quality and Advertising Elastic Demand

Figure 28 — Advertising to Counter Discontinuous Quality Elastic Demand

 

Figure 29 - Advertising to Counter Discontinuous Quality Inelastic Demand

 

 

Figure 30 - Discontinuous Quality and Advertising Inelastic Demand

Figure 31 — Typical sales for dissertation model

 

Figure 32 - Typical NGM sales distribution

 

 

Figure 33 — Typical Erickson Sales Response over Time to Advertising

Figure 34 —- Price Trajectory from this Work

 

Figure 35 -— Typical NGM Price Trajectory

 

 

Figure 36 - Run 5 Scenario 1.0

Figure 37 - Run 6 Scenario 1.0

 

 

Figure 38— Run 7 Scenario 1.0

Figure 39 — Run 8 Scenario 1.0

 

Figure 40 — Run 9 Scenario 1.1

 

 

Figure 41 — Run 10 Scenario 1.1

Figure 42- Run 11 Scenario 1.1

 

Figure 43 — Run 12 Scenario 1.1

 

 

Figure 44 — Run 17 Scenario 1.2

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Figure 45— Run 18 Scenario 1.2

 

 

Figure46 -Run 19 Scenario 1 7

Figure 47 - Run 20. Scenario 1 7

 

Figure 48 - Run 21 Scenario 1 7

 

 

Figure 49 - Run 22 Scenario 1 7

Figure 50 - Run 23 Scenario 1 7

 

Figure 51 - Run 24 Scenario 1 7

 

Figure 52 — Run 25 Scenado 1.3

Figure 53 - Run 26 Scenario 1.3

 

 

 

Figure 54- Run 27 Scenario 1.3

Figure 55— Run 28 Scenario 1.3

 

Figure 56- Run 29 Scenario 1.3

 

Figure 57- Run 30 Scenario 1.3

Figure 58- Run 31 Scenario 1.3

 

 

Figure 59- Run 32 Scenario 1.3
Figure 60 —— Run 33 Scenario 1.4

Figure 61— Run 34 Scenario 1.4

 

 

 

Figure 62— Run 35 Scenario 1.4

Figure 63— Run 36 Scenario 1.4

 

Figure 64— Run 37 Scenario 1.4

 

 

Figure 65— Run 38 Scenario 1.4

Figure 66— Run 40 Scenario 1.4

 

Figure 67-— Run 40 Scenario 1.4

 

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Figure 68 -— Run 1 Scenario 2.0

 

 

Figure 69- Run 2 Scenario 2.0

Figure 70— Run 3 Scenario 2.0

 

Figure 71— Run 4 Scenario 2.0

 

 

Figure 72- Run 5 Scenario 2.0

Figure 73— Run 6 Scenario 2.0

 

Figure 74— Run 7 Scenario 2.0

 

 

Figure 75- Run 8 Scenario 2.0

Figure 76 - Run 9 Scenario 2.1

 

Figure 77- Run 10 Scenario 2.1

 

Figure 78 — Run 11 Scenario 2.1
Figure 79 — Run 12 Scenario 2.1

Figure 80— Run 13 Scenario 2.1

 

 

 

 

Figure 81— Run14 Scenario 2.1

Figure 82— Run 15 Scenario 2.1

 

Figure 83— Run 16 Scenario 2.1

 

 

Figure84—Run17Scenario77

Figure 85— Run 18 Scenario 2.2

 

Figure 86— Run 19 Scenario 2.2

 

 

Figure 87— Run 20 Scenario 2.2

Figure 88— Run 21 Scenario 2.2

 

Figure 89- Run 2 Scenario 2.2

 

 

Figure 90— Run 23 Scenario 2.2

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Figure 91- Run 24 Scenario 2.2

 

 

Figure 92— Run 25 Scenario 2.3

Figure 93— Run 26 Scenario 2.3

 

Figure 94— Run 27 Scenario 2.3

 

 

Figure 95— Run 28 Scenario 2.3

Figure 96— Run 29 Scenario 2.3

 

Figure 97- Run 30 Scenario 2.3

 

 

Figure 98— Run 31 Scenario 2.3

Figure 99— Run 32 Scenario 2.3

 

Figure 100— Run 33 Scenario 2.4
Figure 101— Run 34 Scenario 2.4
Figure 102— Run 35 Scenario 2.4
Figure 103— Run 36 Scenario 2.4
Figure 104— Run 37 Scenario 2.4
Figure 105— Run 38 Scenario 2.4
Figure 106— Run 39 Scenario 2.4
Figure 107- Run 40 Scenario 2.4
Figure 108— Run 41 Scenario 2.5
Figure 109— Run 42 Scenario 2.5
Figure 110— Run 43 Scenario 2.5
Figure 111- Run 44 Scenario 2.5
Figure 112— Run 45 Scenario 2.5

Figure 113— Run 46 Scenario 2.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 114—- Run 47 Scenario 2.5

 

Figure 115 — Run 48 Scenario 2.5
Figure 116 -- Run 49 Scenario 2.6
Figure 117 - Run 50 Scenario 2.6
Figure 118 — Run 51 Scenario 2.6
Figure 119 — Run 52 Scenario 2.6
Figure 120 —- Run 53 Scenafio 2.6
Figure 121 — Run 54 Scenario 2.6

Figure 122— Run 55 Scenario 2.6

 

 

 

 

 

 

 

 

Figure 123 — Run 56 Scenario 2.6
Figure 124 - Run 57 Scenario 2.7
Figure 125 — Run 58 Scenario 2.7
Figure 126 — Run 59 Scenario 2.7
Figure 127 — Run 60 Scenario 2.7
Figure 128 — Run 61 Scenario 2.7
Figure 129 - Run 62 Scenario 2.7
Figure 130 — Run 63 Scenario 2.7
Figure 131 - Run 64 Scenario 2.7
Figure 132 -— Run 65 Scenario 2.8
Figure 133 — Run 66 Scenario 2.8
Figure 134 - Run 67 Scenario 2.8
Figure 135 - Run 68 Scenario 2.8

Figure 136 — Run 69 Scenario 2.8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 137 — Run 70 Scenario 2.8
Figure 138 — Run 71 Scenario 2.8

Figure 139 -— Run 72 Scenario 2.8

 

 

 

 

Figure 140 - Run 1 Scenario 3.0

Figure 141— Run 2 Scenario 3.0

 

Figure 142— Run 3 Scenario 3.0

 

 

Figure 143— Run 4 Scenario 3.0

Figure 144— Run 5 Scenario 3.0

 

Figure 145— Run 6 Scenario 3.0

 

Figure 146— Run 7 Scenario 3.0

 

Figure 147_ Run 8 Scenario 3.0

 

 

Figure 148 —Run 9 Scenario 3.1

Figure 149— Run 10 Scenario 3.1

 

Figure 150— Run 11 Scenario 3.1

 

 

Figure 151- Run 12 Scenario 3.1

Figure 152— Run 13 Scenario 3.1

 

Figure 153— Run 14 Scenario 3.1

 

 

Figure 154—Run 15 Scenario 3.1

Figure 155-— Run 16 Scenario 3.1

 

Figure 156- Run 17 Scenario 3 2

 

Figure 157— Run 18 Scenario 3 7

 

Figure 158— Run 19 Scenario 3 2

 

Figure 159— Run 20 Scenario 3 7

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Figure 160— Run 21 Scenario 3 7

Figure 161— Run 2 Scenario 3 7

 

 

Figure 162— Run 23 Scenario 3 7

Figure 163— Run 24 Scenario 3 7

 

Figure 164 -— Run 25 Scenario 3.3
Figure 165 — Run 26 Scenario 3.3
Figure 166 - Run 27 Scenario 3.3
Figure 167 — Run 28 Scenario 3.3
Figure 168 — Run 29 Scenario 3.3
Figure 169 — Run 30 Scenario 3.3
Figure 170 — Run 31 Scenario 3.3
Figure 171 — Run 32 Scenario 3.3
Figure 172 - Run 33 Scenario 3.4
Figure 173 — Run 34 Scenario 3.4
Figure 174 — Run 35 Scenario 3.4
Figure 175 -— Run 36 Scenario 3.4
Figure 176 - Run 37 Scenario 3.4
Figure 177 — Run 38 Scenario 3.4
Figure 178 - Run 39 Scenario 3.4

Figure 179 — Run 40 Scenario 3.4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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CHAPTER 1
Introduction

Firms and consumers exist as complex adaptive agents in an ever changing and
adapting environment. Finns are continuously modifying their products in the hope that their
products will become more attractive to consumers than their competition’s products. In turn
consumers continuously change their expectations of the performance of products due to
either new product attributes or information gleaned from other information sources. The
result of this bidirectional pressure on products is that functionality that once qualified as an
order winner ceases being an order winner and becomes an order qualifier over time. As a
gross overview this type of complex adaptive system is well established (Axelrod and Cohen
1999). Of greater interest to practitioners than the system is how this pressure on products to
evolve develops. An understanding of this pressure allows firms to modify their policies so
that they may influence the process.

The adaptability of a firm has limitations. David J. Teece (1985) emphasizes this by
noting that the amount or level of a firm’s flexibility is constrained by irreversible investments
that have been made by the firm in the past. Furthermore, a firm’s flexibility is limited by the
number of options available to it in its environment Products that are too great a vafiafion
from the norm accepted by consumers might not be purchased as readily as products offered
by another firm that have been accepted. This limitation of options for an existing resource is
one reason why firms attempt to be selective in their resource selection and why they attempt
to maximize the effectiveness of existing resources after their acquisition.

The acquisition and / or development of unique and rare resources is the basis for the

Resource-Based View (RBV) of the firm (Wemerfelt 1984), (Barney 1991), (\Wernerfelt 1995),

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(Barney 2001). The difficulty in identifying what is a rare and valuable resource before its
acquisition is problematic because of the limited ability of firms to predict the future. The
inability to predict what will be valuable in the future, before the acquisition of a resource has
led to some questioning of the Resource Based View of the firm. (Godfrey and Hill 1995;
Priem and butler 2001). This inability to completely predict what resource will become rare
and valuable in the future emphasizes the need for firms to use policies vis-a—vis price, product
quality and advertising to sway consumers to select its products instead of the competition’s
and hence maximize the firm$ profit stream. Thus the need for firtns to understand the
interactions of their policies and the impact those policies have on consumer purchases
becomes essential. As the policies influence consumer behavior pressure is applied back in
turn to the companies to again adjust their policies.

One simple method firm’s use to gaining an understanding of the pressures acting to
change company policies is active or direct communication with consumers. For example
firms might initiate opinion surveys or they could collect information with respect warranty
repairs. Consumers on their part may contact support units at firms to voice complaints or to
praise products. However, despite the availability of active communication channels passive
communications are more pervasive and exert a great influence both on corporate policies and
products, they are however, far more complicated.

Each factor, pricing, advertising and product quality, influences the other’s ability to
sway consumers in potentially subtle ways. High prices might signal consumers that the
product quality is high relative to the competitions’. Too low a price for a particular level of
product quality might lead to consumers either assuming that the quality level is low or it might
lead consumers to purchase that product in lieu of a product the company has targeted for a

2

market segment requiring a higher level of product quality (Desai 2001). Advertising might
relate the information about product quality but it might be offset by a competitors advertising
or it might lose its effectiveness after consumers become generally aware of the level. The
interactions of the policies might be further complicated by the actions of consumers.

High adoption rates by consumers might be indicative of general enthusiasm for the
product. This enthusiasm might laud to a rapid diffusion of positive information about the
product into the marketplace. This rapid diffusion could signal an extremely effective
advertising campaign or that the pricing policy of the product is such that the company might
not be maximizing their profits. A rapid diffusion of information about the product quality
might also lead to a reduced need for advertising of the product in question. It might justify a
price increase. An understanding of these complex interactions will be of great benefit to
firms in determining the policies that they need to adopt to maximize the profits generated by
a product over its life. This work will examine the interactions of pricing, quality and
advertising in a competitive environment and how changes in pricing, quality and advertising

influence the maximum profits a firm can realize over the life of the product.

Product - Price Interactions

One factor influencing the profitability of a firm is the choice made by that firm
relative to the levels of quality that it incorporates into its products (Jacobson and Aaker 1987;
Ouchi 1982; Phillips et al. 1983). This might be interpreted as the firm’s quality strategy.

Armstrong and Vickers (2001) note that “...the strategy of a firm is to choose the level of

 

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that there exists an optimum level of product quality for a given price to which a quality
strategy should aspire.

The level of quality, like many other factors, may be changed by the firm over time.
The firm may improve the quality it’s offering through two distinct mechanisms. It might
improve quality via continuous quality improvement strategy or it might make significant
discontinuous improvements. While both of these types of quality changes are positive
contfibufions any limitation are imposed due to consumer expectations. Every time a
consumer purchases a product they reevaluate the product and their own expectations. This
evolving expectation sets a new minimum level of quality for a product. This minimum level is
continuously moving up. In other words, today’s order winner is tomorrow’s order qualifier.
Whether a firm relies on continuous quality improvement strategy or on a discontinuous one
the company must decide how to combine their chosen levels of quality with a pricing strategy
so that they can utilize the interactions between price and quality to maximize the profits they
realize over the market life of their product.

Much attention has been paid to the connection between price and quality and the
ability of consumers to make quality judgments based on product price. Scitovsky (1945) noted
that judging a products’ quality by its price is a rational type of behavior. The idea that
consumers used price as an indicator of quality was investigated by Leavitt (1954). He
concluded that a product with a higher price is perceived in the market to have a higher
intrinsic quality. More recently, a positive and statistically significant relationship between price

and perceived quality was found by Rao and Monroe (1989). In another study performed by

 

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4

Irandoust (1998), a connection between pricing and quality was found by in the Swedish
automobile market. Despite these indicators that consumers may be able to identify quality
from a products price there has been research to indicate that they cannot.

Several researchers (Gerstner 1985; Riesz 1978; Riesz 1979; Sprokes 1977) have all
found that that the ability of price to signal quality to the consumer was weak at best.
Lichtenstein and Burton (1989) performed studies using both durable and non-durable goods
in an effort to address how effectively price signals quality to consumers. They found that
consumers’ ability to identify quality from price is only moderate at best. However, they did
find that consumers were able to more accurately identify a price quality relationship for non-
durable goods than they were for durable goods. This interaction with its feedback loop to

corporate policy may be conceptualized as in Figure 1.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Other factors naturally affect how consumers perceive the quality of a product. Prior
experiences with the product or an earlier version of the product greatly impact a decision to
purchase a product another time. Information from other consumers on their experiences with
the product will sway a purchase decision. Information provided by the company in the form

of advertising or promotion is factored into a purchasing decision.

Product - Promotion Interaction

The principal function of Promotion or advertising is to provide information to
consumers about a company’s product in such a way so as to sway the consumer to purchase
that product. Iilien et a1 (1992) note that “. . .advertising is undertaken to increase company
sales and/ or profits over what they other wise would be. However, it is rarely able to create
sales by itself. Whether the customer buys also depends on the product, price. . ...and other
aspects of the marketing process.” 2 This statement clearly shows that while promotion is a
vital marketing function it is usually interacts with other factors. In other words, the product’s
attributes, its quality, and its pricing are factors that interact with advertising and influence
sales. Therefore they have an impact on a company’s promotion policy.

Advertising as a mechanism for transmitting information about the product’s quality
and the ability of consumers to interpret this information has been the focus of much
attention in the literature.(Milgrom and Roberts 1987; Milgrom and Roberts 1986a; Milgrom
and Roberts 1986b; Nelson 1974; Nelson 1970; Shapiro 1982)Of particular interest is Nelson’s

(Nelson 1974; Nelson 1970) division of goods into two different types those that consumers

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may be able to identify by inspection of the product, what Nelson calls search goods, and
those that the consumer cannot assess before they have acquired the product, experience
goods in Nelson’s terminology. This division may be extended into different attributes found
in the same durable good. The fit and finish of an automobile and the ability of the power train
to provide performance over an extended period of time for example. These facets of quality
may also be considered in terms of their improvement functions. Fit and finish improves with
the volume of units produced. The more ‘units are produced the greater the level of quality for
the attribute because of the learning curve in production. Improvements in experience facets
of a product depend on engineering improvements that are designed into the product over its
lifetime. The first may be seen as a continuous improvement factor and the latter as a
discontinuous improvement requiring effort above and beyond production practice.

In the context of search goods and experience it may be seen that advertising can alter
the rate at which information about the product diffuses into the market place but it cannot
alter the consumers experience with the product It is only possible for consumers to gain
experience information after they have purchased the product. Once consumers have
experienced the quality of the product information about it is diffused into the marketplace via
mechanisms that the firm has no control over. That is, direct consumer to consumer
communication or the memory of the experience retained by the consumer. As a result of
these interactions promotion or advertising may begin to lose some of its effectiveness over
time. In this context it becomes necessary for firms to adjust their advertising and quality

policies in such a way so that the body of information accumulated by consumers continues to

 

3 Lilien, Gary L, Philip Kotlcr, and K. Sridhar Moorthy (1992), Marketing Models. Englewood Cliffs, New Jersey:
Prentice Hall. pp263

7

positively influence sales and therefore profits. This feedback loop may be conceptualized by

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.
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Figure 2 -— Quality / Promotion Interactions

Another factor influencing the amount of impact advertising has is the fact that
advertising has a saturation level and is forgotten after a period of time (little 1979; Vidale and
Wolfe 1957).

These facts influence corporate policy in that the value of advertising has an upper
bound beyond which there is no value in spending more on advertising and that the returns
from any given advertisement, diminishes over time. If the diffusion of product quality into the
market place has a longer influence it may be possible to supplant the value of advertising with

a quality policy over the long term.

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Competition

Another major factor influencing consumers’ purchases is the presence of a
competitor in the market place. Both the pricing policies of a finn’s competition and its own
pricing influence the demand for its product (Desai 2001) and thereby its own profits. This
fact necessitates the addition of competition into any effort to understand the interactions of
promotion, product quality and price on the profitability a firm may realize over the life of a

durable product

Research Motivation

Price, quality levels, and advertising expenditures are three aspects of competition that
firms have direct control over. As such their adjustments as strategic levers are vitally
important to the success of the firm. While valuable information may be collected by studying
how quality and advertising individually influence the optimal price of a product the results
may not be the same when interact This suggests that a greater understanding of the system as
a whole may be developed by considering them together. This dissertation will develop a
dynamic game incorporating these factors together in a competitive environment so that an
understanding of their interactions may be developed.

In particular the interactions of advertising and quality, and how this interaction
influences the optimal price trajectory used to maximize profits for a durable good in a

competitive environment are examined. Quality will be divided into two components a

 

 

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continuous quality improvement component and a discontinuous quality component. The

model developed is expected to be able to address several questions.

Q1) What are the optimal price trajectory and optimal advertising level trajectories
when they are impacted by quality and interact with each other in a duopoly?

In its original form the NGM model (Narasimhan et al. 1993) and the modifications
made to it in 1996 (Narasimhan et al. 1996) did not explicitly incorporate competition or
advertising. As such it is possible to. make extensions to the literature from the model
developed in this dissertation by considering competition explicitly. It is to be expected that
the impact quality has on the optimal price trajectory will be different when competition is
explicitly considered than when it is implicit. By adjusting advertising levels to zero the impact
of the optimal price trajectories in a duopoly may be considered and used as a baseline for
comparison with results when competition is not explicit Advertising impact in conjunction
with quality trajectories has not been considered in the literature and an extension is made
herein.

The impact of advertising may be considered in this model independently of the
competitive environment. Setting the market potential of one of the two competitors equal to
zero removes it from the game and allows for an investigation into how advertising might
impact a firm without the competitor. This will establish a baseline for advertising effects.
Once this baseline is established for comparison 'purposes the market potential for the
competitor which was set to zero is reestablished and allowed to vary as is the first
competitor’s. The next set of simulation runs made in the first set of scenarios examines what
impact advertising has when only one competitor engages in advertising. The advertising level

for one competitor is set to a non-zero level and the level for the second is set to zero. This
10

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allows an examination of the diffusion component alone when compared with advertising and
diffusion. See Scenario 1.2 Table 1. A comparison of two different advertising rates when the
two competitors have equal quality trajectories is .made in Scenario 1.3. See Scenario 1.3 Table
1. The last scenario in the first set is intended to examine what happens when one competitor
has an increasing quality trajectory and low levels of advertising when compared with a stead-
state quality position and high levels of advertising. This is examined in Scenario 1.4. See
Scenario 1.4 Table 1. Each of the investigations is made with two different elasticity values and
with two different product lifetimes. The investigations are also considered using two different

lengths of time during which the quality of the product continues to influences purchasers’

decisions, in particular 0.25 and 0.75 the total life expectancy of the product.

Q2) How do difl'erences in a firm’s quality policy interact with its advertising
expenditures to influence the optimal price trajectory to maximize profit?

A baseline is established for comparison by setting the advertising levels for both
competitors. to zero and both quality trajectories equal to each other. See Scenario 2.0 Table
1. The next two scenario groups set the advertising for the first competitor to two different
levels, 1.7% of revenues and 3.5% of revenues. With the base line established advertising will
be effects will be reintroduced to the model The quality trajectories will be varied so that
different quality strategies may be compared when they are influenced by advertising policies.
It is expected that advertising will provide assistance to firms incorporating quality changes in
terms of their short term sales but that it will not provide a substantial increase in sales once

the quality has begun to diffuse into the market.

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Q3) How do advertising policies interact with discontinuous product quality
characteristics over time? Will one balance the other or does the influence of one
or the other become more important as time progresses?

The third scenario introduces a discontinuous quality change. This type of change is
representative of the introduction of a radical process or model change to a durable product.
One competitor in the model will have a discontinuous change in its quality trajectory. Both
firms will have equal advertising. In the next scenarios advertising for the competitors will
change from one firm to the other to consider the impact advertising has in this environment.
See Scenario 3 Table 1.

Summarizing, the interaction of advertising and quality on the profit generated by a
product line over its life will be investigated in this dissertation by considering the impact of
advertising, varying quality strategies and the combination of the two. The NGM model
examined how a continuous quality improvement policy impacts 2 product’ 3 lifelong
profitability, however the potentially mitigating factor of advertising was not addressed.
Neither did the original NGM model explicitly consider competition. Various advertising
models have examined how sales may be influence by advertising. This has been done in
competitive environments but these investigations have not considered quality trajectories in
their analysis. By combining differing advertising efforts for different quality profiles for two
competing companies it becomes possible to investigate what the interactions advertising and
quality have on the optimal price trajectories over the life of a durable good in a competitive

environment. The consideration of these interactions in this dissertation extends the literature

into heretofore unaddressed areas. A summary of the simulation factors is given in Table 1.

12

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CHAPTER 2

Literature Review

The. literature that supports this dissertation includes information on dynamic games,
advertising models, advertising models that include competition, the impact that product
quality has on sales and literature that examines disaggregated quality. Since this dissertation
uses an optimal control methodology the emphasis in searching for literature information has
been placed on models that use optimal control methodology to investigate how a firm’s
profits might be maximized given environmental conditions and the firm responses to those
conditions. The most salient information to this work has been taken from literature that
shows how interactions between advertising, product quality, competition and product pricing
policy impact the profitability of a firm. General information on the framing of the problem is

also included in the following literature summaries.

Game Theory/ Optimal Control Models

Competition between firms may be viewed as an effort to gain levels of sales by one
firm that maximizes its profitability while other firms competing in the same market are
attempting to maximize their own payoffs. It should be noted here that one firm or the other
~ is not attempting to “beat” the competition in the sense that a victory implies the end of the
competition but rather that they are attempting to maximize their own returns. The continued
existence of the competition is not necessarily relevant to maximized profits. This is consistent
with the class of games identified as Strategic-Form Games by Fudenberg and Tirole (1996).

Super imposed on this competition are limiting factors. The most significant of these is the

15

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lack of perfect information available to the competing firms. This limitation on information
takes two forms, first is the lack of information pertaining to the conduct of consumers and
second is the lack of information relative to the actions of the completion. This lack of
information pertains only to future events. The entire set of activities for both the competition
and consumers leading up to the present point in time is available to all parties. These types of
games are classified by Fudenbers and Tirole (1996), as “multi—stage games with observed
actions.” Time in this classification of strategic games is treated as a series of separate and
discrete units or states. Optimal solutions for this type of game take two forms, an open loop
solution and a closed loop solution. This dissertation will use an open loop form of the

optimal control solution.

Advertising Literature

Models that examine how companies use various promotion or advertising policies to
improve sales response have a long history. Dorfman and Steiner (1954) developed a model to
jointly examine optimal advertising expenditures while jointly optimizing pricing and quality.
Vidale and Wolfe, (1957) developed a model that demonstrated the most efficient advertising
policy a company could use to maximize its sales, and therefore its profits. The 1957 work did
not include competition explicitly. Vidale and Wolfe did not incorporate the quality aspects of
the product as a factor in creating sales. Nor did they consider the possible impact a dynamic
pricing policy might have on sales. A graphical representation of the sales response to
advertising as depicted by the Vidale—Wolfe model is shown in Figure 3. The sales response is
depicted by s(t), the total market potential is depicted by m, the advertising pulse is on until

16

time t and the saturation sales response or the maximum sales that may be generated by

infinite advertising expenditures, is shown as r(x).

 

 

 

r(X)

Sales Response s(t)

 

 

 

 

 

 

 

 

Figure 3 - Vidals-Wolfe Sales Response

Little (1979) summarized the state of the art as of that date in aggregate advertising
models. In his summary, be identified five basic principals that a dynamic advertising model
should incorporate. First, that the sales response should change upward or downward in
response to differing levels of advertising expenditure and that these changes may occur at

different rates. Second, he asserts that the steady-state sales response should be either S-shaped

17

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or concave. Also, those sales levels at zero advertising might not be zero. Iittle’s third
requirement for an advertising model is that it includes the influence of competition in its sales
response. Fourth, advertising effectiveness can change over time and fifth that sales increases
due to adverting falls off or decays over time.

Great attention has been paid to considering the optimal pattern of expenditures for
advertising. In particular two researchers (Lilien et aL 1992; Mahajan and Muller 1986) examine
which advertising policies give the most effective sales response to advertising expenditures.
Mahajan and Muller (1986) identify five possible policies for advertising expenditures. The
policies are: the Blitz policy, the Pulsing policy, the Chattering or Flighting policy, the Even
policy and the Pulse / Maintain policy. Several authors have since examined advertising when a
pulsing policy is used. Using several models including the Vidale-Wolfe model, (F einberg
1992) examined the chattering policy, the pulsing policy and the even policy of advertising
expenditures. Feinberg concludes that in general neither the chattering nor the even policies
are optimal and that the optimal policy might be the pulsing policy. Naik et el (1998),
developed a model suggesting that the pulsing strategy was superior to an even strategy but
only because of a wearing out of the advertisement, by which they mean the consumers
become board with the advertisement. Assuming that pulsing policies are adopted Villas-Boas
(1993) showed that advertising pulses of competing firms should be out of phase in order to
maximize profits. Using a dynamic programming approach and a modification of the Vidale-
Wolfe model Mesak et el. (2001) showed that a pulsing policy dominated the continuous or
even advertising strategy.

Models have been developed that consider advertising expenditures without
prescribing the pattern of the advertising expenditures (Fruchter 1999; Fruchter and Kalish

18

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1997; Fruchter and Kalish 1998). Models that do predetermine the advertising patterns, e.g.
pulse vs. even are not limited by having an exogenous spending pattern superimposed on the
sales response function. Not using a predetermined pulsing pattern also eliminates t
discontinuities that are generated when response functions are converted from an advertising
spending period to a non-spending period. It is important to note here that none of the
authors examining advertising pulsation polices have considered quality as a factor impacting
sales.

Optimal control modeling has been used to examine the relationship between sales
and advertising several times. Sethi (1973; 1974; 2000) examined the maximum sales revenue
generated by optimizing advertising expenditures. In all three cases a modified version of the
Vidale-Wolfe model was used as a basis for developing the optimal control model. Erickson
(1991) modified the Vidale-Wolfe model and used the result to analyze market sales in a
duopoly. He considered both the open and closed loop forms of this analytical model.
Erickson (1985; 1997) has also examined applying the Lanchester model to advertising as well
as the Vidale-Wolfe model. None of these investigations into advertising strategies
incorporated the product quality as a factor influencing sale. Since the specific aspects of the
product were not considered it may be surmised that the products under consideration are not
differentiable by the consumer. Two summaries of optimal control models in advertising have
been published (Feichtinger et al. 1994; Sethi 1977).

Bass (1969) introduced a diffusion model that determined the optimal price trajectory
to maximize corporate profits realized over the life of a product This model included dynamic
pricing as a strategic tool for increasing sales but it neither incorporated competition nor
quality as factors impacting sales nor did it incorporate the effect advertising had on the

19

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optimal price trajectory. Mahajan, Muller and Bass (1990) reviewed the state of the art of new
product diffusion models and noted that there was a need for models that incorporated
product i.e. quality, aspects into diffusion models. Krishnan, Bass and Jain (1999) refined the
Bass model and specifically called for the incorporation of competition into diffusion model
research. While addressing quality and competition these authors did not incorporate the

impact of advertising explicitly into their model.

Advertising Literature Including Competition

Several authors have incorporated competition into advertising models. Deal (1979)
developed an extension to the Vidale-Wolfe model to consider optimal advertising
expenditures in a dynamic duopoly. Teng and Thompson (1983) developed a model of
advertising in an oligopoly and included the production costs when they obeyed a learning
curve. Jones (1983) developed a dynamic model of advertising in a duopoly and considered
“Word of Mouth” or the contribution that the diffusion of information makes to sales in
addition to the advertising pursued by the company. Horsky and Simon (1983) considered
advertising as it applied to the diffusion of new products. Erickson (1991) used diffusion
models to examine sales and advertising relationships. Sorger (1989) addressed competitive
dynamic advertising as a Nash equilibria differential game. Chintagunta and Vilcassim (1992)
considered advertising strategies in a dynamic duopoly using empirical data for non-durable

goods.

20

Quality

Quality has been associated with operations strategy as a means of gaining a
competitive edge for many years (Phillips et al. 1983; Swamidas 1986; Teece 1985). Extensive
research on quality and the impact quality has on profitability has been conducted. However,
this work has centered on conformance to specifications as a measure of quality (Fine 1986;
Garvin 1983). For a comprehensive treatment of quality as conformance to specification see.
(Garvin 1988; Juran and Jr. 1980; Montgomery 1985). There has also been some treatment of
quality in other contexts than conformance. Garvin (1988) identifies eight different facets of
quality that may be associated with product quality of these four, performance, features,
durability and reliability, are easily associated with design or engineering quality; Many of these
are interrelated. The quality of a product has been tied to both advertising and price as a means
of enhancing sales.

Dorfman and Steiner (1954) demonstrated that there exists an optimal level of
advertising that should be associated with any given level of product quality at a market price.
The implication of their work is that excessive advertising for a product given a level of quality
is that profits are reduced because of the unproductive advertising. Similarly insufficient levels
of advertising results in too low a sales rate and again profits are not maximized. Dorfman and
Steiner did not examine an explicitly competitive environment but rather adjusted the price,
advertising and quality level of the modeled product to exploit different consumers with
differing price and quality requirements.

Quality and its relationship with price as a signal of quality has been examined for

many years. Scitovsky (1945) connected quality with consumer behavior by establishing the

21

idea that in the absence of other information rational consumers evaluate quality levels with
product price. The relationship between pricing and quality was further investigated and
confirmed by Leavitt (1954). More recently this relationship has been questioned. Several
researchers (Gerstner 1985; Riesz 1978; Riesz 1979; Sprokes 1977) have all found that that the
ability of price to signal quality to the consumer is weak at best In an effort to clarify the
quality-price relationship Lichtenstein and Burton (1989) examined the relationship pertaining
to both durable and non-durable goods. Rao and Monroe (1989) found a positive and
statistically significant relationship between price and quality as it is perceived by the consumer.
El Ouardighi and Tapiero (1998) examine price as a signal of quality in an environment where
demand is more sensitive to quality as new innovations for a product diffuse into the market
place.

Many treatments of product diffusion into a market place where quality is held
constant have been examined (Dolan and Jeuland 1981; Horsky 1990; Horsky 1977; Horsky
and Mate 1988; Horsky and Simon 1983; Kalish 1985; Mahajan et al. 1984; Muller 1983).
While informative this is less beneficial than considering a changing or dynamic quality profile.
The changes in quality that are brought about either continuously, as is the case when applying
a learning curve to production, or discontinuously as when companies design new features and
add them to a product need to be factored into managerial decisions.

Narasimhan, Ghosh and Mendez (1993) developed the N GM model to demonstrate
how quality impacts the evolution of the sales of a durable good over its life with evolving
quality levels. This was the first diffusion model that explicitly incorporated the changing
attributes of a product, its quality. In a subsequent paper Narasimhan, Ghosh and Mendez
(1996) used the NGM model to develop an optimal pricing strategy to maximize profits for a

22

 

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durable good during its life cycle. The NGM model has been referenced when considering
several aspects of quality, including customer loyalty factors, the speed of quality improvement
and strategic factors (Devaraj et al. 2001; Foster and Adam 1996; Narasimhan and Mendez
2001). The NGM model has been considered. when examining advertising diffusion models
for new products and diffusion models considering incorporating replacement purchases
(Mesak and Berg 1995; Mesak and Clark 1998). The NGM model has even been referenced in
the development of a smoking cessation study (Mendez et aL 1998). The NGM model
provides a base to develop the quality and diffusion components of the dynamic model this

dissertation.

Quality including Competition

While optimal control models examining advertising in conjunction have received
extensive attention (see above). Quality in a competitive environment has receives surprisingly
little attention. Kourelis and Mkhopadhyay (1995) examine competition when considering
quality as a strategic factor in the market. They use quality and price as optimal control variable
but do not consider advertising as a modifier to their model Luptacik and Mikulas (1982)

consider quality, advertising in the specialized case of atomistic competition.

23

Disaggregated Quality

Nelson (1970) introduced the concept that consumers deal with two types of quality in
products. The terms he applied are search goods and experience goods. He identified search
goods as those goods that consumers can determine relative quality levels via inspection. In
other words, a consumer may examine a product before purchasing and determine whether or
not it has a higher level of quality than its competition. Alternatively the experience good is
one that the consumer must purchase and use before they are able to establish quality levels.
This distinction of the types of quality is directly applicable to individual durable goods. There
exist two types of quality in a durable good that may be established by inspection, the fit and
finish of an automobile for example and its engineering quality the durability or performance
ability of its components or systems. The concept of search quality and experience quality was
examined again by Nelson (1974) and has also been examined by several other researchers
(Milgrom and Roberts 1987; Milgrom and Roberts 1986a; Milgrom and Roberts 1986b;
Shapiro 1982; Shapiro 1983). Another interesting point that Nelson (1970) makes about two
types of quality is that consumers will collect information from friends and family members
before they begin a trial and error process of experience.

Garvin (1988) identifies eight factors that represent quality aspects of a product. Of
the eight attributes, performance, features, durability and reliability are factors that must be
designed into the product and cannot simple be improved by learning how to build the
product more efficiently. The other factors improve with practice or by learning. It is possible
for improvements in quality to be achieved by methods other than by learning. These have
been termed revolutions or paradigm shifts by Reisman (1992). These paradigm shifts are also

24

 

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referred to as breakthrough improvements associated with the reengineering process and are
commonly taught to undergraduates as strategies for reducing process costs. See for example
(Russell and Taylor 2003). The results of a paradigm shift or discontinuity in quality are two
fold First the increase in quality should increase the number of consumers positively
representing the product to other consumers engaged in collecting information, thereby

increasing the level of sales. Second is the reduction in cost that a firm realizes after having

made a paradigm shift.

Potential Contributions to the Literature

‘There are three areas where the literature may be extended by this work. Generally,
advertising models that examine sales response to advertising levels do not specifically
consider the impact of quality as a factor influencing sales. Advertising models such as the
Brandaid (little 1979) model, might be argued to indirectly incorporate quality as a component
of brand recognition, however quality is not examined explicitly. This is interesting in light of
the established importance of product quality to purchasing decisions.

The second area in the literature that warrants more attention is how competition
influences the diffusion of quality weighted goods into the market place. Few if any
practitioners exist in a monopolistic environment. Models that do not incorporate competition
explicitly when examining quality diffusion are not able to examine questions of effective
responses to a competitor’s quality strategy, and the most opportune time to implement
changes in strategic quality policies. Optimal pricing policies that are suggested by models that
do not incorporate competition have limited application in a competitive environment.

25

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The third potential expansion of the literature is that most models only consider
continuous quality improvements. These models do not allow for the radical change in the
quality of a product that is accompanied by a breakthrough process improvement or
engineering change in the product. The capability of considering this type of change is
important because many durable goods,isuch as automobiles, experience such changes during
their product lifetime. These changes impact the ability of the firm to charge a higher price for
the improved product or at least to realize improved revenue. In fact if the firm is to recover
the costs of such a change it is necessary for the firm to demand a higher price for products
that have undergone such changes or to increase their revenue stream. Table 2 shows the
areas where emphasis has been placed to date on advertising, competition and quality models.
Notable, is the lack of attention Quality has received.

This dissertation will address some of the areas in the literature that have not been well
addressed. It will consider quality in two ways which has not been done. First, it will
incorporate quality as a continuously improving function. Second, it will consider
discontinuous or breakthrough quality improvements, those types of quality improvements
that occur in large increments. This dissertation will also consider the combination of
advertising and quality as factors influencing sales. This dissertation will also consider these
factors in a competitive environment, more specifically in a duopoly. While some of these
factors and how they influence sales have been examined individually the combination has not
been combined into a single model before this time. This combination will allow for insights
into how managers can most efficiently shift resources to focus on those factors that provide

the most retum as time progresses.

26

 

CITATION

ADVERTISING COMPETITION QUALITY

DISAGGREGATED
QUALITY

 

Balachander,
S. and K.

Srinivasan
(1 994)

 

' Bass, F. M.
(1969)

 

Chintagunta.
Pradeep K.
and Naufel J.
Vilcassim

(1992) .

 

. Deal, Kenneth
R (1979)

 

Devaraj, S., K.
F. Matta, and
E. Conlon
(2001)

 

Dorfrnan, R.
and Steiner,
PO. (1954)

 

Erickson,

Gary M.
(1991)

 

Erickson,

Gary M.
(1985)

 

Erickson,

Gary M.
(1997L

 

Feichfingfi.
G., R. F.
Hart], and S.
P. Sethi (1994)

 

Armand V.
(1983)

 

 

F einberg, Fred
M. (1 992)

 

 

 

 

 

Table 2— literature Summary

27

 

 

CITATION

ADVERTISING

COMPETITION

QUALITY

DISAGGREGATED
QUALITY

 

Foster, S. T.
and E. E.
Adam (1996)

 

Fruchter, G. E.
(1999)

 

Kouvelis, P.,
Mukhopadhya,
S.K(1 995

 

Luptacik
Mikulas (1982)

 

Narasimhan,
R. and D.
Mendez (2001)

 

Narasimhan,
Ram, Soumen
Ghosh, and
David Mendez
(1993)

 

Narasimhan,
Ram, David
Mendez, and

Soumen
Ghosh (1996)

 

Nelson, P
(1970)

 

Nelson, P
(1 974)

 

 

Rao, Akshay R.
and Kent B.
Monroe (1989)

 

 

 

 

 

Table 2 (cont’d)

28

 

 

 

 

CITATION

ADVERTISING

COMPETITION

QUALITY

DISAGGREGATED
QUALITY

 

Sethi, Suresh
P. (1977)

 

Sethi, Suresh
P. (1973)

 

Sethi, Suresh
P. (1974)

 

Sethi, Suresh
P. and Gerald
L. (2000)

 

Fruchter, G.
E. and S.
Kalish (1998)

 

Fruchter, Gila
E. and

Sholomo
Kalish (1997)

 

Horsky, Dan
and Leonard S
Simon(1983).

 

Jones, Phillip
C. (1983)

 

Krishnan,
Trichy V.,
Frank M.
Bass, and
Dipak C. Jain
(1999)

 

 

Lilien, Gary
L, Philip
Kotler, and K.
Sridhar
Moorthy

(1992L

 

 

 

 

 

Table 2 (cont’d)

29

 

 

 

 

 

 

 

 

 

 

CITATION

ADVERTISING

COMPETITION QUALITY

DISAGGREGATED
QUALITY

 

little, John D.
C. (1979)

 

Mahajan, Vijay
and Eitan
Muller (1986)

 

Mahajan,
Vijay, Eitan
Muller, and

Frank M. Bass
(1990)

 

Mesak, H. I.
and W. D.
Berg (1995)

 

Mesak, H. I.
and]. W.
Clark (1998)

 

Mesak, HI.
and H. Zhang
@001)

 

 

Naik, Prasad
A., Murali K.
Mantrala, and
Alan G.
Sawyer (1998)

 

 

 

 

 

Table 2 (cont’d)

30

 

 

 

 

IT
l

 

«\llt l l
r i .

 

 

CHAPTER 3

Model Development

This dissertation will develop a dynamic model that will incorporate price, quality and
advertising expenditures for two competing durable goods as inputs and will generate sales
levels and thereby profits as outputs. It will optimize the price trajectory and the advertising
expenditures to maximize profits. Figure 2 shows a schematic view of the proposed model.
The model will be developed using the NGM model, (Narasimhan et al. 1993) as a basis to
determine the diffusion sales of quality weighted goods into the market and how that
influences the optimal price trajectory. This dissertation and will incorporate advertising
components from the Vidale-Wolfe model (V idale and Wolfe 1957) and from Erickson’s
(1985) advertising competition model as the basis for advertising’s contribution to sales. The
model will be bounded by the fact that products have a life cycle. That is, they have a point at
which products are introduced and they have a point at which they are withdrawn from the
market. This period will be twenty years. Tests of the model for forty years will establish that

there are no abnormalities associated with the twenty year time span.

The NGM Model

The objective of the NGM model is to maximize the total discounted profits at a

terminal time T it uses price as the optimal control function. The profit function is:
T
_ “(7')
(3.0.1) Ht _ JI(B — Ct) * St * 6 dt
. 0

Where:
31

 

 

 

 

L23

 

Pt = the price at time t
Ct = the cost at time t
St = the sales at time t
r = the discount rate.

The remainder of the NGM model is specified as follows:

 

 

P0 e

(3.0.2) M(P) - [7;] M0

(3.0.3) Q(t) = D1 * Y(t)

(3.0.4) Ego) = 1)2 * X (1‘)

(3-0-5) 5(1) = a * EQU) * (M (t) - Q(O)

8Y0) 1
3.0.6 =—(S(t)-Y(t))
( ) a: D1
ax (t) 1 *

3.0. =— ((q(t)*S(t)-X(t)))
( 7) a: D2
Where:

M, = Initial market potential

P(t)= Price in dollars

M(P)= Market Potential in units

Q(t)= # of units in the market in units

S(t)= Sales rate in units / time

Y(t)= Rate at which units leave market in units/ time

X(t)= Rate at which quality weighted quantity of goods in the market ceases to influence
consumers’ buying in units/ time

EQ(t)=Quality weighted quantity of goods in the market in units

q(t)=Quality index at time t, q(t)e (0—21)

D1: Average life of the unit in time

D2: Average time of the effect of quality of goods on consumer’s buying behavior

a: Proportionality constant used to calculate sales rate in reciprocal times*units

:1" Price elasticity characterizing how sensitive the market potential is for the specific product
relative to price.

32

 

. /—

Typical price trajectories for the NGM model are shown in Figure 4. Note that the

 

A : D2 = 0.75D1 B : D2 = 0.50D1 C : D2 = 0.25D1
D1 =10 T=20

 

8500
7500 4
6500“
5500 J
4500 -
3500-—
2500 -

1500i++54l.j:....rf.,(j%i

 

 

 

 

 

 

 

 

 

Figure 4 Typical NGM Price Trajectories

price increases before it declines to a final value lower than the initial price point.

This dissertation will retain the NGM objective of maximizing profits generated by a
durable good over its life expectancy. The NGM model will be modified to allow for
advertising and explicit competition. In order to achieve these ends modifications will be
made in several stages. The first modification is the inclusion of advertising into the NGM

model.

Advertising

33

 

 

 

.X.‘ "

B I

I 1.2;

 

The advertising component is developed first from the Vidale-Wolfe model (V idale
and Wolfe 1957). In the odginal monopolistic model the change in sale rate is:

ds
(3.1.1) -d—t—px[l——(s/m)]—/ls

Where:

p = a response constant (sales units / $ / period)
5 = sales '

m = saturation sales rate (sales units/ period)

x = advertising rate (5 / period)

xi. = decay constant (period 1)

Using empirical data they found that the response to advertising in terms of sales could
be divided into two sections if a pulsing advertising policy is followed. This differs if an even
policy is followed and this situation will be addressed later. The responses when the advertising

is on and off were found to be as follows:

r(st(0)—r(x)]e-lWax/MW OStST
(312) S(t)={ s(T)e—/i(’i'-T) T<t

Where:

r(x) = m(px//lm)/[1+ (pxI/im)]

3(0): steady state sales response sans advertising

5 = sales

m = saturation sales rate (sales units / period)

x = advertising rate (3 / period)

,1 = decay constant (period ")

T: Time advertising is on

t= total time including time advertising is on and off
p = a response constant (sales units / 3 / period)

34

 

 

\I

it

Ct

It.)

ml

CO,“

10

prt

 

Conceptually, m represents the total market potential of the segment in question while
r(x) represents the maximum level of sales that can be captured using advertising. The Vidale-
Wolfe does not incorporate competition it was developed in a monopoly setting. It is

therefore necessary to incorporate competition in the basic Vidale-Wolfe structure.

Competitive Advertising

Vidale and Wolfe (1957) demonstrated that advertising expenditures have a
diminishing affect on the level of sales over time. They also showed that the increase in sales
due to advertising continues after the active advertising is discontinued, but that the resultant
sales from advertising decays from the point in time when the advertising ceases. This
response is represented in Figure 2.

An important point should be noted from this representation of the Vidale-Wolfe
model. The fall—off in sales is represented as instantaneous once the advertising is
discontinued. This discontinuity is not realistic in that some time must elapse before
consumers begin to “forget” an advertising campaign. The Vidale—Wolfe model was intended
to capture the level of sales created by advertising above a minimum level of sales. Those
present without any advertising at all. Also, the Vidale-Wolfe model is a monopoly response
and does not consider competition in the market environment.

Erickson (1991; 1985) modified the Vidale-Wolfe equation to allow for competition.
He established the following maximum advertising levels for the two competitors in an open-
loop Nash equilibrium. An open-loop Nash equilibrium is one in which the advertising levels

depend only on time and not the current state of the system at that time.

35

 

(32-1) max Ale-"iii [72:1 xii-Alia
(3.2.2) max Azje‘" (h,[ 72 )5 — A2}: ”

Where:
7,. = the brand strength of the competitors.

 

A, = the advertising of the respective competitor.

h.- = the unit contribution for each competitor to the total sales in the market

5: the total sales into the market.
r = the common discount rate.

These relationships are subject to the following dynamic constraint:

dS

(3.2.3) ‘5' = (IBIAIal + flzAga’ ) * (N — S) - 55

Where:

D = the decay rate of current sales.
N = the maximum'sales potential e.g. the total market
A., A2: the advertising rate of each competitor respectively.

fl,- = the effectiveness of the respective advertising campaign
S = is the sales rate.

a,- = is the elasticity of the advertising for the respective competitor.

ds a a
(3.2.4) E: NflIAIa1 +NflzAz 2 ‘SfllAjal *SflzAz 2 —5S

36

This represents the total sales into the market by both competitors. Like the original
Vidale—Wolfe model Erickson’s adaptation of the Vidale-Wolfe model is only intended to
capture sales that exist in the market above the sales generated without any advertising. So the
market potential N must be reduced by amount of sales that would be generated by diffusion.

Accordingly equation (3.2.4) has been reduced by removing the declining advertising
effectiveness 55 . Where 5 is the rate at which advertising effectiveness declines.

Dockner (1988; 2000) develops an advertising game where the individual cumulative sales

for a competitor are:

dx ,- . . . .
(3.2.5) E=f(Pian)(N‘xi‘xj-), l4J=192 175]

Or

dx ,- . . . .
(3.2.6) Zt-=f(Pi,P,-)(N—(xz+xj))a l,J=1,2 135]

Where:

1),: pdce i

P}: price j
x: cumulative sales for i

x: cumulative sales forj
N: Total market potential

The total sales into the market are the sum of the sales for competitor i and j. The sales

rates xi + x j are influenced by saturation and only impact the remaining market potential after

the existing sales have been removed from the total market potential. If the sales from the

37

 

 

 

m

Erickson extension of the Vidale—Wolfe model are allocated by a function of price in a similar

manner sales for the competitors become:

(3.2.7)

3 _ =f’ (p.12. XNAA“ was"; -SAA."‘ 424:3 «55)

The total sales generated needs to have the diffusion component added before

allocating the market according to price

[3) =f‘(P.,p,-)[N.44“ was“: 444“ 424.“: —6S+
(3.2.8) "

“*EQ *(M.-Q)]

Competitive Market Potential

The market potential Mp for the product was modified in the NGM model from the

original Bass model by expressing the price-market potential in terms of price elasticity.

1%
MUD-[7,-

] M 0 where M o is the initial market P0 is the initial price and R is the price at
1

time t. The price elasticity, e, retains its economic meaning on how sensitive the market is to
price changes for the specific product. M. is the initial market potential 1)., is the initial price P,

is the price at time t and M(P) is the market potential at the price P,. In order to accommodate

the addition of a second product into the market it is necessary to modify this market price
38

relationship. First, the market potential at time zero is restructured so that it is dependant on

both initial prices. The market potential at time zero is modified in the following way.

P ' P °
M =M. —‘—'°— + ii
. - I.) (.2)

In this way M. becomes dependent on both initial prices at time zero. P1 J, represents the price
for product one at time zero. P1,, represents the price for product two at time zero. P1,. is the
price of product 1 at time t and P24, is the price of product 2 at time t. Mmt represents the initial
potential of the market segment at time zero and does not change over time. The market

share for the individual competitor becomes:

P.
3.3.2 M P. =1- -—"'— i, °-_-1,2 i¢'
( ) (...) [ [32+1’ni] J J

Market allocation between the two products may be considered in the following manner. The

market share for product one, M (Pm) , is:

P
M(P )= 1— ———'*'
3.3.3 1,:
‘ ) P...+P2,.

. P
If the price 0f product one at [11. ne t, 11:9 a’pproad1 ES 0 . i 1-( +UP ]
' 4
1,: 2.!

approaches zero reducing the market share of product one to zero. If the price of product one

P1,.

approaches zero then the value 1—[—

1.: 2.:

at Me t, P“,

] approaches one and product

39

one’s share approaches 100% of the market. If the price of product two at time t, P2,
. . P2,.
approaches infinity then the value 1- —— approaches one and product one’s market
1,: 2,:

share again approaches 100% of the market. Conversely, if the price of product two at time

P+P

P
——2"-— approaches zero and product one’s
1,: 2.!

t, Pu , approaches zero and then the value 1-[

share approaches zero. Similar limiting cases apply to the market share of product two at time t

with price P“.

g: _ _ P... * a2- _ a.
(3-3-4) [‘1‘]: - [1 [’11 + P}; ]] [NA/‘10, + NflzAz Sfl‘A‘al $162142 55 +

a*EQ *(M, -Q,)]
Notice that in the limiting case of no advertising (3.3.4) becomes:

ds ._ Pf" * a: *
(3.3.5) 2? ._ 1- 717 [a mm (M (t)-Q(t))]

Notice too, that in the case of one firm or the other exiting the market, their price becoming
identically equal to zero, (3.3.4), forces the market share for their competitor to one and their
market share to zero, no product is available for sale, equation (3.3.4) become equal to the
NGM model with no competition. If one competitor exits the market and there is no
advertising equation (3.3.4) becomes equal to the original NGM equation. Next the cost

relationships for the variable costs of quality and advertising will be addressed.

40

Costs

The original NGM model (Narasimhan et al. 1993) the cost of the product did not
vary with time. The model as modified in 1996 (Narasimhan et al. 1996) used a quality cost
that changed over time. Narasimhan et el. (1996) added a cost function that decreased when
quality ranged from 0.25 to 0.90 and increased when quality increased from 0.9. to 1.0. In
particular they postulated that a plausible representation of the cost of quality would decrease
by 40% from 0.25 to 0.90 and increase by 40% from 0.90 to 1.0. They then used a Lagrange
interpolation polynomial to generate the unit cost as a function of quality. The result was a
forth order polynomial in quality. This was added to a base cost C“. This relationship was
confirmed by interviews with a practitioner. The same cost relationship is applied here to the
cost of quality. The variable cost of quality is then added to the fixed production cost.
Discontinuous quality increases are added to the production cost as an increase in fixed costs
and are incurred in total at the time of the improvement.

The cost of advertising has been modeled in this dissertation as a quadratic function.
This is in keeping with Teng and Thompson (1983) and Dockner et al (2000). Specifically the
cost relationship used by Teng and Thompson is adopted in this dissertation this is

5‘. + [2Ai + “:sz where alpha, beta and delta are constants and A, is the advertising level of the

competitor in question. This variable cost of advertising is added to the fixed cost of
production and the variable cost of quality improvement giving a total cost at time t of C,..

This becomes:

(3-4-1) Ct : Cprod + C0 + (:1qu + Czqizg + C3qi3,: + C442, + CSAx' ‘l" C614:

41

Where:
C,- = Constant

A, = Advertising lever for competitor i
q, = the quality level for competitor i at time t

Quality

The original NGM model and the Bass model both recognize that as products are
purchased the market potential for new sales is reduced by the number of units in the market
place. However, the Bass model does not reflect the fact that products have a life span and will
exit the market. The NGM model does incorporate this fact. The NGM model also reflects
the fact that quality will only impact sales for a limited time. Once this time period has been
exceeded the quality of existing units in the market place will no longer impact sales.

In addition to the continuous improvement policy established by the NGM model this
dissertation will extend that model by adding a discontinuous, or large change, in the quality of
the product not present in a continuous or incremental quality improvement program. This
reflects the potential for an engineering change in the basic product make-up, such as the
introduction of a new process technology to the production of an automobile during its
lifetime. The difference in the impact of this change will be reflected in a longer period of time
needed for the engineering improvement to impact sales.

The NGM model uses two delay factors, D1, and D2, to capture the amount of time
that a product will remain in service and the amount of time that that product will impact sales.
It is foreseen that a discontinuous change in quality will be reflected by altering these
constants. The length of time that products remain in service D2 is foreseen to increase as the

engineering or discontinuous quality improvements begin to diffuse into the market. This
42

 

 

ll“

P C n\\.

Tn

3."

Th

 

 

increase in quality should also increase D1, the length of time that a product influences sales in
the market Conversely, if one firm improves its engineering quality and the other firm does
not then the length of time that the non-improving company’s goods influence sales should
decrease and the length of time the product remains in the market should decrease as the

market perceives the lower quality levels for the static company.

The Complete Model

 

The total profits to be maximized for each firm are:

(3.6.1) '

T
11,: [(13 —C,)*S, *e'(")dt
0

Where:

Pr = the price at time t

C[ = the cost at time t

St = the sales rate at time t and
r = the discount rate.

The sales for each competitor is:

——’— *[Mmq MOE/42“ MA“ MA? —6S+

(3.6.2) I"! 1'4
a*EQ *(M, —Q)] ij 6 1,2 i¢j

The market potential for the entire market at time zero is:

43

 

 

 

 

('31;

Dr

 

 

 

P . P .
M = M 1.0 + 2,0
. (p...) (PM)

The market share for each competitor is:

Pu
(3.6.4) M (Pm) = [1—[fiD

_ P2.
Ma: >- 1— ——
(3.6.5) J P2,: +131

,t

The rate of quality weighted number of units in the market is:

(3.6.6) EQU) = D2 * X (I)

The number of units in the market at time t is:

(3.6.7) Q, = D1 *Y(t)

The rate at which units leave the market is:

BY 1
(3.6.8) E=E(S(t)-Y(t))

The rate at which quality weighted units ceases to influence purchasing decisions.

 

{36.9)

Mere;
P11]
ll?) 1
Qt)
8ft)

Y-ft}

X13)

EQifr} =
qeft) :

.J‘U .—
I H l

TU . TD
1

f;
l

H

S :
a.
The cost

BX1*

 

= * S (t ) - X (t )

3.6.9 q (I)

( ) a: D2 ( )

Where:

P(t) 2 Price in dollars

M(P) = Market Potential in units

Q(t) = # of units in the market in units

S(t) = Sales rate in units / time

Y(t) = Rate at which units leave market in units / time

X(t) = Rate at which quality weighted quantity of goods in the market
ceases to influence consumers’ buying in units / time

EQ(t) = Quality weighted quantity of goods in the market in units

q(t) = Quality index at time, t6 (0—>1)

D1 = Average life of the unit in time

110 = Price of competitor 1 product at time zero

I32.0 = Price of competitor 2 product at time zero

I}, = Price of competitor 1 product at time t

P2,, = Price of competitor 2 product at time t

5 = the decay rate of current sales.

N = the maximum sales potential e.g. the total market.

A, = the advertising level of each competitor respectively.

,6; = the effectiveness of the respective advertising campaign

S = is the sales rate.

a, = is the elasticity of the advertising for the respective competitor

The cost at time t including both quality and advertising is:

(3.6.10)

C; = C + C0 + (:1qu + Czqin + C3qi3.t + C4qi‘it + CSA" + C614:

prod

Where:

C, = Constant
45

A 2 Advertising lever for competitor i
q,- -‘= the quality level for competitor i at time t

A conceptual diagram of the model is depicted in Figure 4

46

 
     
 
     

Continuous Continuous

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Quality Quality
Discontinuous Discontinuous
Quality Cost 2 Cost 1 Quality

Advertising
Market
Potential

Sales Rate # of Comp # of Comp H Sales Rate

. 1 1 Units in 2 Units in F“ 2

Market Market
Unit 1’s 7
Quality lifespan Quality

Weighted Units Weighted Units

1 in Market in Market

 

 

 

 

 

 

\ /

Length of time quality Length of time quality
Comp 1 impacts sales Comp 2 impacts sales

Figure 5-Model Conceptualization

47

 

misc
optim
comp
sccon
This i
detem

prtsec

consm

mom

Values
255nm

be he].

Experimental Design

Several scenarios are developed to investigate how, price, advertising levels, and quality
trajectories influence the profitability of two competing firms producing durable goods. The
optimal price trajectory is determined using the premium version of solver for the first
companies’ product. Price, market potential, sales and quality information are passed to a
second spreadsheet where the optimal price trajectory is determined for the second product.
This infomation is passed to the first sheet where the new price trajectory for the first firm is
determined again. This process is continued until no changes in either price trajectory are
present.

The model in this dissertation incorporates several parameters that will be treated as
constants. There are six cost parameters C,,-C(, plus the production cost Cm“. (Teng and
Thompson 1983) used a value of 0.02 for the value of the coefficient on the first order cost
term C5, 0.01 for the value of the second order term C6 and set the constant term to zero. The
values derived in (Narasimhan et al. 1996) are used for the remaining cost constants. It is
assumed that each competitor has equivalent cost profiles so the costs for each competitor will
be held equal to eaCh other.

Advertising increases the number of sales by increasing the level of product awareness
into the portion of the market that has not been taped without the advertising effort (Erickson
1985; Lilien et aL 1992; Little 1979; Vidale and Wolfe 1957). This consumer product awareness
decays over time. The decay rate of sales generated from advertising has been examined in the

literature, see for example. (Bass and Clarke 1972; Clarke 1976; Clarke 1979; Peles 1979;

Weinberg and Weiss 1982) In particular Clarke (1976)estimated that the decay should be
48

approximately 0.62, however Peles(1979) believed this to be too large and Weinberg et el.
(Weinberg and Weiss 1982) indicates that the delay should be 0.526. (Erickson 1991) indicates
that the range for the decay constant delta is from 0 to 1 and uses 0.5 in his analysis. In
keeping with Erickson and approximating Weinberg and Weiss, a value of 0.5 will be used for
each of the simulation runs in this dissertation. Each competitor is selling product to the same
market segment so the decays will be equal to each other.

Two factors influence advertising sales in this dissertation, the level of advertising
effectiveness, {3, this is the percentage of untapped customers in the market that the advertising
campaign contacts, and advertising elasticity, at, the number of customers that are influenced in
their purchase decision as a result of the advertising campaign (Lilien et al. 1992; little 1979;
Vidale and Wolfe 1957). The values for advertising effectiveness, 5 and advertising elasticity, a
are assigned to 0.5 and 0.05 respectively in keeping with the numerical experiments performed
by Erickson(1991). It is also reasonable to assume that each competitor has available to it the
same ability to develop equivalently effective advertising policies and that the market segment
in which they are competing has the same advertising elasticity. Therefore in each of the
scenarios these values for each competitor will be equal to each other. Advertising budgets for
automotive companies may be found in (Advertisers 1977-2003). Ford motor company spent
1.7% of their sales on advertising. The original NGM model was validated using Ford Mustang
data so this is a reasonable figure for an advertising level. When one competitor has a higher
level of advertising 3.5% of sales or more then twice the level of advertising of the first
competitor is used.

It is necessary to consider different unit lifetimes when considering the total life of a
product line. An individual product may be replacement from the same product line after that

49

unit has reached the end of its useful life. To this end Narasimhan et al.(Narasimhan et a1.
1996) examined different unit life times or delays before the consumer might consider
repurchasing a new unit. They used values for the average life of the product, D1, and gave
them values of 3, 5, and 10 years. Individual units also have a limited period of time during
which they influence purchasing decisions by consumers, the quality persistence D2. In the
NGM model this persistence was given values of 0.25D], 0.5DI and 0.75D,. The planning
horizon, the total life of the product line, T, was set to two levels 0.5Dl and 2D] in the NGM
model The demand elasticity; e was set to two values, inelastic 0.7 and elastic 1.3. Thus 36
separate problems were solved. If each of these parameters is used in each of the scenarios the
result would exceed 468 problem runs. By reducing D,, from three time periods to two time
periods 3 and 10 years, D2 from three time periods to two time pefiods, 0.25D1 and 0.75D,,
keeping e at two values and reducing the planning horizon T to 20 years, the number of
solutions is reduced to 120, a manageable number with little loss of generality. Specific

descfipfion of each set of scenarios follows.

Scenarios 1.0-1.4

Of the five scenarios in scenario group one the first sets advertising to zero for each
competitor so that a baseline may be made for the competition sans advertising in a duopoly.
The second sets the market potential for the second competitor to zero and the advertising
budget for the first competitor to non-zero levels. This is so that a monopoly environment
may be considered with the model incorporating advertising. The third scenario has active
advertising for the first competitor and no advertising for the second thus giving a comparison

of the sales from diffusion combined with advertising and the diffusion sales alone. The fourth
50

 

 

scenario
sales ad‘
compel]
second I
the first
that are
quality <

detaik n

scenario has active advertising for each competitor giving insight into the amount of increased
sales advertising might contribute. The fifth set of runs that comprise scenario 1.5 has one
competitor increase its quality trajectory continuously while advertising at a moderate rate. The
second competitor has its quality level remain constant but has a larger advertising rate than
the first. This considers whether or not advertising can counter the increased levels of quality
that are diffused into the market place over time as more goods are replaced with higher
quality ones. The other parameters are held according to the above discussion and specific

details may be reviewed in Table 3.

51

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53

Scenarios 2.0-2.8

The second set of Scenarios considers the differences between product quality
strategies and how advertising influence their results. In the first scenario group, 2.0, the
advertising is set to zero and the quality profile for the first competitor is changed from 0.5 to
0.9, the second quality profile is changed from an initial value of 0.5 to 0.6. This establishes a
base line for quality changes without the influence of advertising. In the second scenario group
2:1 advertising is held to zero for both firms but the quality for the first company varies from
0.36 to, 0.75 while the second varies again from 0.5 to 0.6. This demonstrates how an
aggressive quality competitor who starts out behind in the level of quality but improves steadily
fairs against a complacent quality competitor who makes no effort to maintain their quality
advantage. In the third scenario group, 2.2, the quality trajectories are kept the same for the
two competitors but the first adds an aggressive advertising policy on top of the quality
changes. In the fourth and fifth scenario groupings different levels of advertising are combined
with two quality policies. In all three the quality trajectories are kept the same. Company one
improves from 0.5 to 0.9 while the second company only improves from 0.5 to 0.6. The first
group in this set, scenario 2.3 adds aggressive advertising to the first competitor and no
advertising to the second. The second set has no advertising for either competitor. The third
set scenario 2.5 has no advertising for the first competitor but adds aggressive advertising to
the second to determine how advertising might mitigate the improvement in the quality of the
first competitor. Scenarios 2.6-2.8 show advertising for both firms at two different rates. The
other parameters are held according to the above discussion and specific details may be

reviewed in Table 4.

54

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57

Scenarios 3-3.4

In the third set of scenarios different rates of continuous quality change are combined
with discontinuous quality changes and advertising. In the first set of scenarios, 3.0, a
discontinuous quality improvement for competitor one is compared with a continuous quality
improvement trajectory for competitor two is combined with zero advertising levels so that
the quality impact may be considered independently of advertising. In the second set, 3.1,
different levels of advertising are combined with the same quality profiles as in scenario 3.0. In
particular a heavy advertising rate is give to the firm with the discontinuous quality profile and
no advertising is given to firm two. In the next set of scenarios, 3.2, heavy advertising is
applied to the firm without any discontinuous quality jump. The fourth set of scenarios, 3.3,
has the second firm introducing a discontinuous quality jump 5 years after the first’s quality
jump and has neither firms one nor two advertising. The fifth and last set of scenarios, 3.4,
combines the quality profiles from scenario 3.3 and has the first firm begin heavy advertising
in the year it introduces the discontinuous quality jump and firm two not advertising at all The

other parameters are held according to the above discussion and may be reviewed in Table 5.

58

 

 

 

 

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59

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60

CHAPTER 4

Simulation Results

Scenarios

In order to examine the results of the simulation under different conditions two values
for the price elasticity of demand have been chosen, an inelastic value, 0.7 and an elastic one,
1.3. Two different values for the durability of the individual units are compared. This is the
parameter D1. The first value is Dl=3 years and the second is D1=10 years. Recognizing that
the individual unit will have a limited time during which it influences sales in the market two
different values for D2 are also used, D230.25Dl and D2=0.7SD1. The first value of D2 sets
the amount of time that the product influences future consumers to 25% of the total unit life
and the second considers how sales are impacted if the unit influences sales for 75% of the
unit life. The life of the product line is set to 20 years. The values for the amount of advertising

and the quality trajectories depend on the individual scenario.
Scenarios LO to 1.3
The scenarios in the first group examine the competitors with and without advertising.

In addition to providing valuable information in and of them selves these scenarios will also

provide a basis for comparison with the other scenarios.

61

Scenario 1.0

The first set scenario 1.0 runs 14 are made with an inelastic demand value of e=0.7.
The quality trajectories are equal and constant. The initial price was offset so that the plots of
the price trajectories would not be superimposed on one another. The results may be seen in
Figure 6 to Figure 9. Please not that Figure 6 to Figure 9 are typical examples of simulation run

results. Hereafter the results of the runs are included in Appendix 1 to 3.

 

Run 1 e=0.7,D1=3, D2=.75

 

 

P—PU
----- P2l

 

 

 

 

 

 

 

 

2000

 

Figure 6 — Run 1 Scenario 1.0

62

 

 

Run 2 e=0.7,D1=3,D2=2.25

 

 

f——P1r

 

 

 

 

 

 

Figure 7 — Run 2 Scenario 1.0

 

Run 3 e=0.7,D1=10,DZ=2.5

 

7000

 

5000 - ,
4000 - ,
3000 ~»
2000

 

 

 

 

 

 

 

Years

Figure 8 -Run 3 Scenario 1.0

63

 

i Run 4 e=0.7,D1 =1 O,D2=7.5

 

 

 

 

 

 

 

 

Years

 

Figure 9 - Run 3 Scenario 1.0

While the prices are closely parallel to each other, as expected, there was a minor
difference from the expected performance in that Competitor two was forced to lower its
pricing to a greater extent then Competitor one during the middle of the 20 year product life
cycle. It was also discovered that when the life expectancy was increased to 10 years there was
more of on offset for the second competitor then when the life expectancy was set to 3 years.
See figure 7 and 8. This difference was further amplified when the elasticity was set to a more
elastic value of 1.3. See Figure 36 to Figure 39 Appendix 1.

It is also interesting to note that under inelastic conditions with a short unit life span
and a relatively long period of influence for the quality weighted goods existing in the
marketplace, see Figure 7, the price that maximizes profits for both firms is much greater than

under other conditions. This is in agreement with Narasimhan and Mendez (2001) who found

64

 

that a globally stable equilibrium exists when q > . Under these conditions they

chD2

conclude that a higher maximum price level exists than under other conditions.

In order to establish that the difference was not an aberration in the model each of the
original 8 runs in scenario 1.0 were run again with the initial cost values set equal to each other
and all other parameters equal. Under these conditions the values were exactly superimposed.

The difference in price when the two prices are offset may be explained by the fact
that the two products are substitute goods for one another. A decrease in the price of one
reduces the demand for the substitute good. In order to compensate and increase its revenues
the firm is forced to reduce its price. Furthermore the number of units, Q, in the market
continues to have an impact on sales via diffusion. The result is that the firm with the higher
price has fewer units in the market In the case where both firms have equal quality profiles the
only mechanism that the trailing firm has to overcome an initial sales difference is via a
reduction in price. The response from the other firm is to lower its price thereby maintaining

its advantage. This sales difference is shown in Figure 10.

65

 

|

Sales Run 1

 

1000 .

 

 

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l
1200 1
l
I
!

 

Sales 1

600‘ — 7 i if 7 I 7 i ------ SalesZ!

200- _. . -_ __ _
I

 

 

Units Sold

 

 

 

 

i 0 5' 10 15 20
I Years

J

 

Figure 10 - Sales Run #1

Scenario 1.1

The second set of scenarios in this group, scenario 1.1 runs 9-16, considers the impact
advertising has on the price trajectory of a firm independently of competition. In addition to
this identifying the amount of sales increase attributable to advertising these runs establish a
baseline for comparison when advertising and competition are use in conjunction with each
other. Eight separate simulation runs are made with the elasticity set to two different values,
the unit duration set to two different values and the amount of time a unit continues to
influence sales set to two different values. The price and market share for the first firm are
allowed to obtain optimal values. The price and market share for the second firm are set and

fixed to null values. The advertising for the firm is set to 1.7% of its revenues. This

66

approximates the amount of money spent by the Ford Motor company on advertising over
several years (Advertisers 1977-2003). The market penetration, Beta, is set to 0.5 and the
effectiveness of the advertising is set to 0.05. These values are in keeping with the values found
by Erickson (1991; 1997)in empirical studies of advertising. The quality trajectory of the firm
varies continuously from 0.5 to 0.6 over the entire time horizon of 20 years. The results of
these runs arehshown in Figure 40 to Figure 43 Appendix 1.

The price trajectories under all conditions are the same as those without advertising
and no competition, which is as expected. The percent added sales that are derived from the
advertising are summarized in Table 6. Under both the elastic and inelastic conditions
advertising has the least impact when the unit product durability is the least, 3 of 20 years
and when the quality impact is the greatest percentage of this time, 75% of D1. Under both
the elastic and inelastic conditions advertising has the most impact when the unit product
durability is the greatest, 10 of 20 years and when the quality impact is the least, 25% of D1.
This suggests that advertising has the most impact when the quality influence dissipates
quickly relative to the life of the product. Managerially this means that if the quality
durability does not continue to influence sales for a large percentage of the live of the
product advertising expenditures show the most return. Conversely advertising expenditures

are not as valuable if the quality durability remains persistent in the market.

67

 

SCENARIO 1.1

 

 

 

 

 

 

 

 

 

 

Run # Conditions Total Sales %Sales Increase from Ad
9 e=0.7,D1=3,D2=.75 143,161.5 3.37%
10 e=0.7,D1=3,D2=2.25 122,827.2 2.06%
11 e=0.7,D1=10,D2=2.5 91,452.56 6.03%
12 e=0.7,D1=10,D2=7.5 98,413.66 5.01%
13 e=1.3,D1=3,D2=.75' 243,821.9 2.34%
14 e=1.3,D1=3,D2=.2.25 254,195.8 1.50%
15 e=1.3,D1 =10,D2=2.5 1457797 4.86%
16 e=1.3,D1=10.D2=7.5 1563635 4.33%

 

 

 

 

Table 6— Sales increase due to Advertising

Scenario 1.2

The set of runs composing Scenario 1.2 numbers 17 to 24 are intended to examine the
impact advertising has in a competitive environment. Scenario 1.3 will continue this analysis.
For each competitor the quality trajectories are established as 0.5 to 0.6 continuously over the
20 year time horizon. Advertising penetration and effectiveness are set to 0.5 and 0.05
respectively. Advertising expenditures for the first competitor are set to 3.5% of revenue or an
aggressive advertising effort as apposed to a normal one of 1.7% while the advertising rate for
the second is set to zero. This is intended to amplify any impact for easy observation. The
results of these runs are shown in Figure 44 to Figure 51 Appendix 1.

As clearly demonstrated by Figure 44 to Figure 51 advertising under these conditions
has a minimal impact on the price trajectory initially and that further diminishes over time until
the difference disappears. This minimal impact is due to two reasons. First advertising as
developed here only addresses the market potential that has not been captured through the
diffusion component and the price positions of the firms. This is further reduced by the
effectiveness of the advertising and the advertising penetration. As a result the total potential

68

 

of advertising into the untapped market is relatively small when compared with the total
market potential. Second, the firm that is not advertising has the ability to overcome the
disadvantage created by advertising by reducing its price so that its market potential increases

and market share is maintained.

Scenario 1.3

The third set of scenarios in the first set, 1.3 runs 25 to 32 adds competitive
advertising to the analysis. All conditions are kept the same as in scenario 1.2 but the second
firm advertises at a rate of 1.7% of revenue. The results are seen in Figure 52 to Figure 59

Appendix 1.

Scenario 1.4

The last group of scenarios in the first set, scenario 1.4 runs 32 to 40 considers what
happens when two firms have two different quality trajectories and two different advertising
policies. Runs are made with two different price elasticity’s, 0.7 and 1.3, two different unit
lifetimes, 3 and 10, and two different period of time when quality has an impact on sales, 25%
and 75% of the unit lifetimes D1. The quality trajectory of the first firm varies from 0.6 to 0.9.
While the quality trajectory of the second firm remains constant at 0.75. Advertising for the
first firm is set to 1.7% of revenues. The second firm advertises aggressively with advertising
set to 3.5% of revenues. This is intended to model a case where one firm attempts to gain sales

by improving its quality position while its competitor attempts to maintain sales with

69

advertising expenditures alone. The results of these run may be seen in Figure 60 to Figure 67

Appendix 1. The quality profiles of the products may be seen in figure 42.

 

Quality Profiles

 

 

 

f Quality 1
l '''' Quality 2

 

 

 

 

 

 

Years

 

 

 

Figure 11 — Quality Profiles Scenario 1.4

In the inelastic cases the price trajectory for the second competitor remains relative
close to that of the first competitor. Iiowering the price to take advantage of its superior
quality early in the time period is of small advantage to the second competitor since the change
in price is greater than the change in demand. The quality advantage allows the firm to keep a
higher price and retain market share despite the fact that it only has a quality advantage for 10
of the 20 year time horizon. Competitor two is able to actually raise its price when the life of
the product is short and the length of time that the quality influences purchase decisions is

small. This situation exists for only the first 5 years of the time horizon. After that the quality

70

difference is diminishing for competitor two and is detrimental to it for the second 10 years of
the time horizon.

In the elastic cases the price trajectory for the second competitor differs more from
that of the first competitor. In these cases where a price change is less than the change in
demand profits may be maximized by lowering the purchase price and increasing market share
in combination with the existing quality advantage. In the two cases where the life of the unit is
much less then the life of the product line maximizes its profits by pricing its product less than
that of competitor one. In the two cases where the life of the product line is closer to the life
of the unit the price positions reverse each other. Competitor one maximizes its sales by
lowering its price below that of competitor two. In both cases this occurs after the quality
advantage has shifted to the first competitor.

It should also be noted here that in both elastic and inelastic cases when the unit life is
very short relative to the time horizon and the influence of existing units in the market is short
both finns increase their prices for a short period before decreasing them. Increases in price
were seen in the original NGM model (Narasimhan et al. 1993; Narasimhan et al. 1996) but
under different time constraints. The explanation comes from the different quality trajectories
in a competitive environment. Initially the quality superiority of the second competitor allows
it to command a higher price relative to the first competitor. Firm one follows the price
increase to maximize its profits. As this differential decays the second firm is forced to lower
its price to gain market share and the first firm is also forced to lower its prices so as not to

lose market share.

71

Scenarios 2.0-2.8

The runs in the second set of scenarios continues the consideration of the interaction
of competition and how it impacts the price trajectory for the two competitors when different
quality trajectories are used by the competitors. The runs also add advertising interactions into

the analysis once more information is collected on competition and quality interactions.

Scenario 2.0

In the group of runs in the first scenario 2.0, runs 1 to 8, the quality for the first
competitor is varied from 0.5 to 0.9 while the quality varies from 0.5 to 0.6 for the second.
See Figure 12. This represents the situation where one company seeks actively to improve its
product quality and the second accepts only those quality improvements that result from
learning how to produce the product better over time without any added effort or TQM
policy. The advertising in these runs is turned off so that the interaction may be considered
without any extenuating circumstances. In later groups of runs the advertising function will
be restored and the interaction between competition and advertising considered. The two
levels of elasticity that have been examined before in this work will be considered again, 0.7
and 1.3. Two different product life spans will be examined, 3 years and 10 years, and in each
case two different lengths of time that the individual units influence sales will be used. These
runs are shown in Figure 68 to Figure 75 Appendix 2. The sales figures for the two

competitors under the four conditions are reported in Figure 13 to Figure 16.

72

flat»! I- ll l
a
.

 

 

Quality Trajectories Runs 1-8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1
0.9
g 0.8 / F:q1
g 0.7 / l _____ qz
0.6 .........................
0.5 """"""""""""""""""""""
0.4 .
o 5 1o 15 20
Years
Figure 12 — Quality Trajectories Runs 1—8
1
Sales Competitor 1, 9:0.7 I
7000 i
I 6000 I
5000 i I ----- 01:3,D2=.075 ‘
1* 4000 ,’ I— - - D1=3,_02=2.25
3000 .1; I— - -— D1=10,D2=2.5
2000 if" ,1 I -- -D1=1o.02=7.5g
1000 .-_-.-.-.-.-..= ,__, ,__, ;,_____,___, ._, ,_. :_—:r_a—»x-‘—’—.Lia !
o __ - .. ,_ fl _, , W ., 1 1
o 5 1o 15 20 I
Years I

 

_J

Figure 13- Sales Competitor 1, e=0.7

73

 

 

 

Sales Competitor 2, e=0.7

 

‘2000. w

1000 ~. --

 

M

r“

I

i

I

I
a I
/. j
’4' ’ 1
5.7.3.3.:- '_.'. u u arm-us; L; H H""".’ g“... “I
.. .m ....,, -......... ._ _ fl _ ..-....... .-... ._.......... w“ ,_ .........- W, ,--

 

 

5 10

T

1 5
Years'

 

I

I ----- 01:3,02=.075
I- -.- -- 01=3,02=2.25
- Dl=10,DZ=2.5
.; ~ ~01=1o,02=7.5

 

 

 

 

Figure 14 - Sales Competitor 2, e=0.7

 

 

 

 

 

 

 

 

 

 

 

r I
I Sales Competitor 1,e=1 .3 I
. I
I 15000 I
I 12“ T _ I
I I """ 01:3, 02:0.75
* 9000 ~ ~ a - a 1 I“ -- -— D1=3,D2=2.25
6000 _ c , 7 , II; I- - - DI=10,DZ=2.5
,' I , - 01=1o,oz=7.5
3000 - — ’ ,4" ‘ I
0 5 10 15 20
Years .
I I

 

Figure 15 - Sales Competitor 1, e=1.3

74

 

 

 

 

 

 

 

 

 

Competitor 2,e=1 .3 I
I
8000 I
i I
6000 ~ , * * 5 I I ----- 01:3,02=0.75
-- — — 01:3 02:2.25
I1 I” ~ ' “r DI=10,DZ=2.5
2000 . f f- V . ,f a ,{u I -- D1=10,D2=7.5
tr/t'
o "i" ”m“ “W "M “”7" I
o 5 1o 15 20 I
I
Years I

 

 

Figure 16 - Sales Competitor 2, e=1.3

In all cases both when the price elasticity of the product is elastic and inelastic the
price for the two competitors declines over time. There is a difference in the response of the
second competitor when the life of the individual unit is much smaller than the life of the
product line, D1=3. In these cases the second competitor maintains a price level lower than

the first competitor until late in the total product life cycle. At that time the second
competitor, who has by then developed a marked deficit in product quality, begins to charge
a price that exceeds that of the first competitor. It is no longer able to command an increase
in sales by lowering price alone. This behavior is seen in all runs to a greater or lesser degree.

This behavior is reflected in the sales plots where it can clearly be seen that sales
toward the end of the product life cycle greatly favor competitor one. The prices for the
second competitor plateaus before the lower prices of competitor one forces them down
again. Profits are maximized without any attempt being made to match the reduction in price

that the first competitor is able to enact. In the inelastic cases where the percent change in

75

demand is less than the percent change in price the second competitor is able to maintain a
price relatively close to that of the first competitor. This price differential is greater in all
four cases when the product price is elastic. Sales in these cases for the first competitor
greatly outstrip those of the second. The profits for all four cases normalized to one are

shown in Table 7.

 

 

 

 

e=0.7 e=1.3
D123, D1=3, D1=10, D1=10, D1=3, D1=3, D1=10, D1=10,
D2=O.75 D2=2.25 D2225 D2275 D220.75 D222.25 D2225 D2=7.5
Profit 1.277 1.101 1.171 1.119 1.310 1.114 1.132 1.061
1
Profit 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2

 

 

 

 

 

 

 

 

 

 

 

Table 7— Relative profits Run 1-8 Scenario 2.0

As can be seen in Table 7 the firm with the superior quality improvements shows a
greater profitability over the life of the product line. In both the elastic and inelastic cases the
lowest profit advantage is seen when the product life is short and the influence of the existing
units in the market is long relative to that life, an inverse relationship. This is in agreement with
Narasimhan and Mendez (2001). When there is a continuous improvement in quality the
earlier goods are of a lower quality level and if their influence is extended over a large
percentage of the life of the unit the new superior quality unit will not be able to influence

sales due to the residual impact from the lower quality goods.

76

Scenarios 2.1 - 2.2

These scenarios examine the influence has when the quality trajectories differ
substantially. The first competitor has a quality trajectory that ranges from 0.35 to 0.9 and
the second has one ranging from 0.5 to 0.6. This mirrors the first scenario in that one
competitor makes a concerted effort to improve its quality position while the second makes
no special effort beyond learning improvements. They differ in that the first company begins
with a marked quality deficit and finishes with a superior quality position. The advertising
contributions fall into two categories. In scenario 2.1 the first company makes no effort to
improve its sales position via advertising while in scenario 2.2 it makes a concerted effort to
improve sales with a strong (expensive) advertising campaign. In both scenarios the second
firm makes no effort to advertise choosing to remain complacent. Consistently with the
other simulation runs in this dissertation two price elasticity’s are used, 0.7 and 1.3. Two unit
life times are used 3 and 10 years, and a fixed 20 year time horizon is used. Two periods of
time where the quality of existing units in the market place influence sales, 0.25*D1 and
0.75*D1, are used. The price trajectories are shown in Figure 76—Figure 91 Appendix 2.

The relative profits realized by both firms are shown in Table 8 normalized to the profits of
company two. Table 8 also shows the increase in profits due to the advertising efforts of

competitor one in scenario 2.2 when its advertising is set to 3.5% of revenues.

77

 

PROFIT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AD COMP 1 PROFIT % 3.5%VS.
CONDITIONS 3 COMPARED COMP 2 INCREASE 1.7%
TO COMP 2

e=0.7,D1=3,D2=0.75 0.0% 0.996 1.000 -0.35%
e=0.7,D1=3,D2=2.25 0.0% 1.000 1.000 0.04%
e=0.7,D1=10,D2=2.5 0.0% 1.059 1.000 5.91%

e=0.7,D1 = 1 0,D2= 7.5 0.0% 1.054 1.000 5.45%
e=1.3,D1=3,D2=0.75 0.0% 1.036 1.000 3.59%

e=1.3,D1 =3,D2= 2.25 0.0% 1.035 1.000 3.47%
e=1.3,D1=10,D2=2.5 0.0% 1.137 1.000 13.65%
e=1.3,D1=10,D2=7.5 0.0% 1.119 1.000 11.93%
e=0.7,D1=3,D2=0.75 3.5% 1.013 1.000 1.34% 1.70%
e=0.7,D1=3,D2=2.25 3.5% 1.010 1.000 1.00% 0.96%
e=0.7,D1=10,D2=2.5 3.5% 1.079 1.000 7.87% 1.96%
e: 0.7,D1 = 10,D2= 7.5 3.5% 1.072 1.000 7.20% 1.75%
e=1.3,D1=3,D2=0.75 3.5% 1.054 1.000 5.43% 1.84%
e=1.3,D1=3,D2=2.25 3.5% 1.046 1.000 4.60% 1.13%
e=1.3,D1=10,D2=2.5 3.5% 1.155 1.000 15.53% 1.88%
e: 1 .3,D1 = 10,D2= 7.5 3.5% 1.134 1.000 13.40% 1.48%

 

 

 

 

 

 

Table 8— Relative profits Scenarios 2.1 and 2.2

The results clearly indicate the advantage quality improvements may make in

its increasing quality trajectory.

corporate revenues. The two quality trajectories intersect at year ten when the two values are
equal to 0.55. See Figure 17. This means that for the first half of the time horizon competitor
2 has a quality advantage and for the second half competitor 1 has an advantage. The relative
profits show that competitor one has an advantage in all but two situations, inelastic price

conditions and short unit life spans where it appears that there is no advantage gained form

This lack of improvement in profitability is attributable to the symmetry of the

78

 

 

Quality Trajectories

0.8
0 7 /

0:6 /

 

 

 

 

 

 

 

 

 

 

 

 

 

3‘ f—
‘a 0.5 - / I ('1
5 04 / I"'—q2
/
0.3
0.2 . . r .
o 5 10 15 20

Years

 

 

 

Figure 17 — Quality Competitors 1 and 2

situation. Each firm has a quality advantage 50% of the time and the short unit life times
under inelastic conditions do not allow profits to be recovered in the second half of the
scenario by the company with a superior quality position.

However, the increase in profits for competitor one under the other conditions,
longer unit life spans and an elastic demand environment cannot be attributed to a generally
superior quality position either. Since each firm has an equal amount of time when their
products have a superior quality position, the increase in profitability must be a result of the
increasing quality over the entire life of the product and the conditions under which it is
sold. In the two inelastic cases where the unit life is long relative to the time horizon
increased profits are seen for competitor one. Longer lived products mean that they must be
replaced more frequently when the quality for competitor one has increased to a greater

extent then in the short time period cases. In the four elastic cases while greater profits are

79

seen in all four situations. In the case of the two short lived unit situations the elastic
conditions allow a greater increase in demand relative to the increase in price so superior
quality goods will command a grater relative price as they replace older units. In the two
cases where the unit lives are long the units must be replaced after the quality improvements
have been implemented.

The advertising impact for these situations may be seen in the increase in profits seen
in the scenario 2.2 runs relative to scenario 2.1 runs. See Table 8. These increases exist in all
cases and range from 0.96% to 1.88% depending on the conditions. Advertising is _most
effective in an elastic environment with a long unit life span and short quality influence periods
and least effective in an inelastic environment with a short unit life span and a relatively long
periods where the quality of previous units influence sales. This indicates that while quality
improvements are effective under most conditions at increasing relative profits they may be
assisted with an advertising campaign in all conditions. These campaigns however, are most
effective with a long unit life span and relative short periods where existing units influence

sales. This suggests that the use of quality as a strategic lever may be improved by the judicious

use of advertising expenditures.

Scenarios 2.3-2.8

To further test this position scenarios 2.3 to 2.5 examine two different quality
trajectories for the two competitors and six different advertising positions. The quality
trajectories are initiated at the same level 0.5, giving neither competitor an initial advantage.

The trajectory of the first competitor improves from 0.5 to 0.9. The trajectory of the second

80

competitor improves from 0.5 to 0.6 this represents the aggressive and passive efforts at
quality improvement as described before. The advertising positions are 3.5% vs. 0.0%, 0.0%
vs. 0.0%, 0.0% vs.3.5%, 3.5% vs. 3.5%, 3.5% vs.1.5% and 1.5% vs. 3.5% respectively. These
represent three situations. First, when a firm aggressively supports its quality improvement
policy against a passive advertising competitor. Second, when a firm relies simply on its
quality improvement, e.g. is passive relative to advertising and is competing against a passive
advertising competitor. The third case is when a firm is passive relative to advertising but is
competing against a competitor who is aggressively attempting to counter the quality strategy
of the first with its advertising. Conditions are the same as in prior simulation runs e=0.7
and 1.3, D1 is 3 and 10, D2 is 0.25*D1 and 0.75*D1. The price trajectories for these run are
shown in Figure 92 tolFigure 139 Appendix 2. The quality trajectories are the same as in
Scenario 2.0 Runs 1-8. See Figure 12.

The price trajectories follow patterns similar to those seen previously. The firm with
the greater rate of quality increase is able to lower prices continuously while the competitive
firm can only lower prices until the quality difference reaches a critical level. At that point it
is unable to lower prices and maintain profitability. After this time it maintains its price level
and begins to charge more for its product than the first competitor. As the end of the
product life cycle approaches the first competitor begins to radically lower prices and the
second firm is forced to lower prices again so that it may maintain market share supporting
its profitability. The quality advantage allows for a loWer price position and therefore
increased profitability. Table 9 shows the three scenarios as run demonstrating the increase

in profits from quality and advertising. Scenario 2.4 is the case where there is no advertising.

81

Scenario 2.3 shows the aggressive advertising for the competitor with the greatest
rate of quality change, e.g. competitor 1 and Scenario 2.5 shows the aggressive advertising
for the competitor with the lowest rate of quality change, competitor 2. Table 9 shows a
comparison when either one firm or neither firm advertises. Table 10, scenarios 2.6-2.8

shows the differences when both firms advertise at some level and compares these values to

the case when neither firm advertises.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. AD PROFITS PROFITS NET %

RUN RATIO CONDITIONS 1 2 mp}, DIFF.
3.5/0.0 e=0.7,D1=3,D2=0.75 1.294 1.000 29.41% 1.752%
3.5/00 e=0.7,D1=3,D2=2.25 1.111 1.000 11.09% 0.945%

3 35/00 e=0.7,D1=10,D2=2.5 1.192 1.000 19.21% 2.092%

.0 35/00 e=0.7,D1=10,D2=7.5 1.137 1.000 13.72% 1.862%

g 3.5/0.0 e=1.3,D1--3,Dz=0.75 1.330 1.000 33.03% 1.994%

()3 35/00 e=1.3,D1=3,D2=2.25 1.125 1.000 12.48% 1.124%
35/00 e=1.3,D1=10,D2=2.5 1.152 1.000 15.20% 1.974%
3.5/0.0 e=1.3,D1=10,D2=7.5 1.077 1.000 7.70% 1.587%
0.0/0.0 e=0.7,D1=3,D2=0.75 1.277 1.000 27.66% —
0.0/0.0 e=0.7,D1=3,D2=2.25 1.101 1.000 10.15% -

g 0.0/0.0 e=0.7,D1=10,Dz:2.5 1.171 1.000 17.12% -

.o 00/00 e=0.7,D1=10,D2=7.5 1.119 1.000 11.86% -

g 0.0/0.0 e=1.3,D1=3,Dz=0._75 1.310 1.000 31.03% -

C}; 00/00 e=1.3,D1=3,D2=2.25 1.114 1.000 11.35% -
0.0/0.0 e=1.3,D1=10,D2=2.5 1.132 1.000 13.22% -
0.0/0.0 e=1.3,D1=10,D2=7.5 1.061 1.000 6.11% -
0.0/3.5 e=0.7,D1=3,D2=0.75 1.254 1.000 25.38% 2.28%
00/35 e=0.7,D1=3,D2=2.25 1.090 1.000 9.04% 4.10%

3 00/35 e=0.7,D1=10,D2=2.5 1.148 1.000 14.75% 2.36%

g 0.0/35 e=0.7,D1=1o,D2=7.5 1.099 1.000 9.85% 2.00%

8 00/35 e=1.3,D1=3,Dz=0.75 1.285 1.000 28.51% 2.52%

a; 00/35 .e=1.3,D1=3,D2=2.25 1.100 1.000 10.00% 4.36%
00/35 e=1.3,D1=10,D2=2.5 1.110 1.000 11.02% 2.20%
00/35 e=1.3,D1=10,D2=7.5 1.044 1.000 4.38% -1.73%

 

Table 9- Profitability differential from advertising

82

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RUN AD$ CONDITIONS COMP COMP NET % % DIFF DUE
# 1 2 DIFF TOAD
35/35 e=0.7,01=3,02=o.75 1.271 1 27.10% 0.56%
35/35 e=0.7,01=3,02=2.25 1.098 1 9.80% 0.35%
g} 3.5/35 e=0.7,D1=10,D2=2.5 1.168 1 16.80% 0.32%
.o 35/35 e=0.7,D1=10,D2=7.5 1.117 1 11.70% 0.16%
8 35/35 e=1.3,01=3,02=0.75 1.305 1 30.50% 0.53%
Si 3.5/35 e=1.3,D1=3,D2=2.25 1.124 1 12.40% 1.05%
35/35 e=1.3,01=1o,02=2.5 1.132 1 13.20% 0.02%
35/35 e=1.3,D1=10,D2=7.5 1.071 1 7.10% 0.99%
3.5/15 e=0.7,D1=3,D2=O.75 1.2842 1 28.42% 0.76%
3.5/15 e=0.7,01=3,02=2.25 1.1062 1 10.62% 0.47%
g 3.5/15 e=0.7,D1=10,D2=2.5 1.1817 1 18.17% 1.05%
.g 3.5/15 =o.7,01=1o,02=75 1.1285 1 12.85% 0.99%
2 3.5/15 e=1.3,D1=3,D2=0.75 1.3128 1 31.28% 0.25%
5; 3.5/15 e=1.3,D1=3,D2=2.25 1.1189 1 11.89% 0.54%
3.5/15 e=1.3,D1=10,D2=2.5 1.1424 1 14.24% 1.02%
35/15 e=1.3,D1=10,D2=7.5 1.0694 1 6.94% 0.83%
1.5/35 e=0.7,D1=3,D2=0.75 1.2611 1 26.11% -155%
- 1.5/3.5 e=0.7,D1=3,D2=2.25 1.0944 1 9.44% 0.71%
g 1.5/3.5 e=0.7,01=1o,02=25 1.1562 1 15.62% -1.50%
.g 1.5/3.5 e=0.7,01=1o,02=75 1.1063 1 10.63% -1.23%
8 1.5/3.5 e=1.3,D1=3,D2=0.75 1.2934 1 29.34% -1.69%
,§ 1.5/3.5 e=1.3,01=3,02=2.25 1.1047 1 10.47% 0.88%
1.5/3.5 e=1.3,01=1o,02=2.5 1.1184 1 11.84% 4.38%
1.5/3.5 e=1.3,D1=10,D2=7.5 -1.0503 1 5.03% 4.08%

 

Clearly advertising increases the percentage of increased profits seen by the firm with
the greater rate of quality improvement and counter advertising decreases that percentage of
increased profits. This is as expected. What was unexpected is that the maximum assistance

to sales for the high quality competitor and the maximum assistance to sales for the low

quality competitor occurred under different conditions.

The basic quality advantage was maximized with advertising in all six scenarios under
elastic price conditions, short unit life spans and short periods of influence. The profit

advantage to competitor one was minimized due to the competitors advertising under

83

Table 10 Profitability differential from advertising 2

 

relatively low price elasticizes, long life spans and long periods of product influence. The
extrmm cases when one firm advertises and the other does not are shown in Table 11 and

Table 12

 

 

 

 

 

 

 

 

 

 

 

 

 

Ad S Conditions Comp 1 ComEZ % Diff
3.5/00 e=1.3,D1=-3,D2=0.75 1.33 1 1.99%
3.5/0.0 e=1.3,D1=10,D2=7.5 1.077 1 1.59%
00/00 e=1.3,D1=3,D2=0.7S 1.31 1 -

0.0/0.0 e=1.3,D1=10,D2=7.5 1.061 1 f-

0.0/35 e=1.3,D1=3,D2=0.75 1.285 1 2.52%
00/35 621.3,D1210Dzz75 1.044 1 173%

 

 

Table 11 - Max and Min quality profit increases

Note that this differs somewhat from the last situation in that there is no quality deficit
to overcome; it is purely a quality improvement situation. While both the minimum sales

assistances due to advertising came

 

 

 

 

 

 

 

 

 

 

 

' Ad 5 Conditions Comp 1 Comp 2 °/o Diff
3.5 / 0.0 e=0.7,D1=3,D2=2.25 1.111 1 0.95%
3.5 / 0.0 e=0.7,D1=10,D2=2.5 1.192 1 2.09%
0.0/ 3.5 e=0.7,D1=3,D2=2.25 1.09 1 -1.10°/o
0.0/ 3.5 e=1.3,D1=3,D2=0.75 1.285 1 -2.52%

 

 

Table 12- Advertising assistance

under inelastic environments the maximums came under different environmental conditions.
It should be noted here that minimum in the case of counter advertising is the least amount of
reduction in the profits generated by firm one when .firm two is using advertising to counter
the quality strategic lever of firm one. In the elastic environment with short unit lives and
relative long quality influence the aggressive advertising by competitor two allows it to install a

larger product base before the quality differential becomes great. The elastic environment also

84

allows it to increase prices without the penalty in demand that it would incur in an inelastic
environment. When firm one pursues its quality strategy in a market where the units are not
replaced frequently with respect to the time horizon advertising allows it to enhance the sales
in the second half of the time horizon when it has a greater quality advantage. The inelastic
environment reduces the ability of the second firm to respond to quality and advertising with a

purely priced based strategy.

Scenarios 3.0-3.4

The forty runs in the last set of scenarios add discontinuous quality improvements into
the analysis. A discontinuous improvement may be viewed as some radical change to the
operational process or the product. This might take the form of a new type of production
equipment reducing imperfections or a new addition to the product itself such as a new power

train in an automobile. An example of this type of improvement is shown in Figure 18.

 

Quality vs Time

 

 

 

 

Qualllty

 

Years

 

 

 

85

Figure 18 - Discontinuous Quality

In this example the first company introduces such a change in year five of the time horizon
while company two makes no radical improvements in their process. In the first three
scenarios advertising is considered in three ways. First, neither fimi makes any advertising
effort. This provides a baseline to see what the discontinuous quality improvement alone
contributes to the relative profits of the firm making the change as opposed to those of the
firm making no radical improvements. Second, Advertising is added to the firm making the
changes to explore what kind of a profit improvement they might see when aggressive
advertising their product while also making the quality improvement. Third, the firm making
the improvement uses no advertising to support their market position in addition to the quality
improvement while the second firm counters the discontinuous change with advertising alone.
In the fourth scenario the second firm counters the discontinuous quality improvement with
an improvement of their own after the first has made their improvement. In the fifth scenario

quality improvements are introduced in the same manner but the first finn begins an

aggressive advertising campaign at the same time that they introduce the improvement.

Scenario 3.0

In this scenario the quality profile for competitor one begins at 0.5 continues
smoothly until year five and then improves by 0.25. It then continues smoothly to a value of
0.85. 0.85 was chosen as a terminus since the continuous improvement until year five
proceeded at this steady rate. The quality profile for the second competitor moves from 0.5

to 0.6 this is at the same rate that the initial and final improvements are made by company
86

one. Advertising for both firms is held to zero. Two different elasticity’s are tested, 0.7 and
1.3. Two different unit lives are considered 10 and 3 years and the length of time that units
in the marketplace continue to influence sales are 75% and 25% of these times. The terminal
time horizon is 20 years. The price trajectories for these runs are shown in Figure 140-Figure
147 Appendix 3.

Prices decay in all eight cases. The price trajectory of competitor one shows a
discontinuous change in year five when the quality change is introduced. Furthermore it
shows a minor increase in price just before the quality discontinuity is introduced. In the two
cases where the unit life is short relative to the time horizon and the length of time that units
in the marketplace influence sales is short, 0.25*D1, the reduction in price is the most radical
followed by a rapid increase in price with a steady decline in price continuing from that
point. See Figure 140 and Figure 144. The price trajectory of competitor two begins below
that of competitor one and eventually crosses that of competitor one so that it is charging a
higher price than competitor one. This cross over occurs more rapidly in the elastic cases
and the price differential is greater in these cases relative to the inelastic cases. This indicates
that when the percent change in demand is less than the percent change in price the first
i competitor is unable to take full advantage of its quality position due to the limitations
imposed by the substitute good in the market. The profits, normalized to competitor two,

are shown in Table 13.

 

 

 

 

 

 

 

 

 

 

RUN # CONDITIONS PROFITS 1 PROFITS 2
Run 1 e=0.7,D1=3,D2=0.75 1.337 1.000
Run 2 e=0.7,D1=3,D2=2.25 1.123 1.000
Run 3 e=0.7,D1=10,D2=2.5 1.206 1.000
Run 4 e=0.7,D1=10,D2=7.5 1.141 1.000

 

87

 

 

 

 

 

 

 

 

Run 5 e=1.3,D1=3,D2=0.75 1.375 1.000
Run 6 e=1.3,D1=3,D2=2.25 1.133 1.000
Run 7 e=1.3,D1=10,D2=2.5 1.150 1.000
Run 8 e=1.3,D1=10,D2_=7.5 1.076 1.000

 

 

Table 13— Profits Runs 1-8 Scenario 3

Under all conditions the firm with the discontinuous quality improvement. The
greatest profit advantage seen by competitor one occurs when the conditions in the market are
elastic and the product life is the shortest and the influence of existing units is also the shortest
Run 5 in Table 13. The least amount of profit advantage seen by competitor one occurs when
the conditions in the market are elastic and the unit life is greatest with the longest amount of
time during which the existing units in the market have influence on sales. This is the same as

Scenario 2.4. Note also that when comparing the continuous quality improvement case and the

 

 

 

 

 

 

 

 

 

 

 

CONT DISCONTINOUS CONT DISCONTINOUS
CASE CASE CASE CASE
Conditions 0.5—0.9 0.5-0.85 0.5-0.9 0.5-0.85
e=0.7,D1=3,D2=0.75 1.277 1.337266 27.66% 33.73%
e=0.7,D1=3,D2-=2.25 1.101 1.12328 10.15% 12.33%
e=0.7,D1=10,D2=2.5 1.171 1.205561 17.12% 20.56%
e=0.7,D1=10,D2=7.5 1.119 1.1413 11.86% 14.13%
e=1.3,D1=3,D2=0.75 1.31 1.374603 31.03% 37.46%
e=1.3,D1=3,D2=2.25 1.114 1.133166 11.35% 13.32%
e=1.3,D1=10,D2=‘-2.5 1.132 1.149707 13.22% 14.97%
e=1.3,D1=10,D2=7.5 1.061 1.075801 6.11% 7.58%

 

 

 

 

 

Table 14—Profits Continuous Improvement and
Discontinuous Improvement

88

 

discontinuous quality improvement cases there is a greater profit advantage in the
discontinuous case despite the fact that the terminal quality is marginally superior in the
continuous case. This may be attributed to the large jump in sales seen after the
discontinuous quality improvement that is not seen in the continuous case See Figure 19 and
Figure 20. In the continuous case the sales for competitor one eventually exceed that of
competitor two, specifically at time mark 2.6, but the increase is gradual so the number of
units influencing sales in the market is low initially. In the case of the discontinuous
improvement the number of units influencing sales is large right away resulting in a boost to

competitor one via the diffusion element.

 

Scenario 3.1 Run 5 Sales, e=1.3,D1=3,D2=0.75

8000

 

. ____ Ha . r—.‘.f m_a_‘

 

 

|
1

Sales 1
. ----- Sales 2

 

 

# of Units
.h
0
8

 

 

 

 

 

 

15 20

 

 

Figure 19 — Sales Discontinuous Quality

89

 

Scenario 2.4 Run 37,e=1 .3,D1=3,D2=0.75

7000

 

5000 ~

 

 

l

. Sales 1
L- - - - - Sales 2

 

3000«
3 2000 « . -
1 10008 9

 

# of units

 

 

 

 

 

 

Figure 20— Sales Continuous Quality

Scenarios 3.1-3.2

The next two scenarios add advertising into the analysis of discontinuous quality. In
scenario 3.1 the firm introducing the discontinuous quality improvement advertises
aggressively during the entire time period. The second firm makes no advertising efforts.
This represents the case where a firm attempts to develop market share in advance of the
improvements it is going to introduce and continues to support the improvement with
advertising efforts for the entire time horizon. Its competitor remains passive during the
entire period. The conditions are the same as in scenario 3.0. The quality profile for
competitor one begins at 0.5 continues smoothly until year five and then improves by 0.25.

It then continues smoothly to a value of 0.85. The quality profile for the second competitor
90

moves from 0.5 to 0.6. Advertising is as described above. Two different elasticity’s are
tested, 0.7 and 1.3. Two different unit lives are considered 10 and 3 years and the length of
time that units in the marketplace continue to influence sales are 75% and 25% of these
times. The terminal time horizon is 20 years. The results are seen in Figure 148-Figure 163
Appendix 3.

The price trajectories are similar in nature to those seen in scenario 3.0 where no
advertising is present; Advertising performed in a similar fashion to the cases where
advertising was present with continuous quality improvement. In all cases it added profits
when used to support firm one’s quality strategy and in all cases when used as a tool to
attempt to retard profits by competitor two it did reduce the net increase in profits realized
by the firm pursuing a quality improvement program. See Table 15. The increase or decrease
in total profit was generally not significant when comparing the discontinuous quality
improvement cases with those of the continuous cases. See Table 16. All maximum and
minimum contributions occurred under the Same environmental conditions in the
discontinuous cases as in the continuous cases. This suggests that advertising is not sensitive
to the type of quality improvement policy pursued by the firm. It is as effective in the
discontinuous case of quality improvement as it is in the case of continuous quality

improvement.

91

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AD Ratio Conditions Profits 1 Profits 2 Diff
0.0/0.0 e=0.7,01=3,02=0.75 1 .337 1.000 -
0.0/0.0 e=0.7,D1=3,D2=2.25 1.123 1.000 -
0.0/0.0 e=0.7,Dt=10,D2=2.5 1.206 1.000 -
0.0/0.0 e=0.7,D1=10,D2=7.5 1.141 1.000 -
0.0/0.0 e=1.3,D1=3,02=0.75 1.375 1.000 -
0.0/0.0 e=1.3,D1=3,D2=2.25 1.133 1.000 -
0.0/0.0 e=1.3,Dt=10,D2=2.5 1.150 1.000 —
0.0/0.0 e=1.3,D1=10,D2=7.5 1.076 1.000 -
3.5/0.0 e=0.7,D1=3,D2=0.75 1.355 1.000 1 .73%
3.5/0.0 e=0.7,D1=3,D2=2.25 1.133 1.000 0.94%
3.5/0.0 e=0.7,D1=10,02=2.5 1.227 1.000 2.11%
3.5/0.0 e=0.7,Dt=10,D2=7.5 1.160 1.000 1.87%
3.5/0.0 e=1 .3,D1=3,D2=0.75 1.394 1.000 1.98%
3.5/0.0 e=1.3,Dt=3,D2=2.25 1.144 1.000 1.11%
3.5/0.0 e=1.3,D1=10,D2=2.5 1.169 1.000 1.96%
3.5/0.0 e=1.3,D1=10,D2=7.5 1.091 1.000 1.51%
00/35 e=0.7,D1=3,D2=0.75 1.313 1.000 -2.40%
00/35 e=0.7,D1=3,02=2.25 1.1 12 1.000 -1.13%
00/35 e=0.7,D1=10,D2=2.5 1.181' 1.000 -2.45%
00/35 e=0.7,D1=10,D2=7.5 1.121 1.000 -2.05%
00/35 e=1.3,D1=3,02=0.75 1.348 1.000 -2.64%
00/35 e=1.3,D1=3,D2=2.25 1.119 1.000 -1.38%
00/35 e=1.3,D1=10,D2=2.5 1.127 1.000 -2.23%
00/35 e=1.3,D1=10,D2=7.5 1.058 1.000 -1.76%

 

Table 15 — Profit Difference from Advertising

92

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AD CONDITIONS DISC. CONT. DIFF
RATIO q q ,
0.0/0.0 e=0.7,D1=3,D2=0.75 1 .337 1.277 0.0600
0.0/0.0 e=0.7,D1=3,02=2.25 1 .123 1.101 0.0220
0.0/0.0 e=0.7,D1=10,DZ=2.5 1 .206 1.171 0.0350
0.0/0.0 e=0.7,D1=10,02=7.5 1.141 1.119 0.0220
0.0/0.0 e=1.3,D1=3,DZ=0.75 1.375 1.31 0.0650
0.0/0.0 e=1.3,D1=3,D2=2.25 1.133 1.114 0.0190
0.0/0.0 e=1.3,D1=10,D2=2.5 1.15 1.132 0.0180
0.0/0.0 e=1.3,D1=10,DZ=7.5 1.076 1.061 0.0150
3.5/0.0 e=0.7,D1=3,02=0.75 1 .355 1.294 0.0610
3.5/0.0 e=0.7,D1=3,D2=2.25 1.133 1.111 0.0220
3.5/0.0 e=0.7,D1=10.02=2.5 1 .227 1.192 0.0350
3.5/0.0 e=0.7,D1=10,02=7.5 1.16 1.137 0.0230
3.5/0.0 e=1.3,D1=3,DZ=0.75 1.394 1.33 0.0640
3.5100 e=1.3,D1=3,D2=2.25 1.144 1,125 0.0190
3.5/0.0 e=1.3.D1=10,02=2.5 1.169 1.152 0.0170
3.5/0.0 e=1.3,Di=10,D2=7.5 1.091 1.077 0.0140
0.0/3.5 e=0.7,D1=3,DZ=0.75 1 .313 1.254 0.0590
0.0/3.5 e=0.7,D1=3,02=2.25 1.1 12 1.09 0.0220
0.0/3.5 e=0.7,Di =10,02=2.5 1.181 1.148 0.0330
0.0/3.5 e=0.7,D1=10,D2=7.5 1 .121 1.099 0.0220
0.0/3.5 e=1 .3,D1=3,02=0.75 1 .348 1.285 0.0630
0.0/3.5 e=1.3,D1=3,DZ=2.25 1.119 1.1 0.0190
0.0/3.5 e=1.3,D1=10,02=2.5 1.127 1.11 0.0170
0.0/3.5 e=1.3,D1=10,DZ=7.5 1.058 1.044 0.0140

 

 

 

 

 

Table 16 - Difference Cont. Case vs.
Discontinuous

93

 

Scenario 3.3

The runs constituting scenario 3.3 consider what happens when the second company
initiates a discontinuous quality improvementprogram of its own at a later date then the first
company. In this scenario the advertising efforts for both companies are set to zero. The
quality profile for the first company is the same as in scenarios 3.0-3.2. It begins at 0.5
improves steadily to year five where it increases by 0.25 and then continues to increase at a
steady rate until year 20 with a terminal value of 0.85. Firm two starts at 0.5 and improves
steadily until year 10 at which time it improves by 0.25 and then it continues to improve at a
steady rate until year 20. Two different elasticity’s are tested, 0.7 and 1.3. Two different unit
lives are considered 10 and 3 years and the length of time that units in the marketplace
continue to influence sales are 75% and 25% of D1. See Figure 164~Figure 171 Appendix3.

The price curves Show that the ability to increase price mirrors each other under all
conditions. The first firm gains some profit advantage when the unit life is short relative to
when the unit life is long. See Table 17. Furthermore, it gains a somewhat greater advantage
when the influence on sales by existing units is short. This advantage is reduced or
disappears when working in an elastic environment. Short unit life spans allows for the
introduction of higher quality units into the market The short influence periods allows for
the newer higher quality units to influence sales quicker and with larger numbers. It is not
surprising that when the percent change in demand is less then the percent change in price
the firm with the early price advantage is not able to create a greater profit margin via an

increase in sales due to a reduction in price.

94

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RUN # CONDITIONS FIRM 1 FIRM 2 ADVANTAGE
25 e=0.7,D1=3,D2=O.75 1.089 1 8.86%
26 e=0.7,D1=3,D2=2.25 1.040 1 3.98%
27 e=0.7,D1 =10,D2=2.5 1.061 1 6.05%
28 e=0.7,D1 = 1 0,D2= 7.5 1.048 1 4.76%
29 e=1.3,D1=3,D2=0.75 1.075 1 7.48%
30 e=1.3,D1=3,D2=2.25 1.018 1 1.79%
31 e=1.3,D1=10,D2=2.5 * 1.001 1 0.10%
32 e=1.3,D1=10,D2=7.5 0.994 - 1 -0.58°/o

Table 17 - Profit Advantage with 2 Discontinuous
q Improvements
Scenario 3.4

The runs in scenario 3.4 use advertising as a purely tactical tool. The first firm with the
discontinuous increase in quality only begins advertising when the quality improvement is
introduced. Firm one begins an advertising policy that uses 3.5% of its revenues in the same
time period that it introduced the discontinuous quality improvement. All other conditions are
the same as for scenario 3.3. The resulting price curves may be seen in Figure 172-Figure 179.

The price curves Show no significant changes from scenario 3.3. There is a difference in the
profit generated under the different conditions. The difference between using advertising
aggressively when the discontinuous quality improvement for the first company is put into
place as a deterrent to the future improvement in the second company and using no

advertising at any time is show in Table 18. These values are normalized to the profits

generated by the second competitor.

95

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CONDITIONS AD=0.0% AD=3.58% ADV.0% ADV.3.5% DIFF.
e=0.7,D1=3,D2=0.75 1.089 1.100 8.86% 9.98% 1.12%
e=0.7,D1=3,D2=2.25 1.040 1.046 3.98% 4.59% 0.61%
e=0.7,D1=10,D2=2.5 1.061 1.076 6.05% 7.62% 1.57%
e: 0.7,D1 = 1 0,D2= 7.5 1.048 1.062 4.76% 6.19% 1.43%
e=1.3,D1=3,D2=0.75 1.075 1.087 7.48% 8.68% 1.20%
e=1.3,D1:3,D2=2.25 1.018 41.025 1.79% 2.50% 0.71 0/o
e=1.3,D1=10,D2=2.5 1.001 1.016 0.10% 1.57% 1.48%
e=1.3,D1=10,D2=7.5 0.994 1.007 0.58% 0.66% 1.24%

Table 18 — Advantage from Advertising Scenario
3.4

Minor increases in profits for firm one relative to firm two are seen in all cases. The
amount of these increases changes depending on the unit life, the length of time the units
existing in the market continue to influence sales and on the price electricity. The least
improvement is seen under short unit life spans, relatively long unit influence on sales and
inelastic conditions. The greatest improvement is seen under long unit life spans, short

influence time and inelastic conditions.

96

CHAPTER 5

Conclusions and Contributions

Contributions

There are three significant areas of understanding to which this work contributes. First,
is the use of quality as a strategic lever in a competitive environment. Second, is how
advertising influences quality as a strategic lever in a competitive environment. Third, is how a
discontinuous quality change alters the use of quality as a strategic lever under competitive
conditions while being influenced by advertising. Each of theses topics has been considered
piecemeal before but they have not been considered together so that the interactions may be

examined.

Quality influences on dynamic pricing in 'a duopoly

When considering how to effectively use an aggressive quality policy, one where the
product quality increases faster than the competition’s quality, as a strategic tool there are three
factors that this dissertation examines which a manager should incorporate into his decision.
These factors are the price elasticity, the length of time that an individual unit will exist in the
market relative to the total life of the product line and the length of time dufing which a unit
will continue to influence sales once it has entered the market i.e., quality perception.

Using elasticity as an environmental factor two by two grids may be developed to

summarize these choices. The first of these two grids is depicted in Figure 140. See also Table
97

7. Under lower price elasticity the greatest relative increases in profit may be seen in quadrant

A.

 

Aggressive quality policy in an elastic environment

 

 

 

 

 

 

 

0

£1

‘8” .
'8 Quadrant B Quadrant D
E. 2“‘1 Most Effective Least Effective
o
21’

.9

0

g Quadrant A Quadrant C
E Most Effective 3rd Most Effective
E

o
”E

8:

c:

3

 

Length of time unit influences sales in market

 

 

 

Figure 21 — Profit Advantage when Price elasticity
is higher
The conditions in this quadrant are thus the life of the unit relative to the life of the product
line is the shortest and the length of time that the unit in the market influences sales is the
shortest. The least profit increase over the competitor derived from an aggressive quality
strategy are when the life of the unit is long and the length of time the unit influences sales is
also long. This is not to suggest that a manager would not want to pursue the added profits
that could be obtained from pursuing an aggressive quality policy under the least effective

conditions. Profit is profit under any conditions. It is only to suggest that the greatest returns

98

from such a strategy will be realized under the conditions existing in quadrant A where the
quality strategy is most effective.

Given environmental conditions where the price elasticity is lower there is a somewhat
different set of conditions that will maximize the profits a company will see relative to its

competitor. See Figure 141. See also Table 7. In this environment there is a change in the

 

Aggressive quality policy in an- inelastic environment

 

 

 

 

 

 

9» A
-.§
U
«‘3 Quadrant B Quadrant C
‘91 2nd Most Effective 3rd Most Effective
"5
98’
8
g
g Quadrant A Quadrant D
9.1 Most Effective Least Effective.
E
o
E
c:
3

 

 

Length of time unit influences sales in market

 

 

 

Figure 22 — Profit Advantage Inelastic Demand

position of the least improvement in profitability, quadrant D; it shifts to the bottom, right
position. The conditions for this are a shorter unit life span and a large percentage of time
when existing units in the market continue to influence sales. Summarizing, a firm pursuing an
aggressive quality improvement strategy relative to its competitor can expect the greatest

improvements in either elastic or inelastic conditions when the unit life is large relative to the

99

amount of time existing units in the market influence its sales. However, when low price
elasticity exists it can expect a larger profit relative to its competitor if the life of the unit is
shorter when there is a long impact on sales by individual units. Conversely, when high price
elasticity exists the firm can expect a larger profit relative to its competitor if the life of the unit
is long when there is a long impact on sales by individual units. The interaction between
durability and quality perception tends to be high as a result market saturation somewhat
offsets this effect.

It is also interesting to note that the initial conditions have an impact on the price
trajectory over the entire life of the product line. If there is an initial price difference the fact
that there is a substitutable good in the market will force the firm with the higher price to
lower its price trajectory below that of the firm with the initial price advantage so as to
maximize its profits. While not surprising in and of itself this does suggest that there are some
characteristic of a complex dynamic system present in the price-quality-competition
relationship. Sensitivity to initial conditions is one of the three conditions describing a formally

defined chaotic system.

Advertising and Quality influences on dynamic pricing in a duopoly

When advertising is added as a moderating factor to the price quality relationship as it
influences maximized profits there are two additional conditions added to the analysis. In
addition to price demand elasticity, the life of the unit relative to the life of the product line
and the length of time the individual unit in the market influences sales, advertising to support

an aggressive quality policy or as a deterrent to sales by the firm not pursuing the aggressive

100

quality policy are also considered. These are summarized in Figures 142 to 145. See also Table

9.

 

Aggressive quality policy in an elastic environment

 

 

 

 

 

 

 

 

o A

-_§ with supportive advertising

‘5

% Quadrant B Quadrant D
g 2"d Most Effective Least Effective
“5

:‘a’

B

E
:3 Quadrant A Quadrant C
8 Most Effective 3“] Most Effective
E

o
'3‘

i

G
3

Length of time unit influences sales in market

 

 

 

Figure 23 - Advertising Impact Supporting Quality
(Elastic Demand)

As can been seen in Figures 142 and 143 the most return on an advertising policy
supporting an aggressive advertising policy may be realized when the influence of the
individual unit is short relative to the life of that unit. A firm can expect that the least return on
an advertising policy supporting an aggressive advertising policy relative to increased profits
when compared with its competitor will be when the units in the market have the longest
influence on sales. Furthermore, as in the case with no advertising, the effectiveness will

change under differing elasticity’s. Under elastic conditions the least effectiveness will he with

101

units that have long life spans and long market influences. Under inelastic conditions the least

effectiveness will be with units that have short life spans and long market influences.

 

Aggressive quality policy in an inelastic environment

 

 

 

 

 

 

U

E A with supportive advertising

8
13 Quadrant B Quadrant C
a 2'“, Most Effective 3rd Most Effective
“5
3:13

9

u o
g Quadrant A Quadrant D

8 Most Effective Least Effective '
E

o
“E

if
.3

 

 

Length of time unit influences sales in market

 

 

 

Figure 24 - Advertising Impact Supporting Quality
Inelastic Demand

These results differ somewhat when a firm uses advertising to counter to an aggressive
quality policy. See Figure 144 and 145. See also Table 9. In the low price elasticity case the
results are the same when advertising is used as a supportive tactic to quality improvement. In
contrast when price elasticity is high the most effective use of advertising occurs when the life
of the individual unit is the longest and the influence of the unit on sales in the market place is
shortest. This suggests that the firm that is choosing not to compete on quality might reduce
the profit advantage seen by the firm competing on quality by heavily advertising under these
conditions. See Figure 145.

102

 

 

Longevity of unit relative to life of product line

>

 

Advertising to counter an aggressive quality policy in
an elastic environment

 

 

 

 

Quadrant B Quadrant C
2nd Most Effective 3rd Most Effective
Quadrant A Quadrant D
Most Effective Least Effective

 

 

 

Length of time unit influences sales in market

1r

 

Figure 25 — Counter Advertising Elastic Demand

103

 

 

Advertising to counter an aggressive quality policy in

 

 

 

 

 

 

o A e n u
E an inelastic env1ronment

‘5
-§ Quadrant A Quadrant C
a Most Effective 3“J Most Effective
“5
£1

9

Q)
g Quadrant B Quadrant D
8 2"d Most Effective Least Effective
E

o
’5

U

8‘

.3

 

 

Length of time unit influences sales in market

 

 

 

Figure 26 — Counter Advertising Inelastic Demand

Advertising and Discontinuous Quality influences in a duopoly

In the examination of discontinuous quality improvements it was found that a large
one time improvement did not provide any significant increase in profitability over the case
where quality was improved continuously over time. This is not surprising. Kaizan, the
Japanese philosophy of making small improvements continuously, has long been accepted as a
desirable process in TQM. It was found that advertising assisted the profit differential in the
same manner when it was used in the discontinuous quality case as it did when it was used in

the continuous quality case. See Figures 146 and 147. See also Tables 14 and 15

104

 

Discontinuous quality policy in an elastic

 

 

 

 

 

 

1» 4
;_§ environment with supportive advertising
‘0’
3 Quadrant B Quadrant D
g 2"d Most Effective Least Effective
“6
fl
8
Q)
g QuadrantA Quadrant C
8 Most Effective 3rd Most Effective
E
o
13
it
.3

 

 

Length of time unit influences sales in market

 

 

 

Figure 27 — Discontinuous Quality and Advertising
Elastic Demand

Neither were any differences in the use of advertising as a counter tool to a
discontinuous quality improvement seen relative to its use when countering a continuous

quality improvement policy. See Figures 147 and 148. See also Table 15.

105

 

 

Longevity of unit relative to life of product line

I

 

Advertising to counter discontinuous quality policy
in an elastic environment

 

 

 

 

Quadrant B Quadrant C
2Ml Most Effective 3rd Most Effective
Quadrant A Quadrant D
Most Effective Least Effective

 

 

Length of time unit influences sales in market

 

Figure 28 — Advertising to Counter Discontinuous
Quality Elastic Demand

106

 

 

 

 

Longevity of unit relative to life of product line

D

 

Advertising to counter a discontinuous quality policy
in an inelastic environment

 

 

 

 

Quadrant A Quadrant C
Most Effective 3'd Most Effective
Quadrant B Quadrant D
2'1d Most Effective Least Effective

 

 

Length of time unit influences sales in market

 

Figure 29 - Advertising to Counter Discontinuous
Quality Inelastic Demand

107

 

 

 

Discontinuous qualitypolicy in an inelastic

 

 

 

 

 

 

a)
E i environment with supportive advertising
‘6
% Quadrant B Quadrant C
2% 2"d Most Effective 3rd Most Effective
“5
:15

8

Q)
g Quadrant A Quadrant D
8 Most Effective Least Effective
E

o

5

3‘

.3

 

 

Length of time unit influences sales in market

 

 

 

Figure 30 - Discontinuous Quality and Advertising
Inelastic Demand

Strategic Implications

In order to properly asses the strategic implications of the results of this dissertation it
is necessary to consider several relevant pieces of information. First is the sales response over
time for the two models used to develop the model in this dissertation, the NGM model and
the Erickson model for competitive advertising and the model developed here in. Figure 31
shows the typical sales distribution over time for the model developed in this dissertation.
Figure 32 shows the typical sales distribution over time of the NGM model and Figure 33

shows the Efickson competitive advertising modes showing sales vs. tima

108

 

Typical Sales Dissertation Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I 3000
I 2500
I 2000 l
I .3 15m /
e a /
1000 /
500 x
I 0 .
0 2 4 6 8 10 12 14 16 18 20
1 Years
I
Figure 31 - Typical sales for dissertation model

I . . I
3 Sales Vs Time Typical NGM results
I .
I 1600 '
I 1400 - --
I 1200 — -:- a
1 1000 4 I
I O I
1 D 1
I '5 800 — -_ ~~ ~~ .
I "’ I

600 -. s= ~ ~ ~ 1
I 400 - I
I 200 —— ~» ~ :
! 0 . I
I 0 2 4 6 8 10 12 14 16 18 20 I
I Years I
I I
. I

 

Figure 32 — Typical NGM sales distribution

109

 

 

Erickson Sales Response to Advertising

 

89le

 

 

Time

 

 

 

Figure 33 — Typical Erickson Sales Response over
Time to Advertising

In the case of the Erickson model sales increase initially and eventual reach a steady
state. This is because the Erickson model incorporates neither dynamic pricing nor improving
product quality into the sales relationship. Both of these factors influence sales above and
beyond the influence that advertising imparts to sales alone. In the case of the NGM model
sales remain relative steady for a period of time and then increase radically as the price is
reduced so the firm may maximize profits. In the case of the model developed in this
dissertation the sales initially decline a small amount and then increase as the price declines.
The initial decline in sales represents the competitive situation created by a substitutable
product in a competitive environment This clearly indicates that a manager should not
attempt to maintain or increase prices early in the life cycle of a product line if they intend to

maximize the total profits for the product line over its life. Of more interest to a manager are

110

the implications a comparison of the price trajectories of the NGM model and the model
developed in this work product The price trajectories are depicted in Figure 34 and Figure 35.
Note that the Erickson model did not incorporate pricing into the sales model and is therefore

not included in this analysis.

 

Typical Price Trajectory from this Work

 

 

 

 

 

 

 

 

 

 

 

 

 

l
I 4000 _\ - V r
I m- - - - - - I
I “r I
I 2000 ~ = - , - I
I 1000 — - I
I o . I
I 0 5 10 15 20 I
I Year: I
I I
Figure 34 -— Price Trajectory from this Work
Typical NGM Price Trajectory
7000
5000
-
3000
1000
Years

 

 

 

Figure 35 — Typical NGM Price Trajectory
1 1 1

In the case of the NGM model where competition is not explicitly modeled the price
trajectory increase initially and then declines while quality continuously increases. This suggests
that to maximize profits a manager should increase prices during the initial phase of the
product life cycle. While a price increase may be interpreted as a signal of quality in accordance
with the idea that consumers equate price with quality, see for example (Irandoust 1998 and
. Rao, 1989 #27), it is not conduciveito maximum profitability in a competitive situation. When
competition is explicitly incorporated into the model in this dissertation the price trajectory
may be seen to decline immediately and it continues down at various rates of change during
the entire life of the product This means that a manager should use the quality diffusion
aspects of the market to signal quality to the consumer. This strategy will increase the number
of units in the market; enhance the rate of diffusion of the quality information to consumers
and increase profits to a greater level than maybe achieved by a short term increase in price.
Conceptually this indicates that the connection between price and quality is not robust The
result of the diffusion of quality units into the market dominates the perception that a high
price indicates higher levels of quality. This position is supported by the concept that quality
and price should not be directly connected in the consumers’ perception. See for example
(Gerstner 1985; Lichtenstein and Burton 1989; Riesz 1978; Riesz 1979; Sprokes 1977). The
concept that consumers will not relay on the price-quality-advertising relationship when
information to the contrary is available via alternative mechanisms, such as individual
information searches, see (Milgrom and Roberts 1986a; Milgrom and Roberts 1990; Nelson
1974; Nelson 1970), is reaffirmed by the model developed in this dissertation.

Relative to continuous and discontinuous quality improvements this work indicates
that the firm should consider the environment, the useful life expectance of a unit and the

112

length of time that a unit influences consumer purchase decisions when using quality as a
strategic lever. When price elasticity is both relatively high and low quality as a strategic lever is
most effective when the unit life is relatively short when compared to the life of the product
line and when the length of time that the unit influences consumer purchasing decisions is
relatively short. Therefore a manager should emphasize discontinuous quality improvements
which will make consumers more inclined to replace the individual unit before its functional
life has expired. For example, a lawn tractor might have a useful life of ten years and a truly
satisfied customer might continue to praise the machine for the majority of that time. If
however during that ten year peiiod a new discontinuous improvement is made to the line of
lawn tractors, such as the development of a cutting mulching system, that consumer while
satisfied will be more inclined to replace that unit before its entire useful life has expired. This
is in contrast to incremental improvements that the consumer might not view as sufficiently
valuable to justify the expense of early unit replacement The implication of this conceptually
is that research and development expenditures that aim at large changes in quality are
potentially beneficial if they reduce the unit life expectancy and the length of time units
influence consumer purchasing decisions.

In all cases studied in this work advertising while providing an increase in profitability
during the life of the product line it is always dominated by a quality strategy. As a result a
manager should consider an advertising policy as a means of assisting a quality strategy or in
the case of a manager seeking a means of reducing the profitability advantage of a competitor,
as a minor counter to a quality strategy; he should not consider it a replacement for either a

continuous or discontinuous quality improvement strategy.

113

Concluding Remarks

This research has examined optimal pricing for two profit maximizing firms using
different advertising and quality policies. An optimal control model utilizing different demand
elasticity’s, different unit life spans and differing lengths of time during which units existing in
the market influenced sales was solved numerically and the results tabulated. Prior to this work
a dynamic pricing optimal control model explicitly including competition had not been
developed. Prior to this work advertising had not been included in this type of quality-price
model. Prior to this work, discontinuous quality improvements had not been explicitly
included in this type of quality-price model.

The results reaffirm the importance of quality as a strategic lever and demonstrate
under what type of conditions a quality based strategy, continuous or discontinuous, might be
most effective in a competitive environment. The results also Show under what conditions
advertising might be most effectively utilized by a firm’s management to increase its
profitability over a competitor and thereby increase its share holder value relative to that
competitor. New areas of investigation are also suggested by the results. Different levels of
advertising effectiveness need to be examined. Different entry times into the market should be

considered. Advertising policies other than continuous ones also might be considered.

114

APPENDICES

Appendix 1

 

Run 5 9:1 .3,D1=3.DZ=.75

 

 

 

 

 

 

Figure 36 - Run 5 Scenario 1.0

Run 6 e=1.3,D1=3,D2=2.25

 

 

 

 

 

 

 

1.01,:

 

 

 

 

 

----- P2II

1____.4 _WW __.—.._. W

 

Figure 37 - Run 6 Scenario 1.0

115

 

 

 

Run 7 8:1 .3,D1=10,02=2.5

 

 

 

 

 

 

 

Figure 38- Run 7 Scenario 1.0

 

 

Run 8 e=1 .3,D1 =1 0,DZ=7.5

 

 

 

 

 

 

 

Figure 39 - Run 8 Scenario 1.0

116

 

 

 

Run 9 e=0.7,D1=3,DZ=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\ ——Price 1—II
1 I
10 15 20 I

Figure 40 — Run 9 Scenario 1.1
Run 10 e=0.7,D1=3,02=2.25 I
30000 .
25000- — - I
20000-« 2 2 I
15000 ~ —» I—Price 1 I
!
10000 «=8 g, = =~=ia - =9 I
5000 . I
0 . I
0 5 10 15 20 I
I

 

Figure 41 — Run 10 Scenario 1.1

117

 

 

Run 11 e=0.7,D1=10,02=2.5

 

 

 

 

1O 15 20

 

 

 

Figure 42— Run 11 Scenario 1.1

 

Run 12 e=0.7,D1 =10,D1 =7.5

 

10000

9000 --

7000~

5000 ~» -~

2000” ,

10001

 

 

 

 

10 20

I—Pricet’

 

 

Figure 43 — Run 12 Scenario 1.1

118

 

 

Run 17, e=0.7,D1=3,02=0.75

 

 

 

 

 

 

mmm_ _ __I

 

 

 

 

 

 

 

 

 

 

 

Figure 45— Run 18 Scenario 1.2

119

 

-——P1
----- P2!
________1
Figure 44 — Run 17 Scenario 1.2
Run 18, e=0.7,D1=3,D2=2.25
22000
I 20000 — =—
18000 1 =
16000 ~ ~ =
14000 -- . - . ”_I.
12000 .- -- ~ P1I
1omo .12 7 7 """ P2:
8000 ~
6000 «— 3 — -=
4000 —= — ~— - —~
2000 I
0 5 10 15 20

 

 

 

 

 

Run 19, e=0.7,D1 =10, D2=2.5

 

 

 

 

 

 

 

Figure 46 - Run 19 Scenario 1.2

 

 

Run 20, e=0.7,D1 =1 0,02=7.5 i

 

 

Prioet
----- P0092i

 

 

 

 

 

 

. Figure 47 - Run 20 Scenario 1.2

120

 

I Run 21, e=1.3,D1=3,D2=.75

 

 

 

 

 

 

 

 

fifirw __ M

 

Figure 48 — Run 21 Scenario 1.2

 

Run 22, e=1.3,D1=3,02=2.25

 

 

2 ‘ 2 , ----- P 2 I

 

 

 

 

 

 

I__ ____._ . _..__._-

Figure 49 - Run 2 Scenario 1.2

121

 

Run 23,e=1.3,D1 =1 0.02:2.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

' 5000
4500 -+ =
4000 2 =
I—-P 1 I
a 3500 - ~ ~ I _____ P2 II
3000 — = r I
2500«~- =2 =- =- = — = I
2000 . 1 I
0 5 10 15 20 I
Years I
I
Figure 50 - Run 23 Scenario 1.2
Run 24,e=1 .3,D1 =1 0,D2=7.5
I - r
2 - _B‘fi
a =~ = ----- P 2 I
0 5 10 15 20
Years

 

Figure 51 - Run 24 Scenario 1.2

122

 

Run 25, e=0.7,D1=3,02=.75

 

 

 

 

 

 

Years

 

Figure 52 — Run 25 Scenario 1.3

 

I Run 26,e=0.7,D1=3,D2=2.25

 

 

 

   

 

 

 

 

I Years

 

Figure 53 - Run 26 Scenario 1.3

123

 

 

Run 27, e=0.7,D1 =10,02=2.5

 

 

 

 

 

 

 

 

Figure 54— Run 27 Scenario 1.3

 

 

 

Run 28,e=0.7,D1 =1 0,02=7.5

 

 

 

 

 

Years

20

 

 

 

 

Figure 55- Run 2881:13an 1.3

124

 

 

 

Run 29,e=1 .3,D1=3,D2=.75

 

 

 

 

10 15
Years

Figure 56- Run 29 Scenario 1.3

20

.---.--P2

I

—P1

 

 

L—

L_ m__

 

 

Run 30,9:1 .3,D1=3,D2=2.25

 

 

 

 

 

 

 

10 15
Years

Figure 57- Run 30 Scenario 1.3

125

20

 

 

 

 

 

 

 

 

Run 31 ,e=1 .3,D1 =1 0,D2=2.5

 

1500 ~

 

 

 

 

 

Years

I
'20 I

 

Figure 58- Run 31 Scenario 1.3

 

 

Run 32,9:1 .3,D1 =1 0,D2=7.5

 

3500 ==~ = ~ = 22 ==2 ==-

25001

1500 -« = = 22 == . ==

 

 

 

 

 

20

 

Figure 59- Run 32 Scenario 1.3

126

 

Run 33,e=0.7,D1 =3,DZ=0.75

 

 

 

 

 

 

 

Figure 60 — Run 33 Scenario 1.4

 

__1

Run 34,e=O.7,D1 =3,D2=2.25

 

 

 

 

 

 

 

 

I
25000 I
|

20000 7 , I
15000 1 -, r 7 ., _—F;TII
10000 7 " ' - -- -— ._.. . ___ fir """ P JII
5000 « = 2 . , \ I

I

0 . ‘ I

0 5 10 15 20 I

Years I

 

Figure 61— Run 34 Scenario 1.4

127

 

Run 35,e=0.7,D1 =1 0,DZ=2.5

 

 

 

 

 

 

 

 

Figure 62— Run 35 Scenario 1.4

 

Run 36,e=0.7,Dt =1 0,D2=7.5

 

 

----- P2

 

 

 

 

Years

 

 

 

Figure 63- Run 36 Scenario 1.4

128

 

 

Run 37,e=1 .3,D1 =3,D2=.75

 

 

 

 

Figure 64— Run 37 Scenario 1.4

 

 

 

 

Run 38,6:1.3,D1 =3,D2=2.25

 

 

 

 

 

 

 

 

15

20

 

 

 

Figure 65— Run 38 Scenario 1.4

129

 

 

 

Run 39,e=1 .3,D1 =1 0,D2=2.5

 

 

 

 

 

 

 

Figure 66— Run 40 Scenaiio 1.4

Run 40,e=1.3,D1=10,D2=7.5 I
I

 

 

 

 

 

 

 

Figure 67— Run 40 Scenario 1.4

130

 

8000

Run 1 ,e=0.7,D1=3,02=0.75

 

7000~

5000~
94000.

3000 ~ --
2000 ~ ,

1000 -

 

 

 

 

""""" WK

 

 

 

Years

 

 

Figure 68 — Run 1 Scenario 2.0

 

 

1 0000
8000
6000
4000
2000

Run 2, e=0.7,D1=3,DZ=2.25

 

 

 

 

 

 

 

Price 1 I
----- Price 2 I

 

 

 

 

 

 

 

 

Years

Figure 69— Run 2 Scenario 2.0

131

 

 

8000

Run 3, e=0.7,D1=10,DZ=2.5

 

7000-I==A

60001

5000-«=k-
4000-wwr=

3000 I

2000-I22
1000-2= 2

 

 

 

Price 1 I

 

 

 

 

 

Years

20

----- Price2 I

 

 

Figure 70— Run 3 Scenario 2.0

 

Run 4,e=0.7,D1=10,02=7.5

 

 

 

Price 1
----- Price 2

 

 

 

 

 

 

 

Figure 71— Run 4 Scenario 2.0

132

 

 

Run 5,e=1.3,D1 =3,02=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Price 1
I ----- Price 2
1000 2 - ~
I 0 . I
I 0 5 10 15 20 I
I Years
I
Figure 72— Run 5 Scenario 2.0
Run 6,e=1 .3,D1 =3,D2=2.25 I
10000 I
8000
6000 \\ I Price 1 II
4000 """""""""""" 2 . . I ----- Price 2 II
2000 l
O . 1
0 5 1O 15 20

Years

 

 

Figure 73— Run 6 Scenario 2.0

133

 

 

Run 7,e=1 .3,D1 =10,DZ=2.5

 

5000

4000 +

3000*

2000 ~ ~

1000 ~

 

 

 

 

Years

Figure 74— Run 7 Scenario 2.0

20

 

 

Price 1
----- Price 2

 

 

 

 

 

Run 8,e=1 ;3,D1=10,02=7.5

 

5000

4000~~ ,

3000 A
2000 _
1000 -

 

 

 

 

Years

20

 

 

Price 1 I
----- Price 2 I

 

 

 

Figure 75— Run 8 Scenario 2.0

134

 

 

 

Run 9,e=0.7,D1 =3,D2=0.75

 

 

 

 

 

Years

 

 

 

 

 

 

Figure 76 — Run 9 Scenario 2.1

 

 

Run 10,e=0.7,D1 =3,D2=2.25

 

 

 

 

 

 

 

 

Years

Figure 77— Run 10 Scenario 2.1

135

 

Price 1
I ----- Price 2

 

 

 

 

Run 11,e=0.7,D1 =10,D2=2.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 5 1O 15 20
I Years
Figure 78 - Run 11 Scenario 2.1
I
Run 12,e=0.7,D1=10,D2=7.5 I
8000 I
7000 I I
6000 ~ I I
5000 _ 1,3,, . I
I » :WI
I 3000 _ I I ----- rice 2
I 2000 — - I
I o T i T I
I O 5 10 15 20 I
I Years

 

Figure 79 — Run 12 Scenario 2.1

136

 

Run 13, e=1.3,D1=3,D2=0.75

 

 

 

 

 

 

 

 

 

..

 

 

 

 

 

 

 

 

 

 

 

Years

 

 

 

0 5 10 15 20
' Years
Figure 80— Run 13 Scenario 2.1

I Run 14,e=1.3,D1=3,D2=2.25 I
I I
I

I 10000 I
I 8000 I
I 6000 \ i I Price 1 II
I 4000 """"""""""" W. V I ----- Price 2 II
I 2000 I
o g I
I 5 10 15 20 I

 

Figure 81— Run14 Scenario 2.1

137

 

 

Run 15,e=1.3,D1=10,D2=2.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Price 1 I
I ----- Price 2 I
5 10 15 20 I
Years I
L
Figure 82- Run 15 Scenario 2.1
I Run 16,e=1.3,D1=10,D2=7.5 I
I I
I I
I I
Price 1
L ----- Price 2
5 10 15 20 I
Years I
J

 

 

Figure 83— Run 16 Scenario 2.1

138

 

 

Run 17,e=0.7,D1=3,D2=0.75

 

 

 

 

 

 

 

Price 1
----- Price 2

 

 

 

 

 

Figure 84 - Run 17 Scenario 2.2

 

 

25000
20000
1 5000
1 0000

5000

Run 18,e=0.7,D1 =3,D2=2.25

 

 

 

 

 

 

 

 

 

I Price 1 I
I ----- Price 2

 

 

 

Figure 85- Run 18 Scenario 2.2

139

 

 

 

 

 

Run 19,e=0.7,D1=10,D2=2.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Price 1
I I ----- Price 2
I
5 10 15 20 I
Years I
I
Figure 86— Run 19 Scenario 2.2
Run 20,e=0.7,D1 =10,D2=7.5

I Price 1 I
I ----- Price 2 ,I

 

 

 

 

Figure 87— Run 20 Scenario 2.2

140

 

 

 

 

Run 21 ,e=1.3,D1=3,D2=0.75

I
I
5000~~— a I e I
moodkn ’7 ' M I I
I
l
I
I

 

 

 

 

 

., 30001 ‘~ ------------ -~—-~\ I P5061 j
-. L ----- Pnce2
2000 « —— , - *

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1000 I —*
o - I
0 5 10 15 20
Years
L I
Figure 88— Run 21 Scenario 2.2
I Run 22,e=1.3,D1=3,D2=2.25 I
I I
I 10000
I
I 8000
i \ I I
I a 6000 \ I Price 1 ‘1
I ................ N w . ‘ I ----- Price 2 I
I 2000
0 . I
I 0 5 10 15 20 I
I Years I

 

Figure 89-— Run 22 Scenario 2.2

141

 

Run 23,e=1.3,D1=10,DZ=2.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Years

20

 

 

 

 

I
I
I
I 500°
I 3000 “i I Price 1 I
I 2000 « -- I ----- Price 2 I-
I _
I 1000 4-
I 0 I
I 0 5 10 15 20 I
I Years I
I ,
Figure 90— Run 23 Scenario 2.2
I Run 24,e=1.3,D1=10,DZ=7.5 7
I I
I
I Price 1
I ----- ' Price 2

 

Figure 91— Run 24 Scenaxio 2.2

142

 

Run 25,e=0.7,D1=3,D2=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Price 1 I
L ----- Price 2 I
I
I I
Figure 92— Run 25 Scenario 2.3
Run 26,e=0.7,D1=3,D2=2.25
25000
20000
15000 I Price 1 I
0’ I ----- Price 2 I
10000 N - - .. I '
5000 \
\
O . I
5 10 1 5 20
Years
Figure 93— Run 26 Scenario 2.3

143

 

 

Run 27, e=0.7,D1 =1 0,D2=2.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Price 1 I
----- Price 2 I
1000 I» e e
O . 1 T
0 5 10 15 20
Years
Figure 94— Run 27 Scenario 2.3
I
I Run 28,e=0.7,D1=10,D2=7.5
8000
7000 1
6000 1
5000 i Price 1 II'
4000 « _____ P, 2
3000 , L "9’9 I
2000 - ‘-
1000 --—~ , we —-
I O I T T
I 0 5 10 15 20

 

 

 

 

 

 

 

 

 

 

 

Figure 95— Run 28 Scenario 2.3

144

 

 

Run 29,e=1 .3,D1 =3,D2=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 I
0 5 10 15 20
Years
Figure 96— Run 29 Scenario 2.3
Run 30,e=1 .3,D1=3,DZ=2.25
10000
8000
6000 I Price 1
6 \Km ________ I . I
4000 ----- , . I ----- Pnce 2
2000
o i T
0 5 10 15 20
Years

 

Figure 97— Run 30 Scenario 2.3

145

 

 

 

Run 31 ,e=1 .3,D1=10,DZ=2.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5000
4000 I
3000 ~ -——Price 1
2000 5 ----- Price 2 I
1000 — i A e i
O 5 = r
0 5 10 15 20
Years
Figure 98— Run 31 Scenario 2.3
Run 32,e=1 .3,D1 =10,DZ=7.5
6000
5000 w
4000 i P ' 1
rice
3000 ~
I ----- Price 2 I
2000 ~ I
1000—- ~= ~ ~ W
0 I I
0 5 10 15 20

Years

 

Figure 99— Run 32 Scenario 2.3

146

 

 

 

 

Run 33,e=0.7,D1 =3,02=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Price 1 "
I """ Price 2 J
'
I O I
I 0 5 10 15 20
I Years .
I I

Figure 100— Run 33 Scenario 2.4

I Run 34,e=0.7,D1=3,D2=2.25
I
I 25000
I 20000
I 15000 I Price 1 I
I 10000 x I ----- Price 2 I
I 5000 \\
I 0 I I

 

Years

 

Figure 101— Run 34 Scenario 2.4

147

 

 

Run 35,e=0.7,D1=10,02=2.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Price 1 E
t- - - - Price 2 i
O I
O 5 1O 15 20
Years
Figure 102— Run 35 Scenario 2.4
Run 36,e=0.7,D1=10,02=7.5

I Price 1 I
----- Price 2 I

I

I

 

 

 

 

 

 

Figure 103— Run 36 Scenario 2.4

148

 

 

Run 37,e=1 .3,D1 =3,02=0.75

 

 

 

 

 

 

___J

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I
I
I Price 1
I ----- Price 2
I
I 0 ,
I 0 5 10 15 20
I Years
Figure 104— Run 37 Scenario 2.4
I Run 38,e=1.3,D1=3,D2=2.25
I 10000
8000
6000 \\ I Price 1 '
4000 """"""""""""" ~ I ----- Price 2
2000
0 I e
5 10 15 20 I
Years .
4

 

 

Figure 105— Run 38 Scenario 2.4

149

 

Run 39,e=1 .3,D1=10,DZ=2.5

 

4000 -

 

3000

 

 

I Price 1 I
L- - - - Price 2

 

 

 

Years

 

Figure 106— Run 39 Scenario 2.4

 

Run 40,9:1 .3,D1 =10,DZ=7.5

 

 

Price 1
----- Price 2

 

 

F...-

 

 

 

 

 

Years

 

Figure 107— Run 40 Scenario 2.4

150

 

——-= “-4

Run 41 ,e=0.7,D1=3,02=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I
I
I
I
I
I
I Price 1 I:
I ' “ * I ----- Price 2 II

, I
I I
I 0 I T
I 0 5 10 15 20 I
I Years I
I

Figure 108- Run 41 Scenario 2.5
I Run 42,e=0.7,D1=3,DZ=2.25
I
I 25000
20000
a 15000 \ I Price 1
, 10000 \ “““ Price 2
5000 \
0 I I
0 5 10 15 20
Years

 

 

Figure 109— Run 42 Scenario 2.5

151

 

Run 43,e=0.7,D1 =1 0,D2=2.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I Price 1
I ----- Price 2

I

I

; O I

I 5 10 15 20

Years
I
Figure 110— Run 43 Scenario 2.5
I Run 44,e=0.7,o1=10,02=7.5 I
Price 1

I ----- Price 2

 

1000

 

 

 

 

Figure 111— Run 44 Scenario 2.5

152

20

 

 

 

Run 45,e=1 .3,D1=3,DZ=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5000
I I
I a 3000 e \ f Price 1
I I—----Pric92
I I
I 1000 —
I 0
I 0 5 10 15 20
I . Years I
I
Figure 112— Run 45 Scenario 2.5
I I
I Run 46, e=1.3,D1=3,DZ=2.25 I
I 10000
I 8000 I
I 6000 ___- IF Price 1 I
I W .............. . I
I 4000 ----- .2 I ----- Price 2 II
2000
O I 7 I
0 5 10 15 20 I
Years '

 

Figure 113— Run 46 Scenario 2.5

153

 

Run 47,e=1.3,D1=1 0,DZ=2.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5000
I 4000 ~- -
I I
I a 3000 ~ I Price 1 II
I 2000 5 """ Price 2 II
I . I
I 1000 — , ~ I
I o I I
I 0 5 10 15 20 I
L I
Figure 114— Run 47 Scenario 2.5
Run 48,e=1 .3,D1 =1 0,DZ=7.5
I I
I
I Price 1
I """ Price 2 I

 

 

 

 

 

 

I
I Years . I
’ I

 

Figure 115 — Run 48 Scenario 2.5

154

 

Run 49,e=O.7,D1 =3,DZ=0.75

 

 

 

 

 

 

 

10 15
Years

 

 

 

 

Figure 116 - Run 49 Scenario 2.6

 

 

Run 50,e=0.7,D1=3,DZ=2.25

 

 

 

 

 

 

Years

 

 

 

 

Figure 117 — Run 50 Scenario 2.6

155

 

 

Run 51 ,e=0.7,D1=10,DZ=2.5

 

 

 

 

 

 

 

Years

 

Figure 118 — Run 51 Scenan'o 2.6

 

 

Run 52,e=0.7,D1=10,02=7.5

 

 

 

 

 

Years

 

Figure 119 — Run 52 Scenario 2.6

156

 

 

 

 

Run 53,6:1.3,D1=3,02=0.75

 

 

 

 

 

 

 

Years

 

Figure 120 — Run 53 Scenario 2.6

 

 

 

 

Run 54,9:1 .3,D1=3,02=2.25

 

 

 

 

 

 

 

 

 

Figure 121 — Run 54 Scenario 2.6

157

 

 

 

 

 

Run 55,9:1 .3,D1 =1 0,DZ=2.5

 

 

 

 

 

Years

 

 

 

Figure 122— Run 55 Scenario 2.6

 

 

Run 56,9:1 .3,D1=10,DZ=7.5

 

 

 

 

 

 

 

 

Years

 

 

Figure 123 — Run 56 Scenario 2.6

158

 

Run 57,e=O.7,D1=3,DZ=0.75

 

 

 

 

   

 

 

 

Years

 

Figure 124 — Run 57 Scenario 2.7

 

 

Run 58,e=0.7,D1 =3,D2=2.25

 

 

P1
....... p2

 

 

 

 

 

 

 

 

 

 

10 15 20
Years

 

Figure 125 — Run 58 Scenario 2.7

159

 

 

Run 59,e=O.7,D1 =1 0,DZ=2.5

 

 

 

 

 

10 15
Years

20

 

 

 

Figure 126 — Run 59 Scenario 2.7

 

 

Run 60,e=O.7,D1 =1 0,02=7.5

 

 

 

 

 

1O 15
Years

20

 

 

 

Figure 127 — Run 60 Scenario 2.7

160

 

Run 61 ,e=1 .3,D1 =3,02=0.75

 

 

 

 

 

 

Yours

éo

 

Figure 128 - Run 61 Scenan'o 2.7

 

 

Run 62,0:1 .3,D1 =3,02=2.25

 

 

 

 

 

Years

 

 

Figure 129 — Run 62 Scenario 2.7

161

 

 

 

 

 

 

 

I
I Ran 63,9:1.3,D1=10,02=2.5

 

 

L;““P2I

 

 

 

 

 

I Yam

 

 

 

Figure 130 — Run 63 Scenario 2.7

 

Run 64,0:1 .3,D1 =10,DZ=7.5

 

 

 

 

 

 

 

Years

 

 

Figure 131 — Run 64 Scenario 2.7

162

 

Run 65,e=o.7,D1=3,02=0.75

 

 

 

 

 

 

 

 

 

Years

 

 

Figure 132 — Run 65 Scenario 2.8

 

Run 66,e=O.7,D1 =3,DZ=2.25

 

 

   

 

 

 

Years

 

 

Figure 133 — Run 66 Scenario 2.8

163

 

 

 

 

 

 

Run 67,e=o.7,D1 =1 0,02=2.5

 

 

 

 

 

1O 15
Your:

Figure 134 — Run 67 Scenario 2.8

20

 

Run 68,8=0.7,D1 =1 0,DZ=7.5

 

 

 

 

 

 

1O 15

 

 

Figure 135 — Run 68 Scenario 2.8

164

 

 

 

Run 69,0:1 .3,D1=3,DZ=0.75

 

 

 

*h————.-.——M_‘

 

 

 

 

10 15 20
Your:

 

 

Figure 136 — Run 69 Scenario 2.8

 

 

 

 

Run 70,e=1 3,01%,DZ=2.25
I
I

 

 

 

 

 

 

 

Yam I

Figure 137 — Run 70 Scenario 2.8

165

 

I Run 71 ,e=1 .3,D1=10,02=2.25

 

 

 

 

 

 

Years I

 

Figure 138 — Run 71 Scenario 2.8

 

 

 

Run 72,e=1 .3,D1=10,Dz=7.5 I
I
I

 

 

 

 

 

 

Years i

 

Figure 139 — Run 72 Scenario 2.8

166

Appendix 3

 

 

Run 1 ,e=0.7,D1 =3,D2=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'— p?
----- P 2
2000 ~r
1000 « i
0 I
0 5 10 15 20
Years
Figure 140 — Run 1 Scenario 3.0
Run 2,e=0.7,D1=3,D2=2.25
25000
20000
15000 __ p 1
a
10000 M ----- P 2
5000 \\
O I I
5 10 15 20
Years

 

Figure 141— Run 2 Scenario 3.0

167

 

 

 

 

 

Run 3,e=0.7,D1 =1 0,DZ=2.5

 

 

 

 

 

 

 

Years

 

Figure 142— Run 3 Scenario 3.0

 

 

 

Run 4,e=0.7,D1 =10,02=7.5

 

 

 

 

 

 

 

 

Figure 143— Run 4 Scenario 3.0

168

 

 

 

 

Run 5,e=1 .3,D1 =3,DZ=0.75

 

 

 

 

 

 

 

 

 

 

 

 

0
0 5 10 15 20
Years
Figure 144— Run 5 Scenario 3.0
Run 6,e=1 .3,D1 =3,02=2.25
10000
8000

 

 

 

 

 

» ~.- --------------
............. P2

‘ ‘

2000 \

 

 

 

 

 

 

Years

 

Figure 145— Run 6 Scenario 3.0

169

 

 

 

 

Run 7,e=1 .3,D1 =1 0,DZ=2.5

 

 

 

 

 

 

Venn:

 

20

 

 

Figure 146— Run 7 Scenario 3.0

 

 

Run 8,e=1 .3,D1 =1 0,DZ=7.5

 

 

 

 

 

 

 

2000 A
1000—I~ c, i
0 I .
0 5 10 15 20
Yeans

 

 

Figure 147— Run 8 Scenario 3.0

170

 

 

 

 

 

 

Run 9,e=0.7,D1 =3,D2=0.75

 

 

 

 

 

 

 

 

 

 

Figure 148 — Run 9 Scenario 3.1

 

 

Run 10,e=0.7,D1=3,Dz=2.25

 

25000
20000

 

 

 

 

15000 I—p1
10000 \\ I """ P2

 

 

 

5000 \

 

 

 

 

Years

 

Figure 149— Run 10 Scenario 3.]

171

 

 

 

Run 1 1 ,e=0.7,D1 =10,D2=2.5

 

 

I——P1

30005 I ..... p2

 

 

 

2000 —

 

 

 

 

Figure 150— Run 11 Scenario 3.1

 

 

Run 12,e=0.7,D1=10,02=7.5

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 151- Run 12 Scenario 3.1

172

 

 

 

 

Run 13,e=1 .3,D1=3,D2=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

— P 1
,_ ----- P 2
0 5 I
0 5 10 15 20
Years
Figure 152— Run 13 Scenario 3.1
Run 14,e=1.3,D1=3,02=2.25
10000
8000
6000 V \I\ — P 1
a " ‘ - ............
4000 ‘ """""" t ----- P 2
2000
0 I . I
0 5 10 15 20
Years

 

Figure 153- Run 14 Scenario 3.1

173

 

 

 

Run 15,e=1 .3,D1 =1 0,02=2.5

 

 

 

 

 

 

 

 

Years

 

Figure 154— Run 15 Scenario 3.1

 

 

Run 16,e=1.3,D1=10,D2=7.5

 

 

 

 

 

 

 

 

 

 

0 5 10 15 20

 

Figure 155— Run 16 Scenario 3.1

174

 

 

 

 

Run 1 7,e=0.7,D1 =3,D2=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o I
0 5 10 15 20
Years
Figure 156— Run 17 Scenario 3.2
Run 1 8,e=0.7,D1=3,D2=2.25
25000
20000
15000 __ P 1
a \ ----- P 2
5000 ‘\
O I
0 5 10 15 20

Years

 

Figure 157— Run 18 Scenario 3.2

175

 

 

Run 1 9,e=0.7,D1=10,02=2.5

 

 

 

 

 

 

 

 

 

Years

 

 

Figure 158— Run 19 Scenario 3.2

 

 

Run 20,e=0.7,D1 =1 0,D2=7.5

 

 

 

 

 

 

 

 

 

 

 

 

Figure 159- Run 20 Scenario 3.2

176

 

 

Run 21 ,e=1.3,D1=3,D2=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5000
4000 \.
‘0 ~ I
2000 x 3 ..... P 2
1000
o .
0 5 10 15 20
Years
Figure 160— Run 21 Scenario 3.2
Run 22,6:1 .3,D1=3,D2=2.25
10000
8000
6000 ._... p 1
a N ..........
4000 x """" = I """ P 2
2000
0 I - r
5 10 15 20
Years

 

Figure 161— Run 22 Scenado 3.2

177

 

 

 

Run 23,e=1 .3,D1 =1 0,D2=2.5

 

 

 

 

 

 

 

 

 

.. I-———P1
2000 ~ 7' ~ ~ . — i=7 \ I ..... p2
1000 . - if r
0 e f
0 5 10 15 20

 

Figure 162— Run 23 Scenario 3.2

 

 

Run 24,e=1 .3,D1 =10,D2=7.5

 

 

 

 

 

 

 

 

 

 

 

 

Figure 163— Run 24 Scenario 3.2

178

 

 

Run 25,e=0.7,D1 =3,D2=0.75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 I
0 5 10 15 20
Years
Figure 164 - Run 25 Scenario 3.3

I
I Run 26,e=0.7,01=3,02=2.25
I 25000
I 20000 - , «

15000 — « - <

10000 -
I 5000 .

0 I

 

 

 

 

 

Figure 165 — Run 26 Scenario 3.3

179

 

 

 

 

 

 

 

 

 

Run 27,e=0.7,D1=10,D2=2.5

 

 

 

 

 

 

 

 

Years

Figure 166 — Run 27 Scenario 3.3

 

Run 28,e=0.7,D1=10,D2=7.5

 

 

 

 

 

 

 

 

 

Figure 167 — Run 28 Scenario 3.3

180

 

Run 29,e=1 .3,D1=3,DZ=0.75

 

Q
a...
-.
‘Q

 

 

 

 

 

 

 

 

 

 

 

 

 

 

' " ‘ ' ~. — P 1
F‘F\\\\ ..... [:2
_
I 0 ,
I 0 5 10 15 20
I Years
I
Figure 168 -— Run 29 Scenario 3.3
F
I Run 30,e=1 .3,D1=3,D2=2.25
— P 1 I
----- P 2

 

 

 

 

 

 

0 5 10 15 20

 

 

I
1

 

Figure 169 - Run 30 Scenario 3.3

181

 

 

 

 

Run 31 ,e=1 .3,D1 =10,DZ=2.5

 

‘ .
~
~
‘ .
. §
‘

 

 

 

 

Years

20

 

 

 

 

Figure 170 — Run 31 Scenario 3.3

 

 

 

Run 32,e=1 .3,D1=10,D2=7.5

 

 

 

 

 

20

 

 

 

 

 

Figure 171 — Run 32 Scenario 3.3

182

 

 

 

Run 33,e=0.7,D1=3,D2=0.75

 

 

 

 

 

Years

20

 

Figure 172 — Run 33 Scenario 3.4

 

 

Run 34,e=0.7,D1 =3,DZ=2.25

 

 

 

 

 

 

 

Figure 173 — Run 34 Scenario 3.4

183

 

 

 

 

 

 

 

 

 

Run 35,e=0.7,D1 =1 0,DZ=2.5

 

 

 

 

 

 

 

Years

 

Figure 174 — Run 35 Scenario 3.4

 

 

 

Run 36,e=O.7,D1 =10,D2=7.5

 

  

 

I—P1.
1 ----- Pa

 

 

1000 ~

 

 

 

Years

Figure 175 - Run 36 Scenario 3.4

184

 

 

Run 37,e=1.3,D1=3,D2=0.75 I

 

 

.
c
. o
.

 

 

 

 

 

 

 

Years

 

 

Figure 176 — Run 37 Scenario 3.4

 

Run 38,e=1 .3,D1=3,DZ=2.25

 

 

 

 

 

 

 

 

 

Figure 177 — Run 38 Scenario 3.4

185

 

Run 39,9:1 .3,D1=10,D2=2.5

 

5000 I
4000 1,-
3000 «

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2000 - ,
1000 ~
0 I I
0 5 10 15 20
Years
Figure 178 — Run 39 Scenario 3.4
Run 40,e=1 .3,D1=10,DZ=7.5
6000
5000 ~
4000 ~ ,
3000 ~ ~ -+ e
2000 _._ _ __..__ ..
1000 — » - e ~ v ~
0 I
0 5 10 15 20

Years

 

Figure 179 — Run 40 Scenario 3.4

186

 

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