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Doktorat der Sozial- und
Wirtschaftswissenschaften
1. Beurteilerin/1. Beurteiler: Ord.Univ.Prof.Dr. Abele
2. Beurteilerin/2. Beurteiler: AOrd.Univ.Prof.Dipl.-Ing.Dr. Winkler
Eingereicht am: 28. Feb. 2002
Dissertation zur Erlangung des akademischen Grades
einer Doktorin/ eines Doktors
der Sozial- und Wirtschaftswissenschaft an der Wirtschaftsuniversität Wien
eingereicht bei
1. Beurteilerin/1. Beurteiler: Ord.Univ.Prof.Dr. Abele
2. Beurteilerin/2. Beurteiler: AOrd.Univ.Prof.Dipl.-Ing.Dr. Winkler
von Mag. Christian Pail
Fachgebiet: Medienökonomie
Wien, im März 2002
Thema der Dissertation:
Influence of the Internet on the market for information
Ich versichere:
1. dass ich die Dissertation selbständig verfasst, andere als die angegebenen Quellen
und Hilfsmittel nicht benutzt und mich auch sonst keiner unerlaubten Hilfe bedient habe.
2. dass ich diese Dissertation bisher weder im In- noch im Ausland (einer Beurteilerin/
einem Beurteiler zur Begutachtung) in irgendeiner Form als Prüfungsarbeit vorgelegt
habe.
3. dass dieses Exemplar mit der beurteilten Arbeit übereinstimmt.
____________ ________________________ Datum Unterschrift
Influence of the Internet on the market for
information
Christian Pail
February 2002
II
CONTENTS
Acknowledgements 1
Abstract 2
1. Introduction 3
1.1. Introduction into herding behaviour and information economics 5
1.1.1. Literature of non-fundamental investment strategies 6
1.1.2. Interpretation of herding strategies 9
1.1.3. Economics of information 13
1.2. Discussion about several publishers
of investment relevant news 15
1.2.1. Broadcasters 15
1.2.2. Newspapers and magazines 16
1.2.3. Banks 17
2. The market for information 18
2.1. Participants 18
2.1.1. Information providers (information providers IP i) 18
2.1.2. Investors 20
2.2. Important topics and aspects 21
2.2.1. The “commodity” information 21
2.2.2. Accuracy of investment advice (quality of information q i) 24
2.2.3. Investigation and monitoring (investigation costs ci) 25
2.2.4. Investigation ability of information sellers (type Θ i) 26
2.2.5. Costs for technical distribution (distribution costs v) 27
2.2.6. Price (price p i) 28
III
2.2.7. Market share (Market share of investors α i) 29
2.2.8. Utilisation of information (expected return R) 29
2.2.9. Externality (externality e) 30
2.2.10. Investor specific expenses
for information receipt (transportation costs t) 31
2.2.11. Market structure 34
3. The model – Variables and Participants 35
3.1. Variables 35
3.2. Information Providers 36
3.2.1. Definitions 36
3.2.2. Profit function of the information provider 37
3.2.3. Type of information provider
and the optimal level o f investigation 37
3.2.4. Indifference conditions for IPs 38
3.3. Investors 40
3.3.1. Definitions 40
3.3.2. Structure of investors 41
3.3.3. Investors maximisation decision 42
3.3.4. Indifference conditions for investors 44
4. The model – Market structure and equilibrium analysis 46
4.1. Market Structure 46
4.2. Determination of market equilibrium 46
4.2.1. Calculation of the market share 47
4.2.2. Providers’ profit optimisation 48
4.3. Stability of equilibrium 51
IV
4.4. Analysis of a symmetric market structure 53
4.4.1. Analytical solution 53
4.4.2. Stable market 55
4.4.3. Unstable market 57
5. The model-Asymmetric scenario 60
5.1. Stable market 60
5.1.1. Effect of type Θ on market equilibrium 62
5.1.2. Effect of t on market equilibrium 63
5.1.3. Market share 65
5.2. Unstable market 66
5.2.1. Effect of type Θ on market equilibrium 67
5.2.2. Effect of t on market equilibrium 68
5.2.3. Discussion of unstable equilibrium 70
6. Model discussion, robustness and extensions 71
6.1. Discussion 71
6.2. Robustness and extensions 73
6.2.1. Duopoly versus oligopoly 73
6.2.2. Symmetric information versus asymmetric information 74
6.2.3. Static environment versus dynamic environment 76
6.3. Implications and suggestions for market participants 77
6.3.1. Implications for investors 78
6.3.2. Implications for information providers 79
6.3.3. Implications for regulators 80
6.3.4. Implications for market efficiency 81
V
Summary and conclusion 83
Appendix 85
References 94
1
Acknowledgements
It is worth mentioning that this work would not exist without the intensive help and
care of Prof. Abele and his team, especially Dr. Ulrich Berger. Uncountable hours of
discussion (not to mention teaching sessions) were necessary to formulate basic
assumptions and to assist me in preparing the model of this thesis. I also want to say
thanks to my parents who helped me to overcome several temporary disappoint-
ments not only during the time of writing this paper.
2
Abstract
The commercialisation of the Internet raises many interesting economic questions of
whether and how the whole economy will be changed. This thesis investigates the
effect of cheaper technical distribution and better access to information systems and
networks on information markets. Because investments are information sensitive, the
market for financial information is used as an example and illustration of a market for
information. A comparative static equilibrium analysis based on the Hotelling-model is
given. Different information providers offer information that can differ in price and
quality. The model also accounts for externalities, which are pivotal for many different
information markets.
3
1. Introduction
This thesis deals with the market for information and its prospects through the
innovation of modern communication technologies like the Internet. The analysis can
be regarded as a further investigation in information economics. Unlike traditional
physical commodities, the commodity information has several characteristics that are
difficult to handle by economic theory. The classification of information as public good
raises the question whether this commodity should be traded in completely free
markets at all. However, this thesis does not primary model the theoretical
implications of the commodity information, but tries to explain how trade in this
commodity is affected by technology. The improved technological environment
makes it possible for companies and private individuals to copy information at lower
expenses. It becomes easier to distribute particular information to a huge number of
individuals. It is not only cheaper to distribute information but it is also easier for
private individuals to receive information needed within short time. Homepages of
search-engines enable them to look for the information they require, nationally and
internationally. A stock investor with real-time information about the value of his
portfolio, whether his portfolio is worldwide diversified or not, serves as good
illustration. Statements from key persons like governors of central banks or CEOs are
available on demand etc.
Information about financial issues is focused in this thesis. (Although the basic
conclusions also apply to other kinds of information). It is difficult to find information
that is of high value to different people at the same time. Knowledge about future
price movements of securities seems to fulfil this requirement. The market for
financial information can be regarded as a market that is approximately efficient in
4
the sense that prices represent values, at least if this market is compared with other
markets for information. There are nearly infinitely many independent investors who
are interested in receiving information. There are also sufficiently many independent
sellers of investment relevant information. Professional investors need access to
much information in short time and have to make sure that networks exist to fulfil this
requirement.
An interesting feature of the discussion of investment strategies is that people often
do not behave fully rational or at least their behaviour is difficult to classify as fully
rational. This behaviour of investors is a pivotal issue in this thesis. Investors tend to
include behaviour and decisions of others in their own decisions. This is often
regarded as justification for the existence of trends and anomalies in financial
markets. Section 1.1. provides an overview about several important theoretical
approaches that deal with investor behaviour. Correlated behaviour among humans
does not seem to be restricted to financial markets but is also important in the
analysis of several other markets where information is pivotal. In any case, financial
markets make it possible for scientists to investigate this behaviour since necessary
observations (e.g. in the form of monitoring price trends) are possible. Herding also
prevails in other social areas but measuring it is more difficult if no actual market
prices are available and no comparison with “fair” market prices can be done.
In addition to the recipients of information also the sellers of information should be
mentioned at this point. Since it is difficult to prove that a particular publisher of
investment advice is not conducting competent investigation, many different sources
for financial information can be found in practice. The conclusions of this thesis are
limited to those publishers who are able to come up with competent investment
5
advice.1 This includes banks, TV-stations, newspapers and magazines, information
systems like Reuters or Bloomberg, some investment newsletters etc. Some aspects
of these kinds of companies are discussed below.
The thesis starts with a short overview about herding behaviour of independent
individuals and a summary of critical papers regarding the efficient market hypothesis
of Fama.2 This part of the thesis aims to point out the importance of externalities in
markets for financial information but also in other markets for information. Section
1.2. continues with a discussion about institutions that are offering financial
information to investors. In chapter 2 several aspects and characteristics of the
market for financial information are discussed and analysed in detail. This section
aims to provide a transition to the model of this thesis. The model starts in chapter 3
defining variables and participants. In Chapter 4 the calculations for equilibrium are
presented. Chapter 5 describes a variation of the basic model with information
providers who differ in their production function. A discussion and summary is
included in Chapter 6.
1.1. Introduction into herding behaviour and information economics
“The history of speculative bubbles begins roughly with the advent of newspapers.
One can assume that, although the record of these early newspapers is mostly lost,
they regularly reported on the first bubble of any consequence, the Dutch tulip mania
of the 1630s. Although the news media - newspaper, magazines, and broadcast
media, along with their new outlet on the internet - present themselves as detached
1 Although it is difficult to define competent advice, especially if herding behaviour prevails.
2 See e.g. Fama (1970).
6
observers of market events, they are themselves an integral part of these events”3
During times of stock market booms people from different sectors raise attention on
this possibility to make “fast money”. Many media offer investment advices to attract
additional customers. A huge share of these advices seems to contradict traditional
valuation approaches. Hirschey, Richardson, Scholz4 reported about the increasing
difficulties of the SEC to handle fraudulent recommendations distributed by using the
Internet. From an economical point of view the question has to be raised why there is
a market for such minor or even manipulative investment advices and how
technology (e.g. the internet) will change the prospects of this market and especially
how this market will interact with the market for fundamental information. Several
economic papers were written about non-fundamental investments. The interaction
between fundamental and non-fundamental aspects is especially difficult to describe
since two completely different approaches have to be related to each other. The
following subsection provides a short overview about several theoretical frameworks
that can be regarded as theoretical background for this thesis.
1.1.1. Literature on non-fundamental investment strategies
Economists have tried for years to explain how investors determine their investment
portfolio if more than one investment strategy is available. According to the portfolio
theory of Markowitz5, investors select assets either to maximise expected investment
return (if risk is predetermined), or to minimise risk (if expected return is
predetermined). Risk is measured as deviation of returns on investment and consists
3 Shiller (2000), p 73.
4 See Hirschey, Richardson, Scholz (2000).
5 See Railly, Brown (1997).
7
of unsystematic risk (which can be reduced by diversification) and systematic risk,
which represents the risk of the market portfolio and cannot be diversified. This
concept explains stock market allocation of investors but does not necessarily explain
how risk (systematic and unsystematic risk) arises. If financial markets are
information efficient6, then stock prices and consequently returns (or the distribution
of returns) only depend on fundamental aspects.7 This means that only factors that
affect the underlying corporation whose stocks are traded cause a change of stock
price and determine return and risk. Several economists argue that stock prices are
not necessarily information efficient.8
Grossman and Stiglitz suggested that stock prices are not efficient if investors must
purchase information.9 If stock prices are information efficient, the incentive for
investors to acquire information is lowered because the fair value of a particular
security can easily be observed by looking at the price. The quality of this information
depends critically on the information efficiency of stock markets. Obviously, if a lot of
investors do not search for information themselves but use the current price as
primary source for fundamental information, the information content of the price will
be lowered and will cause the price to be only a noisy signal of the underlying
fundamental values. The resulting equilibrium cannot be equal to the information
efficient equilibrium as long as fundamental information is not free of charge.
6 There is no single definition for the term “information efficiency”. A comprehensive discussion can be
found e.g. in Fama (1970).
7 This is regarded as the semi-strong form of information efficiency.
8 See e.g. De Long, Shleifer, Summers and Waldmann (1990), or Grossman and Stiglitz (1980),or
Brett Trueman (1994). Additional literature is provided in the references of this thesis.
9 See Grossman and Stiglitz (1980).
8
Another paper, written by Hirschleifer, Subrahmanyam and Titman10, investigates a
scenario where investors do not receive information at the same time. Because
observing only a restricted number of stocks can diminish the average time between
an announcement of a company and the reaction of the investor, investors have a
strong incentive to limit their attention and also their portfolio to fewer stocks
compared with the optimum defined in traditional theory. Because all investors face
similar decision rules, the resulting equilibrium is determined by the strategic
behaviour of all investors. News that are observed by many investors cause higher
stock price responses. Since investors profit if they are observing the same stock(s),
there is a strong incentive to herd. This tendency ends up in an equilibrium in which
stocks of fundamentally identical underlying companies can be valued differently.
If several investors who do not exactly know the fundamental value of securities trade
in financial markets, the interaction between these investors and investors who are
informed about all fundamental aspects should be considered in more detail. De
Long, Shleifer, Summers and Waldmann developed theoretical approaches how
these two types of investors interact and influence the decisions made by the other
type and how the allocation of securities is affected.11 Various investors do not know
exactly the fundamental values of securities. This causes them to trade the securities
at non-fundamental prices. Rational arbitrageurs are, in the short run, not able to
offset this deviation from the fundamental value because they are risk averse and
noise traders (investors with “noise” information about the fundamental value) cause
additional volatility and consequently additional risk. This additional risk lowers the
utility of risky investments for all rational investors and causes a misallocation of
10 See Hirschleifer, Subrahmanyam and Titman (1994).
11 See De Long, Shleifer, Summers and Waldmann (1990).
9
securities. The robustness of this model depends critically on the time horizon of
rational traders.
Another approach, provided by Calvo and Mendoza, explained that the incentive to
purchase costly fundamental information is lowered if financial markets become more
and more international.12 Investors benefit from foreign diversification because they
can reduce unsystematic risk. If the costs of analysing one security are not lowered,
there is a disincentive to acquire fundamental information since investors also benefit
from diversification if they simply imitate the market portfolio (e.g. acquire a specific
country index portfolio). This means an investor who is confronted with the possibility
to invest in an additional country profits more if he just imitates the market portfolio
than if he acquires fundamental information for all additional securities. The incentive
to acquire information for a particular security is lowered if more securities are
available and imitating behaviour is possible. However, the mentioned paper
investigates the effects of internationalisation of financial markets, while this thesis
investigates the effects of technological innovations on information markets (see
below).
1.1.2. Interpretation of herding strategies
In this thesis it is assumed that some investors are not only interested in acquiring
fundamental information but look at the investment behaviour of other investors. As
they can improve their expected utility by doing what other investors are doing, they
are searching for a mechanism to “coordinate” their behaviour. The Internet will be
regarded as a kind of coordination mechanism for these investors because network
10
effects exist. The question has to be raised whether the Internet adversely affects
financial markets because possibilities and profitability of non-fundamental investors
to herd are intensified. On the other side, also strictly fundamental investors may
profit from the possibility to have access to more information at lower expenses
through the Internet.
It should be noted that the benefits of cheaper distribution of fundamental information
are limited. As compared with information for herding where investors try to use just
one source (the source used by most others), the benefits of receiving huge
quantities of fundamental information is constrained because attention does
represent a scarce commodity.13 Fundamental information must normally be
interpreted or “converted” into investment or portfolio decisions. The costs of these
decisions are not lowered by technological progress. There is also a maximum level
for the knowledge of fundamental investors. No investor is able to know more than all
fundamental information. The net result of the spreading of the Internet on the
behaviour of investors is difficult to predict.
Investors using a herding strategy can improve their return on investment and utility if
they know what others will do. It is not possible (or at least difficult) to collect
information about each single investor and summarise the average behaviour of all
these investors. But it is possible to search for signals from which all others think that
12 See Calvo and Mendoza (1999).
13 See Simon (1971). It is argued that the costs of additional information do not only consist of the
money paid for it but also on the time and attention required. E.g. newspapers that are offered to
students at no costs need not necessarily be read because also time represents a valuable
commodity.
11
investors will react on them. A prominent example is a stock market guru who
announces a plunge during the next investment period. An investor who tries to
optimise his behaviour must (if he does not identify fundamental reason for a stock
market crash) anticipate whether other investors will react on this announcement or
not. If the (subjective) probability that other investors react according to the
announcement is higher than the probability that they do not, immediate selling (or
taking a short position) will be optimal. But without fundamental news, the only
reason for the reaction of the other traders is that they believe that people think that
others think that they will react.14 Further signals for the initiation of herding
behaviour may be technical signals that are observable by many investors at the
same time, or even the phase of the moon circle.
The existence of herding strategies are modelled in this thesis by the assumption of a
simple externality, which is granted to every customer of a publisher of investment
relevant information and depends on the number of other customers. This very broad
concept is used to allow for several interpretations and applications of the utility of
herding. Two interpretations why investors may be interested in the behaviour of
other investors are suggested in this subsection. In reality both concepts may apply
but may be difficult to identify and to separate from each other. The model of this
thesis does not exactly specify how the utility improvement explained by herding is
justified. Both concepts may be responsible for the herding effect modelled below.15
14 See Keynes (1936).
15 Even more argumentations in favour of herding are possible if non-fully rational investors are
assumed. Some real investors will feel confirmed if they see that others are doing the same or invest
in the same security. In this case the utility of herding is given to the investor after his decision. He
arranges his portfolio himself and receives additional utility if this portfolio is identical to the portfolio of
12
• Imitating other individuals may be profitable if not sufficient information about
the possible realisation of an event is available. An investor without any
knowledge about the optimal investment decision acts rationally if he imitates
the strategy of other investors if he assumes that some other investors act
rationally and have a positive probability to be better informed. This is an
application of the restaurant searching games developed by Banerjee.16 An
uninformed customer tries to find out which of two restaurants provides better
service. If another customer chooses restaurant A, he can decide whether to
follow or not. If the first customer is informed about the better choice it is
rational to follow him. If he is not informed there is a 50% chance that he visits
the better one. The second customer, observing the first one, acts rationally if
he simply follows the first customer although he is not fully informed about his
type (informed or uninformed). In financial markets this behaviour does not
seem to be unusual. Many private investors are not able to pick lucrative
stocks themselves. Imitating other investment decisions means having a
chance that a lucrative investment is imitated. Grossman and Stiglitz also used
a similar argumentation.17
• Herding strategies may also be profitable if investors do not assume that
others are better informed. The “restaurant” game is also valid if expected
others. But he also partly optimises the portfolio by buying advice from an independent source. If he
has the chance to choose between two sources he will choose the alternative that is (or probably will
be) used by most other investors. But such a psychological approach is difficult to handle by economic
theory.
16 See Banerjee (1992).
17 See Grossman and Stiglitz (1980).
13
return of an investment is not determined by the decision of other investors.
(I.e. the investor invests in a project with constant returns to scale.) In real
financial markets, expected and actual returns are affected by the interaction
between demand and supply of the security. Hence, it is utility improving to
know what other investors are doing or will do in the future. This kind of
herding applies to private (unskilled and uninformed) investors as well as to
professional (skilled) investors.
1.1.3. Economics of information
As will be seen, the variable information is pivotal for the entire analysis below. This
variable will be defined similar to a simple physical commodity. Nevertheless, it is
necessary to include a short introduction into the area of information economics since
all conclusions about a model of the market for information are based on an
adequate handling of this variable.
Attempts to identify and define the characteristics and properties of information are
not restricted to economics. Many other sciences are interested in this area of
research. Braman was able to identify 40 different academic fields that deal with
information.18 Discoveries in one discipline may also be interesting for several other
disciplines. Lamberton himself lists some fields that have linkages to economics like
information sciences, communication studies, organisation science and even
psychology.19 Many other disciplines may have a connection to economics. E.g.
psychologists may draw conclusions about different possibilities of individual
18 See Braman (1989).
19 See Lamberton (1996).
14
perception of information. This knowledge may be interesting for economists in
many areas, e.g. in marketing or even in the understanding of investors’ behaviour.
But also within the science of economics we can identify many sub-areas that deal
with information. Lamberton listed several areas where knowledge about information
contribute to economics like information asymmetry, growth, organisational capital,
taxonomy of information, infrastructure and information as a public good.20
In an economic application the definition of the term information seems to be
especially important. Braham suggests a few different definitions for information.
These are information as a resource, information as a commodity, information as
perception of pattern and information as a constitutive force in society. In their book
Information rules, Shapiro and Varian define information as “anything that can be
digitised”21. It can be seen that no definition can be used extensively. For any (or
most) analyses in economics some characteristic of information have to be neglected
and a particular definition of information must be used.
In any case, information is pivotal for most economic studies and must not be
neglected. Nevertheless, the entire discussion of this important area of research is
too extensive to be described in this thesis. A very good deeper introduction into the
economic meaning of information can be found in The economics of communication
and information.22
20 See Lamberton (1996).
21 Shapiro, Varian (2000), p3.
22 See Lamberton (1996).
15
1.2. Discussion about several publishers of investment relevant news
This section aims to provide a short overview about potential publishers of
investment advice or news, which are modelled in this thesis. Their development
regarding the use of new technologies during recent years is described.
1.2.1. Broadcasters
One important point concerning all kinds of media is that they are exposed to a high
degree of fixed costs. These fixed costs increase business risk and raise incentives
for concentration. The entire broadcasting industry serves as a good illustration. In
the past, broadcasters (and other media) had incentives for horizontal and vertical
integration.23 A broadcaster prevailing in the production phase, in the packing phase
and in the delivery segment can easily dominate the entire market. The benefits of
vertical integration come from economics of scope and risk spreading. A niche player
is not able to provide programs without the risk that the response of customers is not
sufficient. A big player is able to diversify this risk. Economies of scope can be
attributed to a better utilisation of equipment and management. Signal distributors
gain from their strong position in the final stage infrastructure. (Motta and Polo
mention terrestrial transmitters, cable wires, satellites and decoders.) These
technologies can be regarded as natural monopolies.
Since broadcasters are possible sellers of investment relevant information the
influence of the Internet on these companies should be focused. The effect of the
Internet on broadcasting networks cannot be estimated without significant
16
uncertainty. The magazine The Economist24 provided a first review about the inferior
success of the Internet strategies of media companies. Failures are partly explained
by the fact that consumers do not have the necessary technical equipment to receive
contents at their disposal. (In 2001 only a small part of households had broadband
Internet connections that are necessary for the distribution of e.g. videos.) A
complementary problem arises since the lack of infrastructure lowers the incentive for
content providers to offer contents over the Internet. The question how revenues for
Internet services can be secured should also be addressed in the future. Music
represents a good example because it can easily be offered over the Internet but it is
more difficult to convince consumers to pay for it. These aspects make it difficult to
predict the effect of the Internet on the broadcasting industry and how news
broadcasters will use the Internet in the future.
1.2.2. Newspapers and magazines
Not only broadcasters publish information for investors for the optimisation of their
portfolios. Another possibility for the distribution of investment relevant information to
investors is the dissemination through newspapers and magazines. But similar to
broadcasting the distribution of newspapers (printing and physical distribution)
requires high expenditures. A new distribution technology can partly avoid these
costs. (Obviously, it is cheaper to distribute newspapers to subscribers by using the
Internet than by delivering the paper physically.) However, it should be mentioned
that more empirical evidence about the reading behaviour of customers who read
news in the Internet is necessary. News (or any written information) provided on a
23 See Motta and Polo (1997).
24 See The Economist, 19th August 2000.
17
screen must be treated differently than news provided on a paper.25 Many people
do not want to read too many pages online. News providers have to care about
preferences of customers to secure revenues in the future. Several existing
newspapers are experimenting with the new technology. They offer online services of
their papers. These services are normally free of charge but, as a rule, the customer
has to register. (This is a valuable source for demographics of customers.26)
However, it is unclear how online services and offline services will interact in the
future. If customers prefer to read printed news, online services will be simply
additional services and not products on their own.
1.2.3. Banks
Investment advice cannot be regarded as the core business of a bank. Nevertheless,
banks are included as publishers of investment relevant information in this thesis
because the homepages of several banks offer detailed information about financial
markets. The introduction of the Internet has extended the services offered by
traditional banks. Instead of visiting a branch, customers are able to conduct their
banking business via telephone or the Internet. This makes it possible for banks to
transfer up to date information to customers. Many of the so-called online banks offer
their own information system by providing ad hoc publication and direct access to
stock exchanges. This platform improves the distribution of investment advice.
Classifying investor specific characteristics via computer technology and proposing
standardised portfolios can save expensive face-to-face advice.
25 See e.g. ORF (2000).
26 See Shapiro and Varian (2000) for a detailed discussion.
18
2. The market for information
This chapter aims to provide a discussion of relevant aspects (participants, variables,
parameters…) of the market for information and their potential usefulness for
economic modelling. Several features of this markets and their use as model
variables and parameters are analysed. In any model simplifications have to be
made. This chapter also includes justifications for these simplifications and suggests
alternatives for further research.
The following titles of sub-sections include in brackets the designation of variables
used in the following model of later chapters. Within this chapter every sub-section
deals firstly with implications of the particular topic in the real economy. Afterwards
the potential use for economic modelling (including the analysis of alternative
specifications and characteristics) is discussed. The chapter is not necessary for the
mathematical understanding of the model but points out the motivation for the
specifications used below.
2.1. Participants
2.1.1. Information providers (information providers IP i)
In real markets such a provider will be a financial media institution like a newspaper
or a TV-news station. Also banks or similar institutions (especially investment banks)
sell recommendations for portfolio decisions as mentioned above. They do not only
sell particular investment recommendations but also (or only) general factual
information about financial markets and the economy. Usually, such companies
19
distribute their information through a firm-specific network. In the case of TV-
stations this is simply a cable or satellite network. Newspapers have their traditional
distribution network through subscriptions and retailing. Banks use their branches to
distribute investment recommendations to their investors and special financial
information systems use their own, telecommunications based, computer systems.
(Frequently, they even use the Internet as distribution networks.) The reach of these
companies critically depends on extent and size of their distribution system. If a
customer has no access to this system it is extremely difficult for him to receive
information by this particular provider. This is especially true for TV-media but also
applies to several newspapers, which are only available at limited locations. It also
applies to banks that are (or were before the introduction of the internet) only able to
conduct their business through their branch networks. From an economical point of
view the existence of these investment recommendations selling companies is
interesting. They may be regarded as intermediaries between the primary source of
information and the receiver. So the justification for their existence seems to be
similar to the justification of the existence of banks. Banking theory concentrates on
selling banking products to investors and in this thesis information is sold to investors
directly. The basic service is the investigation in economic affairs done by the
intermediary in both cases. The intermediary conducts investigation, acting for all
investors simultaneously and reduces social costs for investment in investigation.
Therefore, either in banking theory or in this broader concept of intermediation,
information asymmetries are pivotal. There must be a credible mechanism to solve
incentive problems between participants. In banking theory this is e.g. a deposit
contract between a customer and a bank. If an investment recommendation is sold,
the mechanism looks differently although it is not obvious how it really looks like. A
20
reputation mechanism may be suggested to solve this problem. This difficulty is not
dealt with by the model.
2.1.2. Investors
Private investors depend on banks and media companies to form their portfolio. But
also institutional investors like fund managers, investment companies, etc. normally
use the services of information systems. The limited ability of investors to conduct
sufficient investigation for themselves seems to apply to any typical investor.
Although the Internet enables private investors to have access to large quantities of
fundamental information at low costs, they will not be able to convert information into
investment strategies. A lot of experience and education is necessary to conduct this
task. Also attention is a limited “commodity” (see subsection 1.1.2.). A single investor
cannot interpret the huge quantities of tiny fundamental information.
In economic modelling it is usual to assume that investors are infinitely small and
equipped with the same initial budget.27 Because mass media are investigated, these
assumptions do not seem to be unjustified.
27 Assumptions about investors with different reservation prices would result in an interesting
extension of this model. In this case also the total number of investors who buy a recommendation
would be changed according to distribution costs etc.
21
2.2. Important topics and aspects
2.2.1. The “commodity” information
The definition of information will be limited to investment recommendations. An
investment recommendation is a suggestion about the optimal allocation of capital,
i.e. a guideline for an investment strategy. This restriction is necessary because a
valuation of this kind of information is possible in theory and practice. The monetary
value of a recommendation can be approximated by the additional expected
improvement in the portfolio value of the receiver of the recommendation. If only
small investors are investigated it is possible to assume that their initial budgets and
their risk preferences (and time horizon etc.) are similar. It is then possible to assume
that investors’ characteristics are equal. In modelling behaviour of investors it is
usually necessary to assume such significant restrictions.
Information that is different from investment recommendation is not examined within
the context of this thesis.28 Any factual information is also valuable although its value
is difficult to measure. Such information need not be related to financial markets.
Investment recommendations are informational “commodities” whose values are
determinable and similar between different investors. News about e.g. social issues
may be valuable for a limited group but not for the entire population and is difficult to
28 It should be mentioned that the interpretation of the term “investment recommendation” could be
very comprehensive. Also simple predictions about future economic events can be included and
utilised in an investment strategy. From a very abstract point of view nearly every piece of economic
information can be “translated” into an investment strategy. However, in this model it is assumed that
only recommendations that can be directly used to form an investment strategy are traded.
22
value even for this group. The model below also assumes that the quality of
information can be improved by investing in economic research. This characteristic
does not apply to all types of news. However, this characteristic also does not apply
to investment recommendations without significant restrictions. Any investment
recommendation has to include (explicitly or implicitly) a prediction of future events.
Because future events are uncertain, it is very difficult to determine the value of a
particular investment recommendation ex ante, i.e. before the event actually occurs.
Many different aspects can influence asset prices and stock market trends. In
addition to unpredictable fundamental aspects also several market anomalies and
herding effects may cause mispricing and reduce the value of fundamental research.
It is a very critical assumption in the model (see Assumption 1 below) that investors
are able to distinguish between several quality levels ex ante. In real financial
markets it is more appropriate to regard investment recommendation as an
experience good or credence good. Many papers have been written about the
performance of different types of investment professionals.29 It seems to be
necessary to investigate the performance of investment professionals over a long
period of time to distinguish between good and bad advisors, even ex post. But if this
task is difficult for economists, it will be difficult for private investors as well. A
mechanism to overcome this information asymmetry must implicitly be assumed. The
solution may be a reputation mechanism or a kind of guarantee. This thesis regards
the market for information from a very broad perspective. Specific assumptions about
how this asymmetry is solved are not made since the mechanism may be different for
different kinds of information or recommendation sellers. (E.g. a bank can signal the
value of its recommendation by investing its own money according to it. This cannot
be done by financial newspapers.) The following model also aims to explain how
23
price and quality are affected by a changing technical environment. The introduction
of asymmetric information regarding the quality of the commodity causes additional
problems, which would enforce a very complex model setting.
Also the possibility to copy information at low costs must be excluded from the model
for simplification (this is done in Assumption 3 below). In real markets, inexpensive
copying will cause free rider problems and probably diminish the incentive to invest in
economic investigation. Private investors buying recommendations from information
providers (newspapers, banks…) can easily copy the information, independently of
whether the recommendation was transferred via Internet or via traditional media.
They can sell or at least distribute these recommendations to other investors without
conducting investigation themselves. Even if the recommendations are passed on
free of charge, this will damage the interests of the initial publisher because it
reduces the number of investors willing to pay for it. The innovation of the Internet
seems to be a special device for private investors to distribute information privately to
a huge number of others, sometimes even without knowing them. Any investor
becomes a possible additional competitor for media companies. Anyway, it is also
argued that the value of a recommendation is improved if the number of receivers is
raised (herding behaviour). This limits the negative impact of copying. The bottom
line is difficult to predict due to these two opposing effects. (On the one side there are
lower incentive to invest in investigation because of free riders but on the other side
usefulness of recommendations is higher because positive externalities exist and it is
possible to sell this information over a secondary market.) However, this thesis
investigates the influence of the Internet on the distribution technology and not the
29 See Jaffe and Mahoney (1999).
24
improved possibility to copy information privately. According assumptions would
have to be made for such an extension.
2.2.2. Accuracy of investment advice (quality of information q i)
The quality of information depends on the costs invested in investigation. It is worth
to mention that the quality of investment recommendations is not only difficult to
observe in reality but also difficult to define in theory. In real financial markets
investors may be interested in the acquisition of good predictions. Because
irrationality may cause mispricing30, investigations in fundamental backgrounds by
providers need not coincide with good stock price predictions. As discussed above,
some offered information will cause stock market movements and can consequently
be seen as good prediction, even if their fundamental value is very low. Investigation
costs for such information (about herding behaviour) can be very high. So, in real
markets the term investigation is not limited to strictly fundamental investigation but
extended to investigations in the strategic behaviour of market participants.
Competent investment institutions will recommend higher risk adjusted expected
return strategies than incompetent institutions. This can e.g. be achieved by
additional diversification in different asset classes not used by competito rs. (Lowering
risk for equal return is equivalent to increasing expected return for equal risk as long
as investors are risk averse). Additional investigation in these areas can be
interpreted as additional investment in quality. However, real investors are able to
buy more than one investment recommendation since it may be profitable for them to
diversify between different sources. But if the recommendation is interpreted as
30 See De Long, Shleifer, Summers and Waldmann (1990) or Hirshleifer, Subrahmanyam and
Titman(1994).
25
suggested portfolio (which is already diversified), additional diversification may be of
little value since the risk reducing effect of diversification is a decreasing function of
the number of different assets.
In the model below the changing behaviour of the buyers of information is not
included in the information. (Although investors receive externalities by buying
information, the provider in this model does not publish the number or potential
behaviour of other buyers.) Investigation costs can be assumed to be an increasing
and convex function of quality. There must be a maximum for the quality if all
possible information is known. This would result in an optimal investment strategy.
Anyway, this strategy will not be achieved in reality but it justifies the assumption that
increasing the quality level of a recommendation is only possible if investigation costs
are raised over-proportionally. Good investment advisors have to investigate in all
areas of investment (e.g. also real estate, venture capital etc.) to optimise portfolio
recommendations. Although the additional benefit of such further diversification may
be demanded by investors, additional costs will exceed benefits of formulating a
completely efficient security portfolio.
2.2.3. Investigation and monitoring (investigation costs ci)
Investigation represents the input into quality and can be different between
information providers. Investigation costs are caused by investigations in balance
sheets and income statements of companies, conducting macroeconomic and
industrial research, estimating future market trends etc. These costs are similar and
comparable to monitoring costs used in banking theory. Investigation costs are fixed
costs since they are unrelated to the number of investors. The formulation of investor
26
specific portfolios is not done by big media companies. (Most banks provide such
services. This is neglected at this point.) Consequently, individual investment
recommendations and strategies are unlikely to be distributed via mass media, which
are investigated in this thesis.
2.2.4. Investigation ability of information sellers (type Θ i)
The higher the investigation ability (economically regarded as type) of the information
provider the lower the necessary investigation costs for achieving a particular
predetermined quality level. The type of an information provider depends on various
factors like history positioning of the corporation etc. It is the ability to conduct
investigation and to formulate an investment strategy according it. Obviously, this
ability also depends critically on education and experience of the staff of the
information provider. It is the average ability of his employees. Quality of information
can be raised by employing better analysts at higher costs or by employing more
analysts.
If type is regarded as the average ability of the staff of the information provider then
this type will be basically an endogenous variable since it can be changed by
changing staff organisation (or e.g. the whole positioning of the corporation), at least
in the long run. The model below does not account for such long-term changes in
company policy. Instead type is defined to be exogenous, i.e. it is not affected in the
same way as investigation costs. As we will see, investigation costs are determined
by the actual equilibrium. The type of a company can be interpreted as long run
positioning of the company. An information provider can be positioned as daily
27
newspaper or as investment bank. Type then depends on the entire pool of
businesses in which a particular company acts.
2.2.5. Costs for technical distribution (distribution costs v)
For distributing the information to the customer the information provider has to pay
costs for physical transmission. The question has to be raised whether these costs
are fixed or variable in reality. If a TV-news broadcaster or an information system is
investigated, the assumption of fixed costs is justified. This also applies partly to
newspapers since they are printed before dissemination. Although all kinds of
information providers have to pay for networks and consequently have to pay fixed
costs, distribution costs are assumed to depend on the number of investors in this
model. It would also be appropriate to assume partly variable expenses for Internet
offering since additional computer servers are necessary to serve additional
investors. The expenditure in the network infrastructure seems to be a function of the
number of investors. (Although variable costs but also revenues per investor are
extremely low, at least if media are investigated.) The model analyses market
equilibria. If one provider serves many customers he has to establish a larger
network. Nevertheless, since many information publishers use the Internet as an
additional service to their traditional service, the resulting effect on distribution costs
is questionable.
Another justification for the assumption of variable costs in economic modelling is to
exclude negative profit in the case of too few investors. It should be mentioned that
substituting these variable costs through fixed costs would not essentially violate the
basic conclusions of this model.
28
Technical distribution costs may be reduced by technological progress, i.e. the
introduction of the Internet. It will be shown in the model how lowering these variable
costs affect information providers and investors.
If asymmetric information regarding the quality of information would be introduced
into the model, the expenses for the mechanism to overcome this asymmetry would
be part of these costs. The provider would be forced to pay for a mechanism
(reputation, guarantee etc.). In this case the introduction of fixed costs may be
necessary since reputation is normally regarded as fixed costs.
2.2.6. Price (price p i)
The price of a recommendation is easy to observe if recommendations are sold via
newspapers. But even in this case, revenues of the publisher do not only consist of
prices but also on selling marketing space to third parties. This is especially true if
TV-news broadcasters are investigated. Also information and recommendations
offered over the Internet are usually financed by selling marketing space to third
parties. This applies to homepages of investment advisory companies as well,
although only few media companies are able to convince customers to pay for their
services.31 The Internet also enables companies to conduct price discrimination (e.g.
by using a discount system) since customer specific and exclusive offers are
possible.32 This is especially important if the corporation raises a big share of its
revenues through advertisements.
31 See The Economist October 7th-13th 2000.
32 See Shapiro and Varian (2000).
29
The assumption of a price-mechanism without any possibility to raise money
through advertisement will be made in the model for simplification. The price can be
interpreted as subscription payment for a newspaper or fee of an information system
(like Reuters, Bloomberg…). The information provider is indifferent between receiving
a charge from the customer or receiving advertisement revenues per customer since
both depend on the number of customers. But investors would change their
behaviour if providers can partly finance their investigation by selling advertisement.
This effect is neglected in this thesis. Also price discrimination is excluded from the
model below.
2.2.7. Market share (Market share of investors α i)
Market share is a measure of the number of investors of a particular information
provider relative to the whole market. The reach of the distribution network of a seller
of information is limited in reality (at least before the introduction of the internet). The
distribution system of a bank is e.g. limited by the location of branches. Newspapers
are often only distributed within a country or a specific region. The demand for
information from a particular provider is consequently limited to the investors within
the range of this provider. Technological progress makes it possible for these
providers to extend their network at very low costs to further regions and customers.
2.2.8. Utilisation of information (expected return R i)
Investors allocate their portfolios according to their pool of information. Even if they
can be sure about the quality of information they cannot be sure about the return of
their portfolios. Different investment recommendations lead to different distributions
30
of investment returns. Even the information itself contains uncertainty because its
“quality” is difficult to estimate. (See the discussion about asymmetric information
above).
The information is interpreted as possible investment allocation that cannot be made
without knowing the information. Higher quality ends up in higher expected return of
this buy and hold strategy. Diversification between different investment allocations is
not possible or does not make sense in the model below. In the model the
information can be translated into an investment strategy where the expected return
of this investment strategy is an increasing and concave function of the inherent
quality. An investor prefers more quality to less quality but at a decreasing rate. The
function itself is similar to a common risk averse utility function but does not account
for risk. Risk is not included in the model to avoid the mathematical handling of
probability distributions. Risk preferences become important if diversification is
possible, which is excluded here. Investors are risk neutral and simply compare the
expected return of different suggested investment strategies.
2.2.9. Externality (externality e)
The utility of an investor grows whenever another investor also buys the same
recommendation and behaves according to it. It is not stipulated whether the
additional utility is caused by increasing asset prices attributed to more demand for
the same assets or simply by psychological considerations. It is explained in
subsection 1.1.2. why it can be fully rational for investors to imitate or to buy the
same information as others. But also if these explanations are not appropriate, the
31
modelling of these externalities may be justified because investors may feel
conformed if others behave similar.
2.2.10. Investor specific expenses for receiving information (“transportation costs” t)
In addition to technical distribution costs, which have to be paid by the providers, also
investors have to pay expenses to receive the information offered by providers.
These costs are lowered through the introduction of the Internet. This subsection
explains the background of these costs and mentions the reasons for the reduction of
this important cost factor.
A newspaper serves as practical illustration to distinguish between price, distribution
costs and these transportation costs. The investor has to pay the price of the paper.
The publisher is forced to pay for the technical distribution. But, if it is a foreign
newspaper, the investor is obliged to pay for additional transportation service since it
does not pay off for the provider to extend his distribution network abroad. This
scenario depends on the availability of the transportation infrastructure. Either the
provider extends his distribution network or the investor is now able to conduct the
transport himself. The Internet diminishes these distribution and transportation
expenses. It is easier for the publisher to serve investors worldwide and it is also
easier for the customer to have access to the paper. These expenses also apply to
more complex model settings where investors can buy different newspapers. In this
case the Internet enables the investor to switch between different newspapers (or
different information providers) within a very short time. A separation between
provider specific distribution costs and investor specific transportation costs is
introduced to separate between costs payable by information providers and costs
32
payable by investors. Investor specific costs need not be measured in terms of
money (e.g. the necessary walk to the kiosk can be regarded as cost payable by the
investor).
The investor also has to pay the costs for Internet access. But the more the Internet
is also used in other areas of human society, the less important are the costs for this
infrastructure necessary for receiving financial news.33 The new technology also
raises the number of receivable broadcasting channels. Although television
distributed through the Internet does not seem to be successful yet, it is possible to
receive information from many international news-broadcasting companies over the
Internet. Information provided by these companies was not available for many
investors in the past but the new technology reduces the difficulties to receive these
channels. Not only regional or national, but also more and more international
channels are available.
A further limitation for international information exchange is given by the large
number of different languages. Translation can be regarded as additional costs that
lower the efficiency of the Internet as a tool to distribute information across the world.
Different languages can be regarded as different technology standards (similar to
different programming languages, which are definitely different technology standards)
that have to be converted. Converting the standard is inefficient because it is costly
and quality may be affected. It is suggested at this point that the existence of the
33 The fixed costs for the infrastructure Internet must be divided by the number of different
applications. As the number of applications grows, the share of the expenditure for financial news
declines. It should be mentioned that this effect strongly depends on the payment structure of Internet
providers.
33
Internet improves the utility of learning a language because more applications are
available34. This growing number of applications improves the average language
skills of individuals and reduces the costs of reading and translating (understanding)
financial news. As the capacity to learn further languages is limited, it is argued that
there is a big tendency for people to search for a common standard (or language).
This process is similar to the coordination problem for the preferred provider
described in this thesis. All agents have a local standard (mother language) and profit
if they change to the standard that is used most commonly.35 Content providers and
receivers can profit if they use a common standard (language). By doing so, they
raise the utility for others also to join and use this standard (learn this language too).
Consequently, the Internet can be regarded as a mechanism to identify one language
that is (also) used by everyone. Such a language will probably be a language that
was spoken by many different individuals before. If mankind agrees on such a
language, it becomes (at least for the receiver) easier and cheaper to distribute and
receive information.
All these investor specific expenditures are modelled by one variable that is different
between investors. Any investor has specific costs for receiving information from a
particular information provider. It is stipulated that consumers (investors) have to pay
for this “connection”. Which participant bears the burden of these expenses will be
shown in the model.
34 Learning e.g. English makes more sense if the number of occasions where it is used rises.
35 Obviously, they do not change but learn a second language.
34
2.2.11. Market structure
In real markets a large number of sellers of investment relevant information is
competing worldwide. However, many of these providers only sell their products in a
limited market or region. Lower expenditures to establish worldwide networks make it
possible for these providers to compete with each other. But this process will take
time and the resulting market need not necessarily be a perfectly competitive price
driven market since also quality and herding effects are decisive for the success of
an information provider.
Consequently, a perfectly competitive market does not seem to be an appropriate
reflection of real conditions. Instead, an oligopoly structure will be used to account for
different market strategies of providers. (They can set price and quality.) A duopoly
structure is analysed in detail to present market equilibrium under the assumptions
made above.36
36 It is discussed after the model how this duopoly structure can be extended to an oligopoly structure.
The basic characteristics of both market structures are identical.
35
3. The model – Variables and Participants
3.1. Variables
This section lists all variables used in this model. The section is included to provide
an overview. It is suggested that the reader uses this section as a reference because
it is of little value to know the formal features of the variables without knowing the
context they are used in.
IPi … Information provider i. Different numbers of information providers may be
assumed. The market is completely analysed for two information providers.
αi … Market share.
pi … Price offered by IP i.
qi … Quality of information offered by IP i.
ci … Costs invested in the quality of information offered by IP i.
Θ i … Type of the information provider. Type affects cost structure.
v … Variable distribution costs for distributing information to one investor.
Πi … Profit of information provider i.
uz … Utility of investor with “address” z. z is uniformly distributed on [0,1] and
describes the location of investors.
t … Transportation costs payable by investors. It is assumed that the distance
between investors and provider causes transaction expenses. Expenditures t
represents the costs of an investor to “move” from the position of one provider
to the other. The actual amount of transportation costs that must be paid by
participating investors depends on their location z.
36
e … Externality. This is the marginal utility if one additional investor buys from the
same provider.
Ri … Expected return. Received by an investor who buys information from IP i. Ri is
an increasing and concave function of q i.
G … Reaction function of IPG on the offered quality level of IP B.
B … Reaction function of IPB on the offered quality level of IP G.
3.2. Information Providers
3.2.1. Definitions
News and recommendation publishers are called information providers or IPs. IPs
are risk neutral profit maximisers and differ in type and location. An IP is an institution
that is able to “produce” information. We assume that he is only able to produce one
unit of information. Units of information can only differ in quality, where quality
depends on the degree of investigation done by the information provider, and on his
type. The limitation of the information provider to produce only one unit of information
excludes the sale of two different quality levels by one provider at the same time. Any
IP is able to serve an arbitrarily large number of investors with this information but is
not able to conduct price discrimination. The information deals with financial issues
and can be interpreted as investment recommendation or investment advice.
Assumption 1:
There are no information asymmetries regarding the price and quality level of both
providers. Also the market share of both providers is observable by investors.
37
3.2.2. Profit function of the information provider
Any information provider i tries to maximise profit. His profit equals the price for his
information multiplied with market share less the investigation costs for producing it
and distribution costs per investor multiplied with market share.
iiii cvpa? −−=
(1)
The market share α i of IP i depends on the price pi, the offered quality level q i and the
externality and can take any value between 0 and 1.
3.2.3. Type of information provider and the optimal level of investigation
The costs for providing information of quality q are
( )
i
i
Tqc
c = , where 2q
qc2
=
(2)
c(q) is a convex function and Θi represents the type of information provider i. I.e., the
higher the type the lower investigation costs for any quality level. Cost functions for
different Θs are illustrated in Figure 1.
38
Figure 1.
3.2.4. Indifference conditions for IPs
Since an information provider sets a price-quality combination, it is not possible to
determine the optimal quality level without regarding the interdependence between
these two variables. Fixing Πi, α i, Θi and price can be written as a function of quality,
ii
2
i
ii
a2Tq
va?
p ++= (3)
allowing us to draw iso-profit curves, as is done in Figure 2.
ci
q
Θlow
Θhigh
39
Figure 2.
The higher the type of the IP the lower will be the price level for equal profit. Because
the provider is obliged to pay for distribution he has to demand at least v to make
non-negative profit. The iso-profit curves for positive values of Πi are parallel shifts of
the zero-profit curve.
It is important to note that not only Θi affects the slope of the iso-profit curves but also
market share α i. The higher market share the higher will be revenue, ceteris paribus.
This relationship is shown in Figure 3.
pi
v
q
Θlow Θhigh
πi=0
rising πi
40
Figure 3.
3.3. Investors
3.3.1. Definitions
Investors are risk neutral buyers of information. 37 They are equipped with a budget to
invest in profitable investments. They are not able to conduct investment
investigation on their own and only invest after purchasing information from an
information provider. Since an investor can purchase only one unit of information,
37 Risk-neutrality is an unusual assumption for investors. This assumption is necessary to avoid further
complications due to difficult interaction between expected return and corresponding utility. Investors
try to maximise utility. Because (see 3.3.3.) expected return is a concave function of the offered quality
level, there is an optimal level of expected return. Additional investor satisfaction is only achievable at
an increasing rate of input q.
pi
q
αlow
αhigh
πi=const.
41
diversification between different investment recommendations (information) is not
possible.
Assumption 2:
All investors are myopic, i.e. they do not anticipate the decisions of other investors.
(Especially they do not anticipate which provider will be chosen by other investors).
But they assume that investors who buy information from a particular information
provider will continue to do so in the future.
Assumption 3:
Investors act independently from each other. Although they profit from combined
action (because of externalities) arrangements are not possible. They are also not
able to sell the information they have bough themselves. (A secondary market is
excluded.)
3.3.2. Structure of investors
The flexibility of every investor is limited by location.38 An investor receives utility if he
buys information from an information provider but he does not only have to pay the
demanded price but also has to pay transaction costs for overcoming the distance
between him and the information provider. Obviously, the distance between different
investors and different providers is not equal. All investors are located between the
two information providers, which are located at the end points of the unit interval. For
38 The term location does not define a geographical location but defines the degree of transaction
costs payable by investors. The investor at t=0 does not have to pay any transaction costs if he buys
from IPG but has to pay t if he buys from IPB. (See Figure 4).
42
simplification, investors are assumed to be uniformly distributed on this line. The
“address” of an investor is denoted by z?[0,1]. Transaction costs for investor z are
proportional to the distance to the provider he buys from, with proportionality factor t.
This is shown in Figure 4.
Figure 4.
The provider on the left side has a competitive advantage for all z between 0 and 0,5.
The provider on the right side has a competitive advantage for all investors on the
other side where the investor located at z=0,5 does not ex ante prefer any provider,
ceteris paribus.
3.3.3. Investors maximisation decision
Investors maximise their utility u. (Since they are risk neutral, this is equivalent to
maximising expected net return in the case of no externalities.) Utility is a function of
Indifferent investor (c.p.) IP2 IP1
0 α1 α2
43
the offered quality level qi and externalities due to the existence of other investors
receiving the same information. The quality dependent part of u (which is increasing
expected return) is a concave function of q and shown in Figure 5.
Figure 5.
In this model we use the functional form
r1
ii rq)R(q = with r>1 (4)
If an additional investor purchases the same information from the same IP, utility of
the investor rises by e. (e represents the magnitude of externality per investor). Total
utility of a typical investor is given in equation 5.
tzzpearquu iiir1
i0 −−−++= (5)
R(qi)
qi
44
where z is the address of the investor and zi is the location of the IP he buys from,
and u0 is some (large) background utility.
The expected return caused by the quality of the information (or recommendation)
from the chosen information provider increases utility. Also the number of further
investors who have chosen the same IP raises the utility for any of these investors.
The demanded price of the chosen IP and the necessary transportation costs to
overcome the distance to the IP reduce utility. The optimisation problem of an
investor is to maximise (5) by choosing an information provider (i?{1,2}). Since this
decision depends upon the decision made by other investors, assumptions about the
strategic behaviour of investors are made in Assumption 3.39 No coordination
between these small investors is possible.
3.3.4. Indifference conditions for investors
Equation 5 can be reformulated as follows:
tzzearquup iir1
i0i −−++−= (6)
This equation allows us to draw the indifference curves of a particular investor, see
Figure 6.
39 E.g. it is possible that the utility of any investor of a particular information provider could be improved
if all simultaneously switch to the other provider. But no investor switches as long as it is not profitable
to be the one switching.
45
Figure 6.
The indifference curves for different utility levels are parallel shifts. A downward shift
results in a higher utility level, an upward shift results in a lower utility level. A higher
value of the transaction costs t leads to a (parallel) downward shift of the curve. (The
same utility level can only be achieved at a lower price for any quality level, ceteris
paribus.) If the externality (α ie) is regarded as a parameter, varying this parameter
simply shifts the curves parallel. The intuition is analogous to varying t. It should be
mentioned that market share α i depends on the offered price and the offered quality.
It is only possible to define α ie as a parameter for the investor because the investors
are assumed to think myopic, i.e. they take the market share as given.
pi
qi
rising u
46
4. The model – Market structure and equilibrium analysis
4.1. Market Structure
The definitions and assumptions made above are necessary to allow a profound
model of a changing technical environment. The limitation to only two providers
enables a one-dimensional map of the location of both providers and allows to model
increased mobility. The structure of the model is the one of Hotelling.40 A line of
length 1 represents the distance between the providers. The good provider (IP G) is
located at the left end of this line (zG=0); the bad provider (IPB) is located at the right
end of this line (zB=1). The providers differ not only in their location but also in their
type Θi, where ΘG ≥ ΘB. Investors are uniformly distributed along the line. The
location of any investor is given by z?[0,1], which represents the distance between
him and IPG. z ranges from 0 to 1. In the following sub-sections only static equilibria
are analysed and compared without investigating the dynamic adjustment process
between equilibria.
4.2. Determination of market equilibrium
A comparative static equilibrium analysis with different levels of transportation costs
(and other parameters) is done. Information providers offer their best price-quality
combination given the offer of the competitor and the demand of investors (Nash
equilibrium). Equilibrium is found at the point of intersection of the reaction functions
of the providers.
40 See Hotelling (1929).
47
4.2.1. Calculation of the market share
In equilibrium both providers set a particular price-quality combination. All investors
choose their own utility maximising provider. Since they get a large autonomous
utility (u0) the market is mature.41 One investor must be indifferent between both
providers. The location of this investor separates the investors of the good provider
from the investors of the bad provider. For this investor the utility of choosing IP G is
equal to the utility of choosing IP B or
( ) ( ) ( ) ( )ta1ea1qRutaeapqRu GGB0GGGG0 −−−++=−+−+ (7)
This investor receives externalities in the amount of the market share of the
according provider. The market share is equal to his location and consequently he
has to pay the market share multiplied with transportation costs for receiving
information. A standard return function defined in (4) is used to determine the utility of
the investor for receiving a particular quality level. (7) can be reformulated to give the
market share of IPG:
+−+−−= etprqprq
s1
a Gr1
GBr1
BG (8)
where ( )te2s −=
41 u0 is assumed to be sufficiently large that investors prefer buying to not to buy from either IP.
48
4.2.2. Providers’ profit maximisation
Equation 8 must hold in any market equilibrium. Improving the market share is
equivalent to changing the location of the indifferent investor. The profits for both
information providers are given in equation 9 and 10.
( )2
qvpa?
2G
GGG −−= (9)
( )( )2
qvpa1?
2B
BGB −−−= (10)
Both providers can attract additional investors either by lowering their price or by
increasing their quality. So if one provider offers a price-quality combination and
some investors decide to buy this offer from him, they receive more utility than they
expected, because of the externality. Since they are myopic they do not anticipate
the behaviour of others. Instead they take the current number of investors to compute
the “expected” degree of externality. In equilibrium both providers must have
optimised their price-quality combination and all investors do not change “their”
provider any more. Both providers optimise their combination by taking the offer of
the competitor as given and searching for their own optimal combination. The
appropriate market share of IPG for any offer is identical with the location of the
indifferent investor. Appendix 1 shows the calculation of equilibrium.
G
r11
GG
Ts
*qv*p −−= (11)
49
B
r11
BB
Ts
*qv*p −−= (12)
*p2t2e2v*p BG −+−= (13)
Prices of both providers can be expressed as functions of the corresponding quality
or as function of the competitor's price level. Unfortunately the equilibrium quality
levels cannot be expressed analytically. Both quality levels can be expressed as
reaction function of the quality level offered by the competitor. This is done in (14)
and (15):
−+=
−
21
Tq
r3s
qqB
r11
Br1
Br1
G (14)
−+=
−
21
Tq
r3s
qqG
r11
Gr1
Gr1
B (15)
Since r1
Gq is strictly increasing in qG, it is possible to reformulate (14) and (15) by
defining r1
GqY = and r1
BqX = . Both functions are reformulated.
G:
−+=
−
21
TX
r3s
XYB
r1r
(16)
50
B:
−+=
−
21
TY
r3s
YXG
r1r
(17)
Both functions are plotted in Figure 7 for positive σ.
Figure 7.
The point of intersection determines the equilibrium levels of qG and qB. It will be
shown in Appendix 4 that this point represents a maximum for the profit functions of
both providers (i.e. the optimisation of Appendix 1 leads to a maximum). In (18) and
(19) the corresponding X and Y values are presented where the G function and the B
function achieve their minimum.42
42 See Appendix 2.
Y
X
G
B
51
G is minimised if
12rr1
B
3sr)T(1
X−
−
−−= (18)
B is minimised if 1r2
r1
G
s3Tr)(1
Y−
−
−
−= (19)
σ must be greater than zero to have a local minimum. The location of this minimum
becomes important in the discussion of dependencies on parameter changes. It is
also important to recognise the point where G(X)=X and B(Y)=Y. (Intersection of the
functions G and the B with the diagonal.) This is where the bracket in (16) or (17)
becomes zero or,
rr1
B
2T
X
−
= (20)
rr1
G
2T
Y
−
= (21)
4.3. Stability of equilibrium
The resulting equilibrium can be stable or unstable. Stable means that any small
deviation from the market equilibrium ends up in an adjustment process that leads
back to the equilibrium. The equilibrium is attracting. If the equilibrium is unstable
then it is repelling. Any small deviation from the calculated equilibrium leads to a new
equilibrium. Then only one provider will sell information to all investors. There will be
an enormous tendency for the investors to herd to only one provider. This is
52
discussed below. The assumption of externalities in the market for information can
easily disturb different equilibria. If, without any rational reason, all investors decide to
buy the information from one particular provider, the position of the other provider is
weakened. A similar situation is possible if externalities are so strong that only the
decision of some investors to join the investors of the other provider results in a self-
enforcing process reinforcing the position of the “lucky” provider. The new equilibrium
market share can be either one or zero in this unstable scenario. Since the externality
depends linearly on the market share, any sudden upward tendency in the market
share of one provider will shift the location of the indifference investor toward the
other provider. This process will reinforce itself until all investors buy their information
from one provider.
Since this model is static, the adjustment-process in the case of instability (but also
the a priori adjustment process to the stable equilibrium) is not analysed. Therefore, it
is necessary to clarify whether the shared market equilibrium is stable or not. For this
reason the candidate equilibrium where all investors buy from IP G is compared with
the equilibrium above (intersection point of reaction functions). If the candidate
equilibrium where IPG serves all investors is stable then the calculated equilibrium is
unstable. The utility of the investor with location z=1 is calculated if he buys from the
good provider (He is the investor with the largest distance to IPG.) If his utility is larger
as if he buys from IPB then a market share of αG=1 marks a stable equilibrium. The
bad provider is not able to attract investors any more since even his “closest” investor
(the investor who shares his location) prefers to buy from his competitor. The shared-
market equilibrium cannot be stable any more. The condition is easy to define:
53
( ) ( ) *p*qRt*pe*qR BBGG −>−−+ or te*p*p*q*q GB
r1
Br1
G >+−+− (22)
By using condition 22 it is possible to analyse the stability of the shared-market
equilibrium.
4.4. Analysis of a symmetric market structure
4.4.1. Analytical solution
The analysis of the market equilibrium becomes much easier if there is no difference
in the type of the providers. (ΘG=ΘB=Θ.) In this case it is possible to formulate an
analytical solution to the optimisation problem of both providers. Equilibrium price and
quality levels are given in equation 23 and 24.43
2s
vp* −= (23)
r1
2T
*q−
= (24)
It is interesting to note that the price does not depend on the type of the providers.
This is because type and quality are not different between both participants. A
different price is demanded if types differ, which also affects the quality levels. A
rising e or a lower t lowers the equilibrium price. Investors gain from higher degree of
externalities because the price is lower and the equilibrium quality level is not
43 See Appendix 3.
54
affected. Providers are not able to absorb the additional utility caused through more
(positive) externalities. More externalities or cheaper technology must end up in even
more tendencies to herd to one provider. Price must be lowered to convince investors
not to herd to the competitor. If technological progress lowers transportation costs t,
investors will profit from this improvement. This seems to be obvious from an
economical point of view since less transportation costs lead to more intensive
competition between providers. All else equal, price must be lower. Also an
improvement in variable distribution costs results in additional utility for investors.
Investors are forced to bear the entire burden of this kind of costs. It should be
mentioned that this is partly explained by the structure of the model. The autonomous
utility term u0 does not allow investors to buy no information at all. Consequently,
providers are able to turn over these costs. The optimal quality level depends on the
type and on the parameter r. e and t are the same for both providers and do not
affect the quality level. The parameter r affects the equilibrium quality level
negatively. It can also be shown that an r near 1 ends up in nearly linear reaction
functions. (The function G is nearly equal to the Y-axis if X is very small and
approaches the line r2s3
XY −= afterwards). Type Θ affects the equilibrium quality
level negatively. This interesting conclusion is explained by the cost function for
producing quality, which is quadratic. Since the utility function of investors is concave,
this non-linear effect is even reinforced. The reduction in investigation costs for a
predetermined reduction in quality is increased if type is raised. As a result, it is profit
maximising for both IPs to hold their price constant and lower their quality level if their
type rises. (A higher price would only raise revenues linearly, whereas a lower quality
level reduces costs quadraticlly.)
55
The equilibrium levels are only achieved if the equilibrium is stable. In the symmetric
scenario the condition for stability (22) or instability becomes quite simple.
Equilibrium quality and price levels are equal between information providers. Only
externalities and transportation costs determine the stability properties.
0s > ( )te > unstable equilibrium (25)
0s < ( )te < stable equilibrium
4.4.2. Stable market
The following figure presents the course of the G and B function in the case of
stability. According to condition 25, transportation costs must exceed externalities in
this (symmetric) scenario. Figure 8 presents a graphical illustration.
Figure 8.
Y
X
Y* 3σ/2r
3σ/2r X*
G
B
56
In the symmetric and stable scenario both functions, G and B, are strictly increasing.
In the mathematical expression of the reaction function G, the X term in the brackets
becomes negative. As X rises, this term becomes more and more unimportant. The
function approximates the line Y=X-r2s3
. Since σ is negative, this line is above and
parallel to the diagonal. It is interesting to note that price only exceeds variable
distribution costs if t exceeds e in the symmetric scenario. Only if the scenario is
stable, both providers are able to receive non-negative profit. If it is unstable, only
one of them will receive revenues and profit at all (see discussion above).
In the symmetric scenario it is easy to determine the welfare of all participants. This is
done in Appendix 5. Equations 26 and 27 show investor and provider surplus.
Equation 28 shows the entire distributed welfare.
0
rr1
1
0
zz uv4t5
2e3
2T
rdu +−−+
=
−
∫ (26)
r21
2T
21
et*?2−
−−= (27)
r21
rr1
0
2T
2T
ruv4t
2e
W−
−
−
++−−= (28)
Investors profit from more externalities since providers have to offer a lower price to
convince investors to buy their information from them. On the other hand, providers
benefit from a lower e. Total welfare climbs in e since the positive e term in (26)
57
exceeds the negative e term in (27). t limits competition and is profit increasing for
providers but utility decreasing for investors. Total welfare is negatively affected by t.
Also variable distribution costs affect welfare negatively. These costs only affect
investors since providers are able to pass this burden onto investors. So, any
technology that makes distribution of information (supply side or demand side)
cheaper is utility improving for investors. A higher Θ lowers the utility of investors. Θ
raises the profit of the providers as shown in (27). The resulting effect of Θ on total
welfare is fastly increasing for small values of Θ and slowly decreasing for high
values of Θ. This is because the term depending on Θ in (27) is very large for small
values of Θ.
In the case of stability the discussion of αG or simply α becomes important. Since
both providers offer the same equilibrium price quality combination, the market must
be separated equally between them. Independent from any initial combination of
market share (e.g. it is possible that before the introduction of cheaper technology, t
is infinite high and two separated monopolies prevail), a symmetric separation of the
market is achieved for any level of t.
4.4.3. Unstable market
If e exceeds t the shared-market equilibrium is unstable if providers do not differ in
their type. Externalities have a stronger impact than transportation costs. If we start at
the symmetric equilibrium, and perturb the market shares such that αG=½+ε, then the
indifferent investor is located at z>½+ε, and hence the share αG grows even further,
58
until αG=1. Similarly, a perturbation αG=½-ε drives this market share to zero. So an
arbitrarily small perturbation drives the market shares to one of the corner equilibria.
The point of intersection for the quality level, mathematically described in (24), is
shown in Figure 9. For comparison with the asymmetric scenario below the functions
G and B are presented.
Figure 9.
The equilibrium point is not achieved in the long run but is described mathematically.
The course of both functions is explained for the G function. If X is very small, the first
term in the bracket of (16) becomes extremely high and mainly determines the value
of the function. If X exceeds unity, this term becomes smaller and smaller and the
entire bracket becomes negative. For high values of X, G is equal to X -3σ/2r. If σ is
raised (rising e or lower t), the extent of this negative term is increased. G is now
higher for any X smaller than the value where the bracket becomes zero (where Y=X)
Y
Y* 3σ/2r
3σ/2r X* X
G
B
59
and lower for any X value exceeding this point. The location of the minimum
(determined in equation 18) is affected by σ and Θ. If σ is higher, the minimum is
located at a higher X value. A higher Θ shifts the location of the minimum to the left
and lowers the minimum of G. The location of this minimum can be either on the left
side or on the right side of the diagonal. An analogous description is valid for the B
function.
If t is lowered sufficiently to fulfil condition 25, the market becomes unstable. The
calculated equilibrium is not achieved any more in the long run. In the short run this
equilibrium may be achieved but any deviation (e.g. a minor miscalculation of any
participant) ends up in a movement away from this equilibrium. Due to the
externalities one provider will then serve all investors. If all investors receive their
information from the same provider it is extremely difficult for the other provider to
convince investors to buy the information from him because the magnitude of
externalities “offered” by his competitor is extremely high. Investors are locked in at
one provider and it is very difficult for the other provider to attract investors from the
market share of the first provider. The equilibrium price level depends on the
possibilities of the provider without investors. This provider may try to attract
investors by offering them information at zero or even negative price and raise this
price after penetration into the market. (The losses in the former periods are offset by
the gains in future periods). This competition fight would require a more complex and
dynamic model structure and is not discussed within this thesis.
60
5. The model - Asymmetric scenario
Analysis of equilibrium results becomes much more complicated if providers differ in
their ability to produce information. Stability condition (22) does not only depend on
the difference between e and t but also on the equilibrium price and quality levels.
Unlike in the symmetric case, a negative or positive σ does not indicate whether the
market equilibrium is stable or unstable. The analysis starts with a scenario where t
exceeds e. This is similar to the stable scenario in the symmetric case but does not
clearly indicate stability in the asymmetric case. However, the equilibrium can be
seen to be stable if t>>e.
5.1. Stable market
The scenario where IPs differ in their type and the equilibrium is stable is the most
interesting scenario analysed in this thesis. Different abilities to produce information
enable a realistic model and equilibrium represents long run equilibrium.
61
Figure 10.
Both reaction functions (G and B) must have a point of intersection with the diagonal.
σ does not affect this point of intersection for both functions since this point is
determined by Θ and r. The justification is similar to the symmetric scenario where
this point is identical for both functions. Function G approximates to the line 2r3s
X + if
the bracket of (16) becomes zero. Since this point does not depend on σ, this
parameter does not affect the point of intersection. The location of this point for both
functions was shown in Figure 10 and is given by (28) and (29).44
( ) XXG = for rr1
B
2T
X
−
= (28)
44 This point can be calculated by setting 2
1
T
Y
i
r1r
−−
equal to zero.
Y
X 3σ/2r
3σ/2r
G
X*
Y*
B
62
( ) YYB = for
rr1
G
2T
Y
−
= (29)
It can be seen that the value must be lower for the B function than for the G function.
This means that this point of the G function lies a the right of the corresponding point
of the B function. The remaining situation is similar to the symmetric situation with
t>e. Both functions do not attain a minimum.
5.1.1. Effect of type Θ on market equilibrium
For the analysis of the effect of ΘG let us start with ΘG=ΘB and then raise ΘG, holding
ΘB constant. This procedure only affects the quality reaction function of IP B. The
bracket of (17) now becomes smaller for any Y value. Since the bracket affects the B
function negatively, B is shifted to the right. Because the G function is not affected, X*
and Y* are both lowered now. This can easily be illustrated, as done in Figure 11.
Figure 11.
Y
3σ/2r
3σ/2r X X*’ X*
Y* Y*’
G
BΘG=ΘB
BΘG>ΘB
63
Shifting B to the right lowers X* and Y*. The new equilibrium point (X*’,Y*’) must be
located on G below the old equilibrium. Since the slope of G exceeds one below the
diagonal, a higher ΘG lowers Y* more than X* or, equivalently qG* is lowered more
than qB*. A lower qB* can be justified economically since αG* now exceeds ½ (see
previous discussion). The decrease in qG* can be interpreted as the reaction of the
good provider.
The effect of a higher ΘG on pB* is strictly positive since qB* becomes lower. The
effect on pG* can be seen by looking at equation (13). (If pB* is increased and v, e, t
are not changed, pG* must be lowered.)
5.1.2. Effect of t on market equilibrium
A closer look at the function G makes it clear that a decline in t (a less negative σ)
lets the function rotate clockwise around the point of intersection with the diagonal.
Any Y value below the diagonal is increased, and any value above the diagonal is
decreased.45 (See Figure 12). The point of intersection of G and B must be located to
the right of the diagonal. This is interesting since the bad provider, who is only able to
45 σ is negative. The bracket of equation 16 (21
TX
B
r1
r
−−
) is large for low values of X and approximates to
21
− for X ⇒∞. The term )21
TX
(r
3sB
r1
r
−−
is negative if 21
TX
B
r1
r
>−
and positive if 21
TX
B
r1
r
<−
. If σ is now less
negative (lower t) the term )21
TX
(r
3sB
r1
r
−−
is now less negative if 21
TX
B
r1
r
>−
and less positive if
21
TX
B
r1
r
<−
. The analogous description applies to reaction function B.
64
produce any quality level at higher costs offers a higher quality level than the good
provider. For a large fall in t (σ becomes much less negative), Y* (qG*) must be
higher and X* (qB*) must be lower. The possibility that Y* is decreased cannot be
excluded if σ is only changed by a very small amount.
Figure 12.
According to (11) and (12), pG* will decline if σ becomes much less negative. (-σ is
lowered and the effect of a higher qG* is also negative, but the fall in -σ must be
sufficiently large). The effect of a less negative σ on pB* is difficult to predict since
(according to equation 12) a less negative σ affects pB* negatively but because qB* is
also lowered there is also a positive (opposing) effect on pB*. It is also not possible to
determine whether pG* exceeds pB* or not. (Although a qG* which is lower than qB*
increases the second term in equation 11 relative to equation 12. But at the same
time a higher ΘG softens this effect.)
Y
X
Gt=high Gt=low
Bt=low
Bt=high
65
The calculated equilibrium describes the resulting long run market equilibrium. A
higher t (which is also significantly higher than e) makes it more difficult for the bad
provider to convince investors to buy from him. Distance matters more and he is
forced to offer a higher quality level to make sure that the good provider does not
catch his market share. If the introduction of the Internet lowers t, the quality level of
the bad provider is lowered. If t is lowered through progress of technology qG* will
rise (for a large change in t) and qB* will fall. Price pG* will fall but the effect on pB* is
not clear since qB* and σ are changed. Although it can be shown that αG* exceeds ½
(see 5.1.3. and Appendix 6) for large changes in t it can unfortunately not be proven
whether a decreasing t raises or lowers αG*. Intuitively we would expect αG* to grow
after the fall in transportation costs.46 In this case IP G lowers his price due to a more
competitive environment. Since he is able to serve more investors and to distribute
information production costs over more investors, he is able to raise his quality level.
IPB serves fewer investors and must diminish his quality level. The new equilibrium
shows that the divergence between both quality levels becomes smaller. (qG* is lower
than qB* but rises, while qB* falls.)
5.1.3. Market share
The value of αG* can be determined by inserting in the reformulation of (8):
−+−+= *p*p*rq*rq
s1
21
*a BGr1
Gr1
BG (30)
46 The offer (price and quality) of IPG becomes more attractive. The offer of IPB becomes less attractive
regarding quality whereas the direction of the price change is unknown. This suggests a higher market
share of IPG.
66
If ΘG=ΘB then qG*=qB* and pG*=pB*. It is also known that a rise in ΘG ends up in a
sharp fall in qG* and a smaller fall in qB*. pB* increases and pG* decreases. It is
interesting to note that a higher ΘG does not necessarily imply an αG* of more than
½. This means that a provider with a higher type might accept a lower market share
and (see previous discussion) a lower equilibrium quality level than his competitor.
This can be attributed to a quadratic cost function for the production of information. If
quality is lowered, profit is strongly raised, ceteris paribus. Since utility of investors is
linear in price but concave in quality, the good provider may raise his profit by
lowering his quality level and also his market share. His decline in costs might
exceed his reduction in revenues due to a lower equilibrium price level. In Appendix
6, however, it is shown that αG* will exceed ½ for high values of t.
5.2. Unstable market
As mentioned before, in the asymmetric case it is difficult to determine whether the
shared-market equilibrium is stable or unstable. In condition 22 qG* is lowered more
than qB*. (At the starting point quality and prices are equal since ΘG=ΘB.) qG*-qB*
must be negative. The effect of the price change on (22) is unclear since the change
in quality is higher for the good provider but partly or fully offset by the rise in ΘG.
Consequently, both stability and instability are possible if t>e or e>t. But it is also
clear that the equilibrium will be stable if t>>e and will be unstable if e>>t. This
conclusion is sufficient for the purpose of this thesis since the exact location of the
changing point may be important in practice but need not be known exactly for this
qualitative discussion.
67
If e>>t the scenario becomes unstable. In this case the point of intersection between
G and B must lie on the left side of the diagonal. This means that Y*>X* or,
equivalently qG*>qB*. The dependency on σ and Θ is nearly identical to the situation
in the symmetric scenario. A higher σ shifts the minimum of the G function to the
right. A higher ΘG lowers the minimum of the B function. (G or qG do not depend on
ΘG.) Raising ΘG shifts the point of intersection of B (with the diagonal and with G) to
the left.
Figure 13.
5.2.1. Effect of type Θ on market equilibrium
The influence of Θ on the equilibrium point is explained by comparing the scenario
with the symmetric scenario. It is assumed that ΘG=ΘB and ΘG is now raised
exogenously. The point of intersection of B with the diagonal is lowered and also the
Y
X
G
B
3σ/2r
3σ/2r
68
minimum of the B function is lowered. Since the G function is not affected, the new
equilibrium must be found on the left side of the old (symmetric) equilibrium on the G
function. The X value of the equilibrium (equivalent to qB) must be lower than before.
Y* may be lower for small increases in ΘG (if the minimum of the reaction function G
is at the left of the diagonal) but will rise for a larger increase in ΘG, see Figure 14.
Figure 14.
5.2.2. Effect of t on market equilibrium
Again the discussion of comparative statics for an unstable equilibrium is enclosed
for the sense of completeness. If σ is raised (or t is lowered), both functions are
affected in a fashion similar to the symmetric scenario. Any value of G left to the
diagonal will be higher than before and any value of G right to the diagonal will be
lower than before. Reaction function B is changed in the same way (left and right
must be exchanged). This is also illustrated in Figure 15. A rising σ (larger rise) must
Y
X
G
BΘG=low
BΘG=high
3σ/2r
3σ/2r
69
end up in a higher Y* (a higher qG*) and a lower X* (a lower qB*). Since the location
of the minimum value of both functions can lie on both sides of the diagonal, it is
possible that qG* is lowered and/or qB* is raised if σ is only raised by a very small
amount.
Figure 15.
Because qG*>qB* the equilibrium price pG* must exceed pB* if σ is positive. (See
equations 11 and 12.) If qG* is raised and qB* is lowered (this is the effect of a large
increase in σ or an improvement in ΘG) pB* must be lowered. A higher qB* affects the
price negatively. This effect is reinforced if σ is also raised. The behaviour of pG* is a
little more difficult to present. If ΘG is increased, qG* is also increased and a higher
pG* is realised. But if the upward tendency in qG* is explained by a higher σ, this
increasing effect is partly or fully offset by the increase in σ . (The negative term in
equation 11 becomes lower as qG* rises but higher as σ rises).
Y
X
Bt=low
Bt=high
Gt=high
Gt=low
70
5.2.3. Discussion of unstable equilibrium
As mentioned above (and like in the symmetric scenario) the unstable equilibrium
cannot be achieved in the long run. Any small deviation from this point ends up in an
adjustment process, which leads to another equilibrium, either at αG equal to 1 or 0.
(Whether the equilibrium is stable at this level depends on the possibilities of the
competitor to re-penetrate or defend his market share. If a temporary negative profit
is allowed and the setting is changed to a dynamic setting the situation becomes very
complicated.) In this simple static model without the possibility to make a negative
profit, one provider will “catch” all investors. It is assumed that after the fall in t both
providers set their equilibrium offer as computed above. Investors react to these
offers but because the equilibrium is unstable they will herd to one provider. The
winner of this competition fight depends on prevailing circumstances before the fall in
t or on microscopic changes if the unstable equilibrium prevailed previously. It could
be possible that the bad provider has a higher market share in a situation where t is
too large for effective competition. This higher initial market share for IPB would be
given exogenously. A lower t can then result in the equilibrium where the bad
provider wins the entire pool of investors and the good provider is squeezed out of
the market.
71
6. Model discussion, robustness and extensions
6.1. Discussion
The model aims to point out dependences of provider decisions on various
exogenous factors, especially the improvement in network and distribution
technology. Although the unstable scenario is difficult to handle mathematically, it is
proved that a sufficient improvement in technology leads to market concentration.
The winner of such a “winner takes all” game need not necessarily be the better
provider. But even if we are only interested in shared markets the model allows us to
take several important conclusions. In the symmetric scenario it is shown that
investor specific and provider specific transmission costs harm the utility of investors.
Any decline in these costs is utility improving for them. If providers who differ in their
ability to conduct investigation compete and t is lowered, the quality level of the better
provider (qG*) is improved and the quality level of the bad provider (qB*) is lowered.
Unfortunately, we are only able to determine the direction of change of pG*, but not of
pB*. Even the movement of market shares after a technological innovation is difficult
to determine. We are not able to compute the sensitivity of the average quality level
(αG*qG*+αB*qB*) on t. But even without this knowledge it is interesting that the quality
level of the bad provider deteriorates and this decline need not necessarily be based
on a reduction of the according market share. In any case the degree of externalities
received by investors will be higher if the market becomes unstable.47 More herding
47 It can easily be shown that the sum of all distributed externalities is minimised if the market is
separated between both (or more) providers. (See Appendix 6). If the separation point is shifted
toward one provider, investors receive more externalities but also a higher quality level from this
provider since he is able to split up investigation costs over more investors.
72
behaviour prevails in such a market and investors will tend to value fundamental
information less than before. (In the model the degree of externalities received by
investors in the unstable scenario is exorbitantly high. Since also quality is raised in a
“winner takes all” there is a trade-off between better fundamental information and
more disturbing herding.) Therefore, any potential decline in the quality of traded
information and any upward tendency in the degree of externalities (more herding)
may be interesting for the discussion of information efficiency of financial markets.
Investment behaviour of investors worldwide during the last years of the 20th century
can be regarded as a perfect illustration of the benefits but also of the dangers of
technological progress in information technologies. Within extremely short time, stock
prices were raised without regarding information about business fundamentals.48
Anyway, such developments are not unusual after the invention of new technologies
or during the turn of a century.49 Also the invention of cars, trains, planes etc. caused
abnormal stock price behaviour. It is difficult to say whether these recent
developments in stock markets were caused by the innovation of a new technology
or by the use of the technology itself, which is suggested in this thesis.
In existing financial markets investors profit if they know or are able to estimate the
trading behaviour of other investors. It is impossible to observe the actions of all other
traders but it is possible to look at the information sources of other traders. According
to technical development it becomes more and more easier to distribute information
internationally. Consequently, it becomes easier to observe more information
48 See Hirschey (1998), or look at the course of indices like the German Neuer Markt or NASDAQ
during recent years.
49 See Shiller (2000).
73
providers than in the past. In worldwide-integrated financial markets it is possible to
monitor providers of other countries and information from international providers,
which were difficult to receive in the past. All investors have an incentive to search for
an information source that is observed by many other investors. This possibility is
increased through new information technologies. The Internet homepage of the
investment newsletter “The Motley fool” serves as an illustration50 that investors may
be interested in the behaviour of others. (The quality of the provided information is
not examined in this illustration.)
6.2. Robustness and extensions
6.2.1. Duopoly versus oligopoly
A duopoly market structure was assumed to avoid extremely complex equilibrium
descriptions. In real markets (and especially in financial markets) several providers of
information try to sell their products. Lower technical distribution costs will result in a
more intensive integration of this market. The analysis of more than two providers
becomes enormously complex since even in the case of only three providers any of
them is able to attract the investors of the two other providers. Assumptions about the
relative location of all providers are necessary. (E.g. if a third provider is introduced
he may be located on the left side of IPG, which increases the distance to IP B, or he
may be located at any point in a two dimensional plane.) Due to the externality any
additional customer that is “conquered” from a competitor raises the incentive of
customers from other providers also to join his investors. Even without competent
investigation abilities it is possible that several providers can significantly improve
74
their market share due to their location within the market. Depending on the market
structure externalities may be more important than quality and good providers may
be squeezed out of the market as shown above. The scenario can be compared with
a fight for a common standard where the “better” standard often fails to be broadly
accepted. Even if the average quality level is improved (this is one possible
conclusion of the model above) some investors will receive information of lower
quality and many more investors will receive a big part of their utility in the form of
externalities. In financial markets these additional externalities may cause
concentration on particular stocks or investments. Big news providing agencies
distribute information to a huge number of investors and these investors know the
number of investors and may invest accordingly. The fewer independent information
providers offer information the lower may be the diversity of different investment
strategies. (E.g. concentration on particular industries and avoidance of other
industries without economic justification.) However, the investment process is too
complicate to confirm such predictions without investigating this model extension
more closely. In this thesis the investment process is modelled by using extreme
simplifications. The influence of the Internet on the actual investment behaviour is
much more complicated and much empirical investigation has to be done to come up
with further results. Nevertheless, this thesis discusses several important issues that
should be interesting at least for investors, providers, regulators and not to mention
economists.
6.2.2. Symmetric information versus asymmetric information
50See Hirschey, Richardson, Susan (2000).
75
In reality the quality of an investment recommendation is not observable ex ante.
Since several anomalies can cause unpredictable stock market behaviour, it is not
even easily determinable ex post. The existence of herding may end up in self-
enforcing predictions where no fundamental research is conducted to formulate a
recommendation. An investment recommendation seems to fulfil the characteristics
of a credence good (i.e. the quality is not observable before or after the trade has
taken place). If investors are not able to distinguish between “good” and “bad”
information they will (from a theoretical point of view) only get zero quality information
and receive their utility through herding. Since this mechanism does not make sense,
it would be necessary to introduce a mechanism to overcome the information
asymmetry. Reputation or a kind of guarantee (or e.g. participation by the provider)
may be suggested at this point. This mechanism will cause additional expenses. It
may also be suggested that these expenses have to be raised if quality is
increased.51 But also if the level of quality does not affect the costs of the
mechanism, these costs make the sale of every quality level more expensive. If the
possibility to overcome the asymmetry is not different between providers this will
narrow the range between the quality-costs ratio of the good and the bad information
provider. It is also possible that some investors have better ability to distinguish
between different quality levels than others. Such a distribution of abilities would be
51 This means high quality levels are more difficult to prove than low quality levels. If you have to prove
that a particular commodity is at least of a particular characteristic (e.g. a low quality level) this is
easier to prove (and consequently cheaper) than if it is necessary to prove that the commodity has this
characteristic plus an additional (where the additional characteristic is interpreted as higher quality).
E.g. diversification between two securities (low quality diversification) will be easier to examine than a
recommendation to diversify between 30 securities (high quality diversification) since additional
securities must be examined.
76
another cause for herding behaviour since low ability investors would try to imitate
high ability investors.
Therefore, the introduction of asymmetric information would only reinforce the
conclusion of this thesis, that the commercialisation of the Internet raises concerns
about the distribution of bad quality information.
6.2.3. Static environment versus dynamic environment
The scenario is analysed in detail for a static environment. However, in real markets
not only technological progress over time but also time itself will affect several
resulting equilibriums. This is especially important in winner takes it all markets (or
the unstable scenario described here) because once a provider successfully captured
the entire market, his competitor(s) is(are) faced with an even more difficult
competition fight. This is due to the high degree of fixed costs but also externalities. If
all investors use the information of one provider, they receive a high amount of
externalities that cannot be offered by the competitor. The only possibility to stay in
the market is to attract a high share of the market before the other is able to do so.
Such a fight does not seem to be unusual in media markets (as discussed in 1.2.1.)
but is not the primary focus this model. Further variables about financing possibilities
and marketing strategies would be necessary. Provider would be able to offer their
information without covering their costs if they could expect to squeeze the
competitor out of the market and demand a premium price afterwards.52 The fight for
52 In this case a premium price would be set as high as possible but as low as necessary to avoid any
further attempt of the competitor to penetrate the market. But even this price would be difficult to
determine since it depends on the optimal possible penetration strategy of the competitor.
77
the market would be determined by the interaction of the pricing strategies of both
providers and would also depend on their possibilities to borrow money to cover
losses caused by price discounts and penetration pricing. A rational expectation
equilibrium analysis can be used to analyse such a competition fight. However, the
introduction of this fight would not alter the conclusions about the market drawn here.
In the unstable scenario one, but not necessarily the better provider, wins the entire
market share. In a dynamic environment the provider with superior access to
borrowing funds will be the primary candidate for winning . This provider need not be
the one with the better ability to produce information of high quality. Consequently, a
dynamic setting would not change the basic conclusions in the unstable scenario.
In the stable scenario the introduction of time would enable us to draw conclusions
about the adjustment process to the stable equilibrium. However, the resulting long
run equilibrium would not be affected. Again we can introduce several different
penetration strategies of providers, but such strategies are more relevant in a winner
takes it all battle. We can conclude that some interesting details can be seen if time is
introduced into the model but the main conclusions are also valid in a static
environment.
6.3. Implications and suggestions for market participants
A primary target of economic modelling is to help participants in real markets to
understand all implications and to assist them in formulating decision. The following
sub-sections are included to translate the formal conclusions of the model into
suggestions and advices for market participants how to react to the development of
new technologies.
78
6.3.1. Implications for investors
It is proved that any decrease in the costs for transmitting information is utility
improving for investors. On the one side, investors have to bear the burden of
variable distribution costs. Any decrease in this kind of costs is beneficial for them.
On the other side, better access to information providers (especially the possibility to
receive information from providers where access was not available before) lowers the
market price of information. In real markets this may lead to a higher proportion of
investors who invest in information sensitive securities.53
The effect of the Internet on the quality of information is very interesting for the stable
scenario. The quality of the good provider increases, the quality of the bad provider
decreases and the range between both quality levels becomes smaller. The average
quality level cannot be calculated without the knowledge of the market share. We are
able to advice investors to look closely on the quality of information, especially if they
are buying from a bad provider54, but it is also far from sure that the average quality
level is improved. Because the quality is difficult to examine in practice, it is
recommended that investors only use providers if quality is proven or they are
familiar with his offerings.
53 In the model the number of information buyers is not changed by the introduction of the Internet. But
since information is expected to be cheaper (in a symmetric market the price falls if t falls, in an
asymmetric market at least pG* falls) it can be suggested that more investors than before use their
Internet access to gather information and make portfolio decisions themselves. If we regard savings
accounts as investments with low need for information gathering and stocks as investments with high
need for information gathering, saving accounts will be replaced by more investments in stocks.
79
Since cheaper information transmission also raises the possibilities of market
concentration (as in the unstable scenario) investors have to be aware that the
winner of such a fight need not be the provider with better research capabilities. This
is especially important if it is difficult for at least some investors to distinguish
between different quality levels of information. Although even if a “bad” provider wins
the battle, he is able to raise his quality level. In a concentrated market investors
have to be aware that the provider need not be the one with better research
capabilities and that (even if the provider is the better one) they are partly following a
herding strategy. 55
6.3.2. Implications for information providers
From the point of view of information providers (in section 1.2. broadcasters,
newspapers, magazines and banks are introduced) the Internet seems to be a
challenging development. As long as technical distribution costs are similar (and also
the change in these costs is similar) between competitors, they do not affect
providers directly because the burden of these costs must be borne by investors.
They may even profit from lower costs for technical distribution because more
investors may be attracted to join the market. On the other side, the better access of
investors to other providers harms their interests since competition becomes more
critical. (This is even true in the stable market since more competition affects profit
54 Since it is proved that the quality level offered by this type deteriorates.
55 Investors in the model are assumed to be aware of this, but it may be necessary to inform real
investors about this issue.
80
negatively.) Small regional providers may be squeezed out of the market due to the
Internet.
This result does not only apply for providers of investment recommendations but also
for several other providers who offer information of similar value to buyers at different
locations. E.g. computer programs offered over the Internet, international weather
forecast, news about international politics, sport results, information about star actors
or even movies themselves etc.56 Small providers within one of these categories will
have difficulties in the future due to the new environment. Niche strategies can be
suggested as one alternative business segment for these unluckily media companies.
These providers will offer information about regional or specialised issues. The
separation between these classes of providers and the class investigated in this
thesis is the degree of externalities. Although it can be argued that externalities also
prevail in the classes mentioned above, externalities in market for financial
information seem more usual, resulting in an even stronger trend for market
concentration and will force some providers to develop defence strategies.
6.3.3. Implications for regulators
The possibility of worsening information efficiency (see discussion in the next sub-
section) and the danger of a loss in quality of investment relevant information should
be interesting for regulators as well. If bad quality is interpreted as incorrect
information, security-monitoring agencies should reinforce their efforts to avoid these
kinds of information. In existent markets this problem becomes even more acute in
the case of a winner takes it all battle since providers often lower costs in areas
56 But as mentioned above not only technical access, but also language can be a constraint for the
receipt of information.
81
where customers or investors have difficulties in identifying these cuts like in the
quality level. The underdog provider of such a winner takes it all battle may be try to
avoid his fall by offering a quality level even below the prediction o f this model.
But regulatory agencies should also increasingly pay attention to herding since the
easier possibility for investors to herd intensifies fears of market manipulation and
market trends that are not justified fundamentally. Individuals who are able to
understand the social mechanism behind herding would be able to affect
(manipulate) security prices or (as shown in this model) to sell information and
recommendations without conducting professional economic investigation. Hirschey,
Richardson and Scholz show the increasing troubles of the SEC (responsible for
monitoring security trades in the USA) of handling fraud over the Internet.57
6.3.4. Implications for market efficiency
As described in section 1.1.1. one important area of research in financial markets is
the efficiency of financial markets. Since the Internet enables all classes of investors
to improve their access to information, the influence of the Internet on market
efficiency should be discussed. However, this analysis does not investigate the
financial market itself but investigates the market for information directly. Since
“commodities” bought in this market are the primary input (beside money) into
financial market, the analysis above becomes relevant. Unfortunately this analysis
shows a trade-off between more externalities and the possibility for a better quality
level of information. (Although conclusions about the change of direction of quality
are also very limited. But in the unstable scenario we are able to conclude that more
82
externalities are distributed but also quality will be raised due to the concentration
process.) Externalities are interpreted as a kind of imitating behaviour. Although
imitating behaviour need not necessarily result in deviations from efficient markets, it
is implicitly assumed to do so in this analysis.58 We can conclude that better access
to information not necessarily improves market efficiency if externalities or imitating
behaviour are existent and can even distort the market price.
57 See Hirschey, Richardson and Scholz (2000).
58 If the investment behaviour of others is observable and an investor assumes that at least a few
investors are informed about fundamentals, it is possible to draw conclusions about the fundamental
value without knowing any fundamental information. The constraints of this possibility are discussed in
section 1.1.1. But in this thesis investors do not react on investing behaviour of others directly, but are
interested in the information received by many others. I.e. they get “informed” about the information
itself but profit even more if others also use the same information. Consequently, the externality does
not help to identify fundamental values.
83
Summary and conclusion
Reading important and well known daily newspapers (also newspapers which are
actually distributing fundamental information) may be of high value for herding
investors because they expect other investors to react on published news. Compared
with the past, these news and information can be published in every country (with
internet penetration) at low costs. The greater variety of offered information facilitates
herding investors to receive information received by most others. Hirschey,
Richardson and Scholz report in their article “How foolish are Internet Investors?” that
1.5 millions59 regularly visit(ed) the homepage of “The Motley Fool” (an online
investment newsletter). It can be suggested that not all of them are (were) exclusively
interested in fundamental information but (also) in information about the signals
distributed to others. More such examples will be found in the future and it can be
expected that not all of these publishers publish strictly fundamental information only.
This thesis was written60 during a period of significant ups and downs in financial
markets (especially in the technology and communication area of business). The
increasing price volatility during this period, which coincides with the worldwide use of
the Internet, supports the hypotheses of this investigation. It cannot be proven
whether the higher volatility is attributable to the introduction of a new technology
(which often causes stock markets booms) or due to the concentration process (or
even due to perfect fundamental investment decisions). Empirical work has to be
done to support or reject the conclusions of this thesis. It will be difficult to determine
the type of the winners of competition battles (profitable media). No profitable
publisher of news or investment recommendation will agree that externalities are
59 See Hirschey, Richardson and Scholz (2000).
84
responsible for his success. But it can be empirically investigated whether the
quality of investment news and recommendations is improved or deteriorated in the
future and whether more or less investors react on the same publications. The fear
that increasing herding behaviour makes it possible for “unproductive” publishers to
squeeze productive publishers out of the market and the fear of more herding
behaviour and manipulation should be taken very seriously by regulators. Anyway, if
mechanisms are established to prevent these dangers, the Internet (like other
improvements in information technologies) helps to lead to cheaper distribution of
high quality information to investors.
60 This thesis was written during the second half of 2000 and 2001.
85
Appendix
Appendix 1
ΠG is differentiated with respect to pG and qG:
=−−=G
2G
GGG
T2q
v)(pa?
G
2G
Gr1
GBr1
BGG2
Gr1
GGBGr1
BG
T2q
evtvpvrqvpvrqeptpprqppprqps1
−
−+−++−+−+−−=
FOC:
( ) 0vetp2rqprqs1
avppa
p?
Gr1
GBr1
BGG
G
G
G
G=
−+−+−−=+−
∂∂
=∂∂
(I)
0Tq
qpvqs1
q)c(q
qa
v)(pq?
G
Gr
r1
GGrr1
G
G
G
G
GG
G
G=−
−=
∂∂
−∂∂
−=∂∂ −−
(II)
ΠB is differentiated with respect to pB and qB:
( )( ) =−−−=B
2B
BGB
T2q
vpa1?
−
+−+−−+−+−++= vevtvpvrqvpvrqvse-ptppprqpprqp-sp
s1
Gr1
GBr1
BBBGBr1
GBBr1
BBB2
B
2B
T2q
−
86
FOC:
( ) ( ) 0vetprqp2rqs-s1
a-1vppa
p?
Gr1
GBr1
BGB
B
G
B
B=
−−+−++=+−
∂∂
−=∂∂
(III)
0Tq
qpvqs1
q)c(q
qa
v)(pq?
B
Brr1
BBr
r1
B
B
B
B
GB
B
B=−
−=
∂∂
−∂∂
−−=∂∂ −−
(IV)
(II) can be reformulated:
0T1
qvqs1
qps1
G
r1r1
Grr1
Grr1
GG =−+− −−−−
multiplied with r1r
Gq −
0T1
qvs1
ps1
G
r11
GG =−+− −
=> G
r11
GG
Ts
qvp −−= => equation 11
(IV) can be reformulated:
0T1
qvqs1
qps1
B
r1r1
Br
r1
Brr1
BB =−+− −−−−
multiplied with r1r
Bq −
0T1
qvs1
ps1
B
r11
BB =−+− −
=> B
r11
BB
Ts
qvp −−= => equation 12
(I) and (III) are added:
0v2pps GB =−++ => equation 13
Now pG and pB (see above) are inserted in (I) and (III):
(I): 0etTs
q2rqTs
qrqG
r11
Gr1
G
B
r11
Br1
B =+−−−+ −− (V)
87
(II): 0et
Ts
qrqTs
q2rqG
r11
Gr1
G
B
r11
Br1
B =+−++−− −− (VI)
These terms are added:
0sTs
qTs
qG
r11
G
B
r11
B =+−− −−
=> B
r11
B
G
r11
G
Ts
qsTs
q −− −= or G
r11
G
B
r11
B
Ts
qsTs
q −− −=
Both terms are inserted into (V) and (VI):
(V): 0etTs
q2rqTs
qsrqG
r11
Gr1
G
G
r11
Gr1
B =+−−−−+ −−
=> r1
G
G
r11
Gr1
B rqTs
q3e3t3rq ++−= −
=>
−+=
−
21
Tq
rs3
qqG
r11
Gr1
Gr1
B => equation 15
(VI): 0etTs
q2rqTs
qsrqG
r11
Gr1
G
G
r11
Gr1
B =+−−−−+ −−
=> e3t3Ts
q3rqrqB
r11
Br1
Br1
G −++= −
=>
−+=
−
21
Tq
rs3
qqB
r11
Br1
Br1
G => equation 14
88
Appendix 2
The minimum of G is calculated for σ>0.
−+=
−
21
TX
rs3
XGr1
r
0XrT
s3r1
r1
XG
r1r1
r1r
=
−+=
∂∂
−−
−−
( )r11r2
XTr1r
rs31 −
−
−+=
=> ( ) 1r2
r1
s3Tr1
X−
−
−
−= equation 18
Since r>1, the bracket is positive if σ>0. G is convex. Consequently, the extreme
value can only be a minimum. The location of the minimum value for B can be
calculated analogously.
Appendix 3
In the symmetric scenario ΘG=ΘB=Θ and qG=qB=q and pG=pB=p.
−+=
−
21
Tq*
rs3
q*q*r1
1
r1
r1
=> 21
q*T1
0 r11
−= −
=> r11
q*2T
−=
=> r1
2T
*q−
= equation 24
89
2s
vq*Ts
v*p r11
−=−= − equation 23
Appendix 4
In subsection 4.2.2. it was assumed that the market equilibrium shown in Figure 9
represents a solution the profit maximisation of both providers. The calculation of the
second order condition would be useful but is not included in this thesis because it
would require enormous mathematics although it is also possible to argue that the
equilibrium is a maximum without complicated mathematics. This is done for the
symmetric scenario. If the equilibrium (equation 23 and 24) were stable and a
minimum, any change of the demanded price would cause an increase (or at least no
decrease) in profit. Also a price level of zero would cause a profit at least as great as
the calculated equilibrium level. Because this does not make sense in the stable
scenario, it can be assumed that the resulting equilibrium is a maximum.
Appendix 5
∫++=1
0
zBG dzu*?*?W
Since the e term is linear, depending only on the market share, it is possible to
calculate the cumulative utility of investors. As can be seen in Figure 16 the
indifferent investor in the middle receives the least utility. Investors at z=0 and z=1
receive the most utility. Since the t term is linear, the utility decrease of investors
between z=0 and z=1 for more distance is constant up to the indifferent investor. The
area can be calculated by the average utility between z=0 and z=0,5.
90
( )∫
+
=1
0 221
u0udzu(z)
Figure 16.
0
rr1
0r1
0z utev2e
2T
rup*2e
rq*u +−+−+
=+−+=
−
=
0
rr1
0r1
0,5z utev2t
2e
2T
rup*2t
2e
rq*u +−+−−+
=+−−+=
−
=
∫ +−−+
=
−1
0
0
rr1
z uv4t5
2e3
2T
rdzu
uz
z=0 z=0,5 z=1
91
The profit of one provider is given by
( )
( )
T22T
2vtev
T2q*
vp*21
*?
r12
2
−
−−+−
=−−=
*2?r21
2T
21
et−
−−=
Total welfare is given by adding utility of investors and providers.
r21r
r1
0
2T
2T
ruv4t
2e
W−
−
−
++−−=
Appendix 6
From equation 30 it is known that
−+−+= BG
r1
Gr1
BG pprqrqs1
21
*a
From equation 13 it is known that
sv2*p2*p*p BBG −+−=−
It is also known (equation 12) that
B
r11
BB
Ts
qv*p −−=
92
If pB* in equation 30 is replaced by this term we get
−+−+=
−
1Tq2
srqrqs1
21
*aB
r11
Br1
Gr1
BG
If qB*=qG* (ΘB=ΘG) the term
−−
1Tq2
sB
r11
B must be zero.
B
r11
B
Tq2 −
must be equal to 1.
If ΘG is raised, qB* is lowered. B
r11
B
Tq2 −
will now exceed 1. If t is very large
−−
1Tq2
sB
r11
B will also be strongly and negative. rqB*-rqG* will be positive since qG* is
lowered more than qB*, but the bracketed term will exceed this number. The resulting
negative term is multiplied with s1
, where σ is negative. The resulting αG* must
therefore exceed 21
.
Appendix 7
It is proved that the sum of all externalities distributed to investors is minimised if αG*
is 21
. ez is the externality received by investor at location z.
( ) eea2ea2eaea2eaea1eadze G2
G2
GG2
G
1
0
2G
2Gz +−=+−+=−+=∫
FOC: 0e2ea4da
dzedG
G
1
0
z
=−=∫
93
21
a minG, = (The FOC must lead to a minimum since the second
derivative is 4e, which is positive).
94
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