%Paper: ewp-io/9502002
%From: Neil Gandal <gandal@econ.tau.ac.il>
%Date: Thu, 23 Feb 1995 10:19:12 +0200 (IST)

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\pagestyle{myheading}\markright{NEVER WORKS}
\begin{document}
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\begin{titlepage} \vspace*{0.2in}
\begin{center}
{\Large\bf  Adoptions and Orphans in the \\
Early Microcomputer
Market:} \\
%Chickens and Eggs, Hardware and Software. \\
%PRELIMINARY and INCOMPLETE}  \\
%Not for Circulation \\
\vspace{.2in} Neil Gandal (gandal@ccsg.tau.ac.il)\\
Tel Aviv University \\
Shane Greenstein (grnstn@vmd.cso.uiuc.edu)\\ University of
Illinois, Urbana-Champaign\\ and \\ David Salant
(ds20@gte.com) \\ GTE Laboratories 

\vspace{0.1in}\today \\
\vspace{.2in}{\bf Abstract}\\
\end{center}

\noindent In this paper we develop a model with (1)
differentiated
consumers, (2)  endogenous adoption times, (3) technical
uncertainty, and (4) alternative technologies sponsored by 
competing vendors.  We identify conditions under which orphaning
arises endogenously in a framework of dynamic competition.  We
then use the model to examine the development of the
micro-computer market in the
early 1980s, when the orphaning of a widely-adopted operating
system occurred. We find that the data characterizing this event
are consistent with our theoretical framework.




\vspace*{2 mm}
\noindent JEL Classification Numbers:  L86, O33.
\vspace*{3 mm}

\noindent We are grateful to Richard Arnott, Tim Bresnahan,
Francesca Cornelli, Gregory Duncan,
Raphael Rob, Yishai Yafeh and seminar participants at the 1994
Winter Econometric meetings,
the University of Pennsylvania, and INSEAD for helpful comments.
We received outstanding research assistance from Subhendu Roy and
Susan McMaster. Greenstein would like to acknowledge partial
funding from NSF IRI-92-09321.  Please
address all correspondence to David Salant, Principle Member
Technical Staff, GTE Laboratories Incorporated, Waltham, MA
02254.
\vspace{0.1in}\noindent
\end{titlepage}

\baselineskip=0.3in

\section{Introduction}


     Technical change in competitive economies is characterized
by cycles of creative destruction. Users adopt new products and
abandon others. In this paper we examine the relationship
between adoption of technologies  and the phenomenon of
``orphaning."  Orphaning occurs when late users adopt a
technology incompatible with the technology adopted by early
users,
and suppliers of supporting
services (complementary products) cease to provide their
products for the old technology.
These issues are of 
concern to vendors and users in electronics
markets
where technical
standards and product designs
are fluid.  Recent examples include (1) personal computer
operating systems (CP/M was the
early de facto standard and was  subsequently replaced by
MS-DOS),
(2) videocassette recorders
(Betamax versus VHS), and (3) Stereo systems (Digital Compact
Cassettes versus the SONY
Minidisk and Cassettes versus 8-track tapes).  In all of these
examples, the technologies were incompatible, that is, 
supporting
services or software written for one system did not work on the
other system.


In this paper we develop a model with (1) differentiated
consumers,
(2)  endogenous adoption times,
(3) technical uncertainty, and (4) alternative technologies
sponsored by
 competing vendors.  We identify conditions under which orphaning
arises endogenously in a framework of dynamic
competition. 

  Our theoretical analysis contains several insights about the
factors
producing orphans. We show that orphaning occurs 
in part,  because of the heterogeneity in consumer evaluations. 
In
particular, our model generates a
diffusion process  in which high value users are the first
to adopt new technologies.    Uncertainty regarding the
availability of complementary software also plays a key role. 
Early
and late buyers are likely to make
different choices when there are significant changes in the
availability of complementary services over time.  Finally, 
competition plays a role in discouraging orphaning; intense
competition among vendors translates
into lower prices in the present, and encourages
early adoption by all groups.

In the second part of the paper, we
use the model to analyze data on the
micro-computer market
 in the
early 1980s, when most of the original operating systems
technologies were orphaned.
In particular, we examine
the role played by increases in the
availability of software and peripherals for the competing
platforms. These increases were viewed
as far from certain at the time and played  a significant role in
the orphaning process.  We find that in contrast to
CP/M, the success of MS-DOS largely revolved around the significant
provision of DOS compatible application software programs.  The
data are consistent with our theoretical framework.



\subsection{Related Literature}

Our paper adds to an already sizeable literature on platform
competition and technology
adoption.
In a departure from the literature, our analysis of platform
competition is both theoretical and empirical; the empirical
portion builds on previous studies
of the microcomputer industry.  Gabel [1991] and Langlois and
Robertson
[1992] provide an extended economic history
of the personal computer industry. The latter identify factors
leading
to open platforms in the long run, while the former is a detailed
case study concerning the role of {\em de facto} standardization on
the evolution of the microcomputer industry.   In contrast to these
two studies, our empirical work is quantitative rather than
descriptive.
Our empirical analysis also builds on
Bresnahan and Greenstein [1992], who characterize
platform competition in the first
three decades of the computer industry.  They identify the
factors determining outcomes in platform competition.  Our work
differs in
that we provide a formal theoretical analysis of competition
between ``open"
platforms and we employ an original data set to perform the
empirical analysis. 

Our theoretical analysis of platform competition resembles in
spirit two dynamic models by Katz and
Shapiro of technological
adoption in the presence of network externalities.\footnote{Other
dynamic models of technology adoption
in
the presence of network externalities include Farrell and Saloner
[1986] and Arthur [1989].  In both of these models, consumers
purchase at different dates from {\em competitive} firms.}  Katz
and Shapiro [1986] investigate whether the market, by adopting one
of two
competing incompatible technologies, in both periods of a two
period model, establishes a de facto standard.  They show that an
emerging (superior) technology is overadopted, ie, is adopted for
parameter values for which it is socially optimal to adopt the
other technology.  In Katz and Shapiro [1992], an entrant must
decide when to
enter
and whether to make its product compatible with that of the
incumbent.  They show that when an entrant chooses to make its
product incompatible, it enters earlier than the socially optimal
date.  Further there is suboptimal standardization.

Our model makes departures both in structure and focus. The
common theme of the Katz and Shapiro papers is an
examination of the social and private incentives to obtain
compatibility, that is, standardization. In contrast, we focus on
understanding conditions under which 
different types of consumers
purchase different systems at different
 dates, which an explicit
model of adoptions and orphans requires. Hence, we place importance
on the uncertainty about the development of
complementary software for the incompatible technologies and
consumer heterogeneity. In addition, we tailor our analysis
to fit conditions in the PC market. This enables us to
statistically analyze historical data from this market
and compare the results with our theoretical framework. 

A related series of papers examine technological adoption in the
presence of {\em indirect network
externalities},  that is, when  the link between the number of
users
occurs through the variety of
compatible software products.  See Chou and Shy [1990] and
Church and Gandal [1992,1993].  Similar to these settings, we also
examine how  complementary products affects both vendor and buyer
decision-making.  Again, our theoretical focus differs. In Chou
and Shy and Church and Gandal, all
consumers make adoption decisions simultaneously.  Hence
orphaning cannot arise in equilibrium in their models. 

Finally, we overlap with the themes found in several 
decision-theoretic papers of investment under uncertainty. 
Sanchez [1994],
and Dixit and Pindyck (1994)
consider a setting  under which firms make discrete and
irreversible investments in emerging
technologies under uncertainty. Orphaning  occurs exogenously in
their models, and  buyers take
action in  anticipation of it.  Although we embed similar buyer
behavior in
our analysis, we focus on how
the interaction between buyers and sellers can produce orphaning
in equilibrium.

 
In the following section, we develop the basic model.  Sections 3
\& 4
characterize equilibria for the basic model.  In sections 5 \&
6,
we enrich the
model.
Sections 7 \& 8 provide 
anecdotal and statistical evidence consistent with our
theoretical
model.  Section 9
provides brief  conclusions.

\section{The Basic Model}



We develop a simple two-period model in which two  firms offering
incompatible systems (supporting
services
or software written for one system will not work on the other
system) compete for sales.  Each
system will, with a positive probability, experience some
innovation; by
innovation, we mean the
development of supporting services or complementary ``software"
which increases
the value of the system.\footnote{Supporting services
can take the form of  application software, peripheral
devices,
retail service, distribution facilities and information and
literature about the products.}

There are two types  of  consumers, denoted ``techies"
(T)
 and
``non-techies" (N), and a probability of
innovation which is independent of the number of early
users.\footnote{In
section 4, we extend the basic model to
the setting in which the probability of innovation depends on the
number
of early users.} The key features of the model are that (1) a
system is durable, i.e.,  a system purchased in the first period
will also provide service in the second period,  (2)
either,
neither, or both systems can experience innovation (between the
two periods) which will
enhance the value of the systems, and  (3)  consumers can defer
their purchase decisions to see the outcome of the innovation, if
any.  For analytical simplicity, we assume that consumers can
make
at most one purchase, and that this purchase can occur in either
of
the two periods.\footnote{In section 6, we show that are results
are robust to the setting in which early adopters can abandon the
system they purchased in the first period and buy a different
system in the second period.}

\noindent We make the following assumptions:
\vspace{2 mm}

\noindent (1) The value techies (non-techies) derive in each
period
from a system
without any innovation is $\theta^T$ ($\theta^N$). We let $N^j$
denote the number of consumers of type $j, j
= T$ or $N$.  $N \equiv N^T+N^N.$
\vspace{2 mm}

\noindent (2) $\theta^T  > \theta^N > 0,$  that is, techies
derive
more ``standalone"
utility from the basic system than do non-techies.
\vspace{2 mm}

\noindent (3) The systems have
identical marginal costs of production in each period (This is
for ease of exposition and can be relaxed). The first
period marginal costs for both technologies are denoted  $c_0$
and
the second period marginal costs are denoted $c_1.$ We assume
that
the marginal costs either fall or remain constant over time,
i.e.,
$c_0 \geq c_1.$  For the case in which costs remain constant over
time, we denote the common marginal cost by $c.$
\vspace{2 mm}


\noindent (4) Each consumer purchases  at
most one system.
\vspace{2 mm}


\noindent (5) A consumer of type $j = N$ or $T$ that purchases
system $i = a,b$ in the initial period (T=0) receives expected
utility   over the
two periods
equal to

\begin{equation}
V_i^j = 2\theta^j + \rho_i U_i - p^0_i,
\label{buy0}
\end{equation}

\noindent where $\rho_i$ is the probability that system $i$
experiences innovation and $U_i$ is the added utility either type
of consumer derives from system $i$ should innovation
occur, and $p^0_i$ is the price charged by firm $i$ in the
initial period.

If a consumer of
type
$j$ waits until the final period (T=1) and then purchases system
$i$,
the
utility derived is $V^j_i = \theta^j + U_i-p^1_i$ if
innovation
occurs, and $V^j_i = \theta^j - p^1_i ,$ if there is no
innovation, where
$p^1_i$ is the price charged by firm $i$ in the final period.
\vspace{2 mm}

Recall that innovation means the
development of supporting services or complementary ``software"
which increases the value of the system.  In our model, the
$U_i$'s
represent the increase in value that comes from the increase in
the {\em availability} of complementary software, rather than the
actual consumption of the software.

\noindent (6)   For ease of notation, let $\Delta U \equiv U_a -
U_b$ denote the difference in value added by complementary
software
for the two systems. 
Without loss of generality
we assume $\Delta U \geq 0,$ i.e.,  system ``a" is {\em ex post}
superior.   The interpretation is that if
complementary software indeed becomes available for both systems,
the value of system ``a" is enhanced by more than the value of
system ``b." 
\vspace{2 mm}

\noindent Finally, we introduce some notation:
\vspace{2 mm}


\noindent Let $\delta \equiv (\delta^N,\delta^T)$
denote the initial period purchasing decisions of the two types,
where
$\delta^j = i$ indicates type $j$ purchased system $i = a,b$ in
the initial period.  $\delta^j = 0$ denotes the state in which
type
j consumers make no purchase in the initial period.
\vspace{2 mm}

\noindent Further, let
$\alpha \equiv (\alpha_a,\alpha_b)$ denote whether innovation
occurred, ie, whether complementary software, appeared between 
the
initial and final periods.






  In the following two sections, we consider two cases.  In
the first case (section 3), the equilibrium is always characterized
by early
adoption, that is, for all parameter values, all consumers
purchase in the initial period.  In the second case (section 4) ,
outcomes in
which non-techies do not purchase in the initial period are
possible.  In both cases, if  consumers make a purchase in the
first period, they always purchase the ex ante superior system.
The motivation behind these sections is to establish conditions
in which some consumers wait and early purchasers are orphaned.


\section{Early Adoptions}

Here we consider a special case under which all consumers will
purchase the ex ante superior system in the first period, despite
the uncertainty.  This case obtains even when the potential
benefits from innovation (the $U_i$'s) are large.  The intuition
is
that competition between the systems for ex ante purchases leads
to
relatively low initial period prices.
This case obtains under the following two assumptions:

\begin{itemize}

\item Marginal costs are identical in both periods.

\item The standalone value of a system exceeds the marginal cost
of production for both types of consumers.

\end{itemize}
Recall that in this case $c $ denotes the constant per period
marginal costs.  Thus the
second condition above  becomes $ \theta^N > c.$  To find
equilibrium prices and purchase decisions, we
work backwards starting with the last period.

\subsection{Last Period (T=1) Pricing.}

Since  $\alpha$ can assume four values and $\delta$ can assume
nine
values, there are thirty-six cases.  Fortunately, the analysis
simplifies
considerably.  First note that if ${\bf \delta} = (a,a), (a,b),
(b,a)$ or
$(b,b)$, so that
all consumers made purchases in the initial period, final
period prices
are irrelevant.  The following lemma shows that there are
effectively four
cases.

\begin{lem}
\vspace{2 mm}

\noindent (i)  If  both firms innovated between the initial and
final periods, i.e., ${\bf \alpha} = (1,1)$ and if 
${\bf \delta}
 \in
\{(a,0),(b,0),(0,b),(0,a),(0,0)\},$ i.e., some consumers made no
purchase in the initial period, then equilibrium last period
prices
are
$p_a^1 = \Delta U +c$ and $p_b^1= c.$
\vspace{2 mm}

\noindent (ii)  When ${\bf \alpha} = (1,0),$ and ${\bf \delta}
\in
\{(a,0),(b,0),(0,b),(0,a),(0,0)\},$ then equilibrium last period
prices are
$p_a^1 = U_a+c$ and $p_b^1=c.$
\vspace{2 mm}

\noindent (iii)   When ${\bf \alpha} = (0,1),$ and ${\bf \delta}
\in
\{(a,0),(b,0),(0,b),(0,a),(0,0)\}, \; p_a^1 =c$ and $p_b^1=
U_b+c.$
\vspace{2 mm}

\noindent (iv)  When ${\bf \alpha} = (0,0),$ and ${\bf \delta}
\in
\{(a,0),(b,0),(0,b),(0,a),(0,0)\}, \; p_a^1 = c$ and $p_b^1=c.$
\vspace{2 mm}

\noindent Further, the expected utility of waiting for a consumer
of
type j
is

\begin{equation}
E V^j =\theta^j + \rho_a \rho_b U_b - c.
\label{euwait}
\end{equation}
\label{lem1}
\end{lem}

\noindent {\bf Proof:} The equilibrium prices in cases (i) - (iv)
are straightforward.  A
consumer of type $j$ will derive utility net of price paid of
$\theta^j-c$ in cases (ii)-(iv); in case (i) a consumer
receives net utility of $\theta_j + U_b-c$.  Since case (i)
occurs
with
probability
$\rho_a \rho_b$, the expression $E V^j$ follows immediately.
\hfill \rule{2mm}{2mm}

We will employ (\ref{euwait})  to determine whether a
consumer of type $j$ will buy one system or the other given any
pair of prices in the initial period ${\bf p}^0 \equiv
(p_a^0,p_b^0).$

\subsection{Equilibrium Initial Period (T=0) Pricing}

Suppose, system $h$  is ex ante superior, that is, $\rho_h U_h
\geq
\rho_j U_j$, for $h,j = a$ or $b$, and  $h \neq j.$   Recall we
assume that $\Delta U \equiv U_a - U_b \geq 0.$  When  $\rho_b
U_b
\geq \rho_a U_a$, it must be the case that system ``b" has a
higher
probability of experiencing innovation than does system
``a."
Although system ``a" would dominate system
``b" when both have software, it is possible for system ``b" to
be
ex
ante superior.

A consumer of type $j$ will prefer purchasing system
``b" to system ``a" in the initial period, period $0$, if and
only
if
$2\theta^j + \rho_a U_a - p_a^0 < 2\theta^j + \rho_b U_b -
p_b^0$ or iff  $p_a^0 - p_b^0 > \rho_a U_a - \rho_b U_b.$

When $ \rho_a U_a < \rho_b U_b$, all consumers  prefer system
``b''
to system ``a'' in
the initial period whenever firm ``b's" price, $p_b^0$, is
less
than $\rho_b U_b - \rho_aU_a +c$, and the  price charged by
firm ``a'' is equal to marginal cost c.  Conversely, when
$\rho_aU_a > \rho_bU_b$,
all consumers will prefer  system ``a'' to
system ``b'' in
the
initial period, whenever $p_a^0 \leq \rho_aU_a - \rho_b U_b  + c$
and $p^0_b \geq c.$

The question remains as to whether consumers
will purchase in the first period or wait.
The following proposition shows that in this case, competition
induces all consumers to buy in the initial period.


\begin{prop}  (Early Adoption) Suppose $\theta^N > c$.  The
unique
subgame prefect equilibrium is
characterized by

$$p^0_a = \max\{-\Gamma +c,c\} \hspace{2 mm} and \hspace{2 mm}
p^0_b = \max\{\Gamma +c,c\},$$
where $\Gamma \equiv \rho_bU_b - \rho_aU_a$.  All consumers buy
the
same system in the first period and from the firm that has the ex
ante superior system, i.e., from firm ``a" iff $\rho_aU_a \geq
\rho_bU_b.$ \label{earlyprop}
\end{prop}

\noindent {\bf Proof:} First notice that price competition
between the two firms
will drive first period prices to $p_a =c\;$ and $p_b = \Gamma +
c$
or $p_a = -\Gamma + c$ and $p_b = c$;  the firm with the ex ante
superior system makes all the sales and its rival has zero sales
and profits.

If the firm with positive sales were to delay
selling until the last period - in hopes of earning greater
profits -
then its rival would sell to all consumers in the initial period.
Thus, the firm
with the ex ante superior system will not be able to earn more by
setting an initial period price above $|\Gamma| + c$ (and
possibly
delaying sales).

Further, the firm with the ex ante superior system will earn less
if its initial period price is less than $|\Gamma| + c$.  A best
response for its rival to a first period price of $|\Gamma| + c$
is
to set its initial period price at c.

We now show that when initial
period prices are $|\Gamma| + c$ and c, both types of
consumers
will purchase early rather than wait.   First suppose that
system
``b"
is ex ante
superior.
Then the expected utility for a consumer of type $j$ buying
system ``b"  in period $0$ is
$$ 2\theta^j + \rho_bU_b - \Gamma -c  = 2       \theta^j +
\rho_aU_a - c.$$

Now suppose that system ``a" is ex ante superior.  Then the
expected
utility for a consumer of type $j$ buying
system ``b"  in period $0$ is

$$ 2\theta^j + \rho_aU_a + \Gamma - c = 2\theta^j + \rho_bU_b
-c.$$

Since both of the above utilities are greater than the expected
utility from
waiting from (\ref{euwait}), all consumers purchase in the
initial
period.
\hfill \rule{2mm}{2mm}
\vspace{3 mm}

The above proposition indicates that competition will induce both
types of consumers to buy early from the same firm, whenever
standalone system values ($\theta^N$ and $\theta^T$) are 
relatively large for both types of
consumers and when production costs are not declining over time.


\section{Waiting Games}

Here we consider a more general model, in which we relax the
assumptions we made in the previous section. 
We consider the case in which marginal costs fall over time, while
maintaining the assumption that stand-alone system values exceed
the latter period marginal costs for all consumers.  In the
Appendix we formally 
examine a qualitatively similar, but algebraically more tedious,
case in which ``non-techie" preferences are 
such that will not purchase a system without complementary software
at any price which covers marginal production costs, but would be
willing to pay a positive price for either system if software were
to become available.

When marginal production costs initial period are $c_0$ and fall
over time to $c_1$ in the final period, two 
outcomes are possible:


\begin{enumerate}

\item All consumers purchase the ex ante superior system in the
initial period.

\item Techies purchase the ex ante superior system in the initial
period.  Non-techies purchase in the final 
period.\footnote{In the case we consider in the appendix, an
additional (third) outcome in which techies purchase the ex ante
superior system in the first period and non-techies make never
purchase is possible.
In outcomes 2 and 3, techies getting stuck with orphan
technologies.  The only qualitative difference between the case of
falling costs and the case we consider in the appendix is that in
the former, non-techies eventually always make a 
purchase.  In the latter case, if non-techies have low stand-alone
valuations and neither system experiences an 
innovation, they will make no purchases.}

\end{enumerate}

In the second outcome, techies get can stuck with orphan
technologies depending on which system experiences 
innovation.  The reason non-techies wait is that the firm with the
ex ante superior system cannot price 
discriminate among consumers in the initial period.  When costs
fall significantly, this firm would prefer to sell only   to 
techies than to set price so low as to attract both techies and
non-techies.  Whence adoptions and then 
orphans!




\begin{prop}
Suppose that $c_0 - c_1 - \rho_b (1- \rho_a) U_b \leq
\theta^T. $   \\

(I) In the case in which system A is both ex post superior and ex
ante superior so  that $\rho_a U_a > \rho_b U_b$
there is a unique equilibrium in which:

\begin{enumerate}

\item  All consumers purchase system ``a" early
if $\theta^N \geq c_0 - c_1 - \rho_b (1- \rho_a) U_b.$  Initial
period prices are ${\bf
p}^0
= (c_0 - \Gamma , c_0 ).$

\item For $\theta^N < c_0 - c_1 - \rho_b (1- \rho_a) U_b \leq
\theta^T $, techies purchase
the
ex ante superior system in the initial period.  Non-techies
purchase in the final period. Initial 
period prices are ${\bf p}^0 = ( c_0,c_0 + \Gamma).$


\end{enumerate}


(II) In the case in which the ex post superior system is
inferior ex ante there is a unique equilibrium in which:

\begin{enumerate}

\item  All consumers buy early from the ex ante superior system
if $\theta^N \geq c_0 - c_1 - \rho_a (U_a - \rho_b U_b)$.
Initial
period prices are ${\bf
p}^0
= (- \Gamma+c_0,c_0).$

\item For $\theta^N < c_0 - c_1 - \rho_a (U_a - \rho_b U_b) \leq
\theta^T$, techies purchase
the
ex ante superior system in the initial period.  Non-techies
purchase in the final period. Initial 
period prices are ${\bf p}^0 = (- \Gamma+c_0,c_0).$


\end{enumerate}


\label{main2}
\end{prop}

\noindent {\bf Proof:} We first prove the result for case
when the ex ante
superior system
is also superior ex post, that is,  for
$\Gamma =
\rho_b U_b - \rho_a U_a < 0$ and  $U_a \geq U_b.$
 Suppose that the
techies buy the ex ante superior system in the first period.  We
will show
later that this will be true in equilibrium.


Suppose the initial period price for system a is $p_a^0 =
- \Gamma +c_0,$
and the initial period price for system b is $p_b^0 = c_0.$  Note
that if all consumers buy early, the fact that there is price
competition and the difference in expected values of the two
systems is $\Gamma$ implies that these would have to be the first
period equilibrium prices.  If firm A were to raise its price,
firm B, which otherwise would not make any sales, could then
charge
a positive price and earn profits.

Given these prices, the expected utility of  non-techies from
buying early
is

$$\rho_aU_a + 2\theta^N -(- \Gamma + c_0) =
\rho_bU_b + 2\theta^N - c_0.$$
If the non-techies wait, from Lemma 1, they receive an  expected
utility of
$ \theta^N + \rho_a \rho_b U_b- c_1.$

Comparing the above two equations, buying early yields higher
utility for non-techies
at prices $- \Gamma +c_0, c_0$ whenever

$$\theta^N \geq c_0 - c_1 - \rho_b (1- \rho_a) U_b.$$


So for $\theta^N $ exceeding the above critical value,
all consumers (techies and
non-techies) alike purchase system A, the ex ante superior
system,
in the first period.


Now consider the case in which $\theta^N$ is below the above
critical value. If firm A
wants to sell to
both types in the first period, then it must set $p_a^0$ low
enough to attract non-techies.   Following the same argument used
in Proposition 2, the maximum price that firm A can charge and
sell to both cohorts is

$$p_a^0= \rho_a(U_a - \rho_bU_b) +
\theta^N + c_1.$$


The profits from selling
to all
consumers in the first period when $\theta^N$ is below the above
critical value
are $N[p_a^0 -c]$ and the expected profits from selling
only
to the
techies in the first period are
$$-N^T \Gamma +
 N^N[\rho_a(1-\rho_b)U_a +
\rho_a\rho_b(U_a - U_b)],$$ where the second term
represents the
expected profits from selling to non-techies in the second
period.
The profits to selling to both types are larger whenever

$$\theta^N \geq c_0 - c_1 - {N^T (\rho_b (1- \rho_a) U_b) \over
N}$$.

Since this critical value exceeds the above critical value,  part
(I) of the proposition follows immediately.  The proof of part
(II)
is analogous and hence omitted.\hfill \rule{2mm}{2mm}
\vspace{3 mm}

As in Proposition \ref{earlyprop}, competition drives initial
period prices down
 to (or just below) the point
at which the firm with the ex ante inferior system could make
sales
and earn
 zero profits.  These prices
will induce techies to buy the ex ante superior in the initial
period.\footnote{Note that when
$\theta^T < c_0 - c_1 - (1- \rho_a)\rho_bU_b,$ 
a third case in which techies also  wait obtains. 
We  are using a discrete time model to approximate what are
essentially continuous
 time events. So we simplify the choice of adoption dates to
either
early or
 late, and therefore we have restricted attention to cases in
which
at least
 techies will buy early.}

The proposition shows that non-techies will not purchase in the
initial period when  (1) the fall in marginal cost ($c_0 - c_1,$)
is large relative to the standalone value, $\theta^N$, (2) the
probability that the ex ante superior system will experience
innovation is high relative to the probability that the  ex ante
inferior system will experience innovation, and (3) the
additional
utility $U_i$ associated with the introduction of complementary
products for the ex ante inferior system is low relative to the
additional utility associated with the ex ante superior system. 
Clearly (1) is obvious, that is large decreases in marginal costs
encourage low-value consumers to delay purchases; on the other
hand,  (2) and (3) may seem surprising.  The intuition is that
under these conditions, the ex ante superior system is much more
attractive than the  ex ante inferior system and hence there is
not intense price competition between the systems; in such a case,
it is optimal for non-techies to wait.

Part II of Proposition 2 shows that under the above  conditions,
early and late buyers will make different choices when there are
significant changes in the availability of complementary services
over time.

\section{Network Externalities}

In Propositions 1 and 2, the probabilities of innovation
(the $\rho$'s) are independent of the number of
consumers who purchase each product in the initial period.  Our
interpretation of innovation is the appearance of
complementary products, such as
software.  The incentives of third parties to develop
software may depend on the number of early adopters.  In this
section, we consider the case when the
probabilities of innovation are
increasing functions of the number of initial period adopters,
that
is, there are direct network externalities.  For simplicity, we
again consider the basic case in which marginal costs are
constant
over time. 
We consider  network externalities of
the form

\begin{equation}
\rho_i = \rho_i (N_i),
\hspace{2 mm} i = a,b.
\label{net}
\end{equation}

\noindent where $ {\partial \rho_i \over \partial N_i} \geq 0.$
When there are direct network externalities, multiple equilibria
can exist, as the following proposition illustrates:

\begin{prop}

Suppose that

\noindent(1) $\theta^N > c,$
\vspace{2 mm}

\noindent (2) $\rho_a(N) U_a > \rho_b(0) U_b,$ and
\vspace{2 mm}

\noindent (3)  $\rho_b(N)U_b > \rho_a(0)U_a,$
\vspace{2 mm}

\noindent where $N$ is the number early adopters.


\noindent (I) An equilibrium in which all consumers
adopt system ``a" in the initial period exists.  Equilibrium
prices are  $p_a^0 = \rho_a(N)U_a- \rho_b(0) U_b + c$, and $p_b^0
= c.$
\vspace{2 mm}

\noindent (II)   An equilibrium in which all consumers
adopt system ``b" in the initial period exists.  Equilibrium
prices are $p_b^0 = \rho_b(N) U_b - \rho_a(0)U_a + c $, and
$p_a^0 = c.$
\vspace{2 mm}

\label{netprop}
\end{prop}

\noindent {\bf Proof:}  In the first equilibria, everyone, both
firms and each individual consumer, anticipates that consumers
will
purchase system ``a."  These beliefs are self-fulfilling,
provided
that firm ``a" sets its price at $p_a^0 = \rho_a(N) U_a-
\rho_b(0) U_b + c$.  In the second equilibria, everyone
(correctly)
anticipates
that early adopters will purchase system ``b."  These beliefs are
self-fulfilling, provided that firm ``b" sets its price at $p_b^c
=\rho_b(N)U_b- \rho_a(0) U_a + c$.  Then, the result follows
immediately from Proposition 1.  \hfill \rule{2mm}{2mm}

Hence  the result is as characterized in  Proposition 1,
with the exception that there are multiple equilibria.

\section{Second Purchases}

Here  we  consider the case in which early period adopters
can purchase the other hardware technology in the final period.
We  illustrate that the possibility of re-purchase  has no
qualitative effect on the equilibrium
outcomes characterized in Proposition 2.
We consider the case in which technology A is both ex ante and ex
post superior and only techies made initial period
purchases. 

The
techies'
final period utility of staying
with the
early period system $a$ is
$  \theta^T + \alpha_a U_a$, while the utility of switching to
system ``b"  is
$ \theta^T + \alpha_b U_b - p_b^1.$
Since technology ``a" is ex post superior, the techies would not
switch to technology ``b" in cases
$\alpha = (0,0),\alpha = (1,0),$ and $\alpha
= (1,1)$) at any
non-negative price.
Hence the equilibrium final period prices are as characterized in
Lemma 1 with ``c" replaced by ``$c_1.$"  For the case in which
$\alpha = (0,1)$, the techies
might make an additional purchase.

Lemma 1  shows that when re-purchase is not possible, the
equilibrium final period prices in case $\alpha = (0,1)$
 are
 $p_a^1 = c_1$ and $p_b^1 = U_b + c_1$.   Notice that at
these prices,
 only non-techies would
purchase in the final period.  If firm ``b" charged $p_j^1 \leq
U_b$, techies would
indeed make a
 second purchase.   Thus if
$N(U_b-c_1) < N^N U_b $, so that it is not profitable for
firm ``b" to sell to both cohorts, final period prices are
identical to those characterized by Lemma
1, and no re-purchase occurs despite the fact
that re-purchase is possible.  Thus, the expected utility of
waiting does not change for any type.
If on the other hand, it is profitable for firm ``b" to sell to
both cohorts, final period prices are $p_b^1=U_b$ and $p_a^1=c$.
Here, the expected utility of waiting for
non-techies increases by the factor of  $\rho_b (1- \rho_a) c_1$.


Alternatively, if price discrimination (based on whether a consumer
already has an ``old" product) is feasible,
consumers (techies) who turned in their ``old" systems would be
charged $p_b^1=U_b$ and $p_a^1=c_1$, while consumers who did not
turn
in an old system would be charged $p_b^1 = U_b + c_1$ and $p_a^1
=
c_1.$  In the case of price discrimination, the  expected utility
of waiting does not change for any type, regardless of the
distribution of techies in the population.

Hence  the equilibrium is as characterized in  Proposition 2,
with the exception that  techies may make multiple purchases.  We
conjecture that this argument generalizes to other cases.

In summary, our theoretical analysis contains several insights
about the factors
producing orphans. Orphaning occurs 
in part,  because of the heterogeneity in consumer evaluations,
ie., high value users are the first
to adopt new technologies. However, uncertainty regarding the
availability of complementary software also plays a role. 
Proposition 2 shows that early
and late buyers will make
different choices when there are significant changes in the
availability of complementary services over time.  Finally, 
competition plays a role in encouraging
early adoption by all groups, which should discourage orphaning.

\section{Platform competition in the micro computer market}

    It is not our intention to recount the economic
history of the personal computer industry.\footnote{See
 Gabel [1991], Bresnahan and Greenstein [1992], and
Langlois and Robertson [1992].}  Here we explain how our model
captures many of
the factors that shaped a key episode of platform competition,
between the CP/M and DOS operating systems that occurred
in the early 1980s.

There were a number of other
operating systems that competed with CP/M and DOS in that
period, most notably Apple, as well as Unix, TRS, and Atari.  The
evidence (see Figures 1-3) suggests
the preeminence of the fully open platforms, CP/M, MS-DOS, and
partially-open Apple platforms. However,
Apple appeared to serve a different market than did CP/M and DOS
(See Gabel [1991], and Langlois [1992]).\footnote{There is a
literature that argues 
that IBM/DOS succeeded, in part, due to the openness of its
architecture as
compared to Apple's. In contrast, we want to focus on the factors
that determined the success and failure of the two fully open
platforms, an issue that has largely escaped analysis. Hence, our
analysis focuses on the role
stochastic,
network-related, events had on adoption decisions and platform
competition between the two fully open platforms. }


Before we begin our discussion we briefly explain our data,
which we assembled for this study.  Figures 1-3 show the
quarterly
number of pages of
advertisements in Byte magazine devoted to hardware, software,
and peripherals (respectively) using different competing
platforms. 
We chose Byte
because unlike other computer magazines, Byte is a general
magazine
that covered developments for all operating systems.    Some
software was compatible with several platforms and was advertised
in that manner.  In such a case, each platform receives an equal
proportion of the advertisement.

Recall that the $U_i's$ represent the availability of software
and
peripherals, not actual sales. 
We believe that the amount of
software
and peripheral advertising data is a natural proxy for the
relative number
of complementary products available for a particular operating
system.  Since the advertisements in Byte magazine during the
relevant period were for particular software products and
peripherals
rather than advertisements for mail order software companies, we
believe that the data are a good proxy for availability of
complementary products.\footnote{Of course, actual sales of
software would also probably be a good proxy for the availability
of complementary
products.}

We use the hardware advertising data as a proxy for the
sales of the various operating systems.  We employ hardware
advertising data rather hardware sales data in order to be
consistent with the software/peripheral data and because 
it is extremely difficult to
obtain detailed sales information, which is consistent over time,
about
all suppliers and products for each platform.

This data has strengths and weakness for our purpose. Its
main strength is that it provides a quantitative and consistent
indication of the growth, commercial success, and failure of all
the categories of components associated with these different
computing platforms. Because it is so difficult to construct
consistent measurement of new or incipient markets, this may be
the only measure that can do so. However,
there is no
generally accepted theory of advertising for high-technology
markets, nor any systematic empirical literature on the
topic.\footnote{Despite economists' general interest in the
phenomena of advertising, as a research topic in itself, there is
almost no precedent for using this type of data to learn about
features of the underlying high technology market. We are aware
of only one other attempt to examine advertising in high-
technology markets. Klenow, 1994, uses news releases and
announcements to track the entry of new goods.}  So there is no
commonly
 accepted way of relating advertising to the rate of sales, or
the
installed
 base.
     We are convinced, however, that the observed level of these
ads
positively correlates with real economic activity. We are
especially confident of this conclusion when we examine aggregate
statistics, which averages out many potential small errors at
individual companies.
First, we are confident that as the total sales for a type of
product increases,
so too do the total level of advertising.  Second, the lags
between
advertising and real economic activity do not appear to be long
-- e.g., conventional wisdom places this industry among the
fastest in
its responsive to market signals and new sales trends. Third, we
are also convinced that advertising is segmented across different
sub-component markets, so we can differentiate between different
types of advertising for different components in a sensible way.
     Therefore, we posit that the total advertising for a
category of
components positively correlates with the growth and commercial
success or failure of the category of components in this market.
The total of commercial advertising for a component category
reflects the underlying adoption behavior of users and
equilibrium outcomes
of inter-platform competition. This  is surely right
in the long run, since vendors in this market responded to
successful sales with more advertising and to commercial failure
with less (or none). The main reason for expecting difficulty
for our purposes is that some advertising has speculative
and signalling motives in the short run, as new products are
rolled out. These problems suggests that we should take great
care below not to overstep our interpretation.

 Several vendors sold machines to customers between
1975 and 1980. The vast majority of these early users tended
to be, and perhaps needed to be, computer literate, and likely
included many
 tinkerers and hobbyists.  These are the techies in our model. 
The
benefits
 derived by the early users from their microcomputers were to a
much greater
 extent a function of the user's ability to  experiment and do
much of
programming, as compared to later users - who are the non-techies
of the model.

{}From the figures, it is obvious that CP/M was the dominant
operating
system.   One reason for the success of CP/M  was relative
abundance of available application software, which was available
for free within the hobbyist
community.  Since the standalone system values were relatively
low,
the market was (as predicted by Proposition 2) limited
to techies.

A dramatic change in the market for operating systems occurred in
the early 1980s shortly after the introduction of the IBM PC  in
1981.  The IBM personal computer primarily used the 
MS-DOS operating system.\footnote{The IBM PC
also
could run the  CP/M operating system.} 

  As Langlois and Robertson [1992] document, the
change in platforms underwent two phases. One occurred within the
1981-1982 period, when CP/M and DOS operating
systems competed and the outcome was uncertain.  Indeed, the July
1982 edition of Byte magazine devoted 26 pages to an analysis  of
the two 16 bit operating systems (the CP/M-86 and MS-DOS)
competing
for dominance. 
During this phase,
there was not yet sufficient appeal for non-techies to enter the
market, despite the competition between the two
platforms. 

There is evidence that during this phase, CP/M, the
early leader, was viewed as the
ex ante superior system, at least concerning expectations about
the number of complementary software products that were likely to
be available in the immediate future.    In the detailed
comparison
of the
CP/M-86 and the MS-DOS operating systems
that appeared in Byte magazine in 1982, Richard
Lomas, a system
manufacturer wrote, ``In seeking languages and applications, I
have
found more
available for CP/M-86 than MS-DOS."\footnote{Note that this edge
in
application programs corresponds with figure 2.}
More importantly, there were expectations that CP/M would retain
this relative edge
over time.  Lomas noted that
the
CP/M software was
also compatible
with
MP/M-86, a multi user system.  The upward
compatibility of
MS-DOS software to Xenix (the multi user system specified by
Microsoft) was
less certain.  Lomas remarked that ``most if not all software
running under MS-DOS will not run under Xenix."

Thus, many of the techies adopted CP/M systems in the 1981-1982
period.  Figure 2 shows that as late as 1983, software vendors
using CP/M invested almost
as
heavily in advertising as those using MS-DOS.

On the other hand, MS-DOS was viewed by many as the ex post
superior system, that is, if the applications software for MS-DOS
did materialize, there was general agreement that MS-DOS was ``a
better and
faster single-user single-tasking operating system for
nontechnical
users."\footnote{BYTE Magazine, July 1982, p 331.} In terms of
the model, many believed that
that the
$U_i$ for MS-DOS was larger than the $U_i$ for CP/M. 

One reason  for this assessment was that IBM had
tremendous existing customer base in traditional data processing
shops throughout large corporations.  Its existing marketing and
support network initially viewed the PC as a complement to
already established mainframe networks, where most users had
experience with terminals. PCs could act as intelligent
terminals, and with a bit of technical gerrymandering at first,
and less so as IBM improved the system software, could transfer
data from mainframes to small applications on the PC. When
user-friendly spreadsheets, databases and wordprocessors appeared
on DOS, these PCs were able to perform simple analytical and
word-processing tasks while by-passing capacity constraints
associated  with the use of a central data base on a mainframe. 
The Techie-oriented systems that preceded the IBM
PC were less able to address both sets of needs. 
In sum, the initial IBM PC initially represented a promise of
increased functionality to a large class of new PC users: existing
mainframe users.\footnote{This alone, of course, cannot explain the
IBM PC's success. Even as
late as 1983, there was widespread dissatisfaction among Data
Processing  managers with
functionality of personal computers in business environment
(Friedman and Cornford [1989]).}

The installed base of mainframe users perhaps also provided greater
assurances of a market for software, and  provided software
developers incentives to develop software for DOS-based systems.
Other factors also affected the outcome. In contrast to the early
Apple line of microcomputers, the IBM PC with its MS-DOS operating
system was an open architecture system.  Gabel [1991] provides
evidence that software applications for the proprietary Apple
operating system declined significantly with the advent of the IBM
PC.  Of course, CP/M was also an open system.\footnote{Openness
eventually became
 associated with
cloning.  Yet, the significant clone occurred  in 1985-87,  after
the dominance of
the standard was established.} Indeed both DOS and CP/M operating
systems could be run on
 the early Intel 8086 chips.\footnote{See the Lomas article in
{\em Byte} 1982.}

Nevertheless, by 1984, Gabel [1991] notes that there were 11,000
different software programs available for the MS-DOS operating
system.  By the 1984-1985 period (Langlois and Robertson's second
phase),  the IBM PC with its
MS-DOS operating system had
supplanted the CP/M machines.  Figures 1-3 show that CP/M
hardware and peripheral advertisements ceased to exist and
software
advertisements had declined significantly.


Thus,  a snap shot of the industry in
1985 hardly resembled a snap shot of the industry in 1981. The
primary users were technically sophisticated in 1981. They were
general purpose by 1985. The main applications were limited in
1981 and often were not user friendly. In 1985 applications
were varied and many emphasized their ``ease-of-use". And most
interesting for our purposes,
the dominant technical standards embedded in the operating
systems of the majority of PCs in 1981 differed from those
embedded in the majority of PCs in 1985. Since most of the new
application software was incompatible with the CP/M systems, a
large fraction
of the users of PCs in 1981 found themselves orphaned by 1985.
Figure 4 summarizes these ``snapshots."

In the next Section, we examine the
advertising
 data to look for differences in the combinations of software,
hardware and
 peripherals sold to early users and late users.   Based on these
historical
 facts and the theoretical model, we expect that the later
(general purpose)  users
would be more
 reluctant than early (technical) users to purchase systems
without
the availability of a significant amount of complementary
software.




\section{Econometric Evidence}


The empirical analysis investigates the early PC computing
market.   Our
theoretical model
 suggests that where orphaning occurs, the early adopters and the
later adopters
 would have qualitatively different characteristics.  In
particular, early adopters would be less reliant on software than
later  adopters.  Hence, we  expect a
 different pattern of sales for hardware and software (and
peripherals) between
 CP/M in the early years in which it was more dominant and MS-DOS
in
the later
 years in which it was dominant.  More precisely, for MS-DOS, we 
expect that
previous sales of applications software will be a better
predictor 
of future hardware and 
 software sales than previous hardware sales. 

We track the history of
components associated with DOS and CP/M, the two dominant ``open"
platforms.  Both were ``open" in the sense that their operating
system specifications were known to potential third-party
vendors of software and peripheral hardware.   For each platform,
we collected advertising data for the following three
categories: hardware, software and peripherals. For reasons
explained below, we focus on describing and interpreting the
relationship between contemporaneous and lagged commercial
activity associated with hardware and software. First we discuss
characteristics of the data and then perform our analysis.

We track the CP/M
market from April 1978 to October 1986, which is almost the
entire lifetime of products associated with the platform. We
track the DOS platform from July 1981, the date any product on
the DOS platform was first advertised, to October 1986. We stop
at this point primarily because the advertising associated with
products using the CP/M platform is so scattered and rare as to
no longer warrant much interest.\footnote{While there was
advertising for other proprietary platforms in this period,
notably Apple, TRS, and Atari, these are less interesting. First,
they are quantitatively less important. Second, the platforms are
not consistently open, so our theoretical framework has less to
say about their characteristics. Third, our impression is that
these platforms were almost exclusively aimed at the market for
games and, ultimately, a different set of consumers.}


 We collect quarterly observations, which results in 35 and
22 complete observations for CP/M and DOS
respectively. Table 1 presents some basic summary statistics and
the figures display histories. As shown in the figures,
advertising for the DOS platform grows over the entire period,
while advertising for the CP/M platform peaks around 1982-3.
Total advertising grows over the whole period, reflecting the
entry of many new consumers into this market. The growth
and death of total advertising conforms closely to industry
perceptions about the growth and death of these platforms, which
we take as further assurance that total advertising tracks
commercial activity.

     It is insightful to compare that the relative amounts of
software and peripheral advertising with that for hardware. The
summary statistics in Table 1 show that the
two platforms have very different patterns. MS-DOS has a much
higher
proportion
of software and peripheral advertising relative to hardware
advertising. This most
certainly reflects a real economic phenomenon.\footnote{Indeed
the
life-cycle of the CP/M platform suggests that the CP/M ratios of
software/hardware and peripherals/hardware  were biased
upwards.  Near the time of CP/M's death there was
almost no hardware
advertising while there was still plenty of software and
peripheral
advertising.} We interpret this pattern additional  evidence that
these data are good 
proxies for sales.


    To further examine if there are dynamic differences in these
variables for the two operating systems, we use regression
analysis
to summarize the history of DOS
and CP/M. Tables 2 and 3 present OLS regression results
from regressions of hardware on software and peripherals and
visa-versa.\footnote{The numbers in parentheses in tables 2 and 3
are the standard errors.  A ``*" means that the t-stat exceeds
1.64, while ``**" means that the t-stat exceeds 1.96.} We include
only one lag. A second lag does not
markedly change the coefficients on the first lag.\footnote{For
many specifications, we cannot reject the hypothesis that all
second lags are
jointly zero.}

     Because our theoretical framework provides no
natural specification for the different effects of software and
peripherals, we also show three alternative non-tested
specifications of the non-hardware variables. In model 1 we use
all three variables. In model 2 we use only hardware and
software. In model 3 we add peripherals to software. Most
specifications fit well, even though we never use  more than
three
explanatory variables. Therefore, we conclude that these
specifications provide a reasonable and concise description of
the market's change over time.

     First we examine the question: what is the relationship
between lagged values and contemporaneous values of hardware and
software? In the case of CP/M, lagged software and peripherals
significantly predicts later hardware advertising, controlling
for lagged hardware. For example, an extra page of page of
software advertising precedes one-third of a page of hardware
advertising. Similarly, lagged hardware significantly predicts
software in most specifications, though the same is not
necessarily so for peripherals. For example, an extra page of
page of hardware advertising precedes almost half a page of
software advertising. We conclude that there is a statistically
robust and economically important interaction between lagged
commercial activity and contemporaneous activity across hardware
and software components in the CP/M platform.

We observe a different relationship in the case of DOS.
First, lagged software does significantly predict hardware
advertising in all of our specifications. For example, an extra
page of software advertising precedes one-half of a page
of hardware advertising. However, lagged hardware does not
significantly predict software advertising in any of our
specifications. Nor does peripheral advertising predict hardware
or software advertising. We conclude that there is an
economically important relationship between lagged commercial
activity in DOS software and later DOS hardware. However, the
relationship is unidirectional: lagged hardware does not predict
software.

     Now we can examine the question: are the coefficients
describing the commercial activity for DOS the same as those
describing CP/M? The answer is clearly no. On a specification by
specification comparison, the two regression results are not
similar. Coefficients take on different signs, magnitudes, and
significance. Coefficients describing the relationship between
contemporaneous and lagged values differ. 
The
patterns associated with DOS advertising contrasts sharply with
those associated with CP/M. Our interpretation is that the success
of DOS depended largely
 on the availability of software.   CP/M displays  patterns
reflecting its
 appeal primarily to early adopters.


\begin{table}[ht]
\begin{center}
\begin{tabular}{r||c|c|c|c||}
                 \\ \hline 
 $Category$            & $Mean$     & $Std. Dev.$     & $Minimum$

   & $Maximum$ 
\\ \hline
\\ \hline
 Hard CPM &   7.28 &  6.43 &  0.00  & 20.00
\\ \hline
 Soft CPM &  11.54 &  7.74 &  0.50  & 27.50
\\ \hline
 Periph   CPM &   3.60 &  2.79 &  0.00  & 10.00
 \\ \hline
\\ \hline
 Hard DOS &  11.75 &  8.75 &  0.00  &  29.50
\\ \hline
  Soft DOS &  25.02 & 17.56 & 0.00  &   62.00
\\ \hline
 Periph DOS &   22.11 & 11.32 & 0.00  &  38.00
\\ \hline
\end{tabular}
\end{center}
\caption{CPM: April 1978- Oct. 1986; DOS: July 1981 - Oct. 1986}
\label{means.t}\end{table}

\pagebreak


\begin{table}[ht]
\begin{center}
\begin{tabular}{r||c|c|c||c|c||c|c||}
\\ \hline 
    & \multicolumn{3}{c||}{Model 1} 
&   \multicolumn{2}{c||}{Model 2}
& \multicolumn{2}{c||}{Model 3}
\\ \hline
Dept. Var. &  Hard  & Soft &  Periph &    Hard  & Soft  &  Hard 
& 
 Soft+Periph
\\ \hline
\\ \hline
Const  &    -0.87 &  1.7* &  0.35 &   -0.69 &  1.6* &-0.89 & 2.2*
\\ 
       &  (0.74)& (0.88)& (0.50)& (0.77)& (3.6)  &  (0.74) &
(1.2)
\\ \hline
Lag Hard & 0.39**& 0.45**& 0.04 & 0.43**& 0.44**& 0.38**& 0.58**
\\ 
       &  (0.14)&(0.17)& (0.10) & (0.15)& (0.17)& (0.14)& (0.23)
\\ \hline
Lag Soft & 0.32** & 0.60**& 0.27**&   0.41**& 0.58** & &
\\
         &  (0.13)& (0.15)& (0.09)&   (0.12)& (0.29) & &
\\ \hline
Lag Periph & 0.45*& -0.12&  -0.06 & & &  &
\\
          & (0.25)& (0.29)& (0.17)& & & &
\\ \hline
Lag Soft+Periph & & & & & &    0.35** & 0.56**
\\ & & & & & &  (0.09) & (0.14)
\\ \hline
\\ \hline
R-squared &  0.86 &  0.86 &  0.65 &    0.84 &  0.86 & 0.86 & 
0.85 
\\ \hline
\end{tabular}
\end{center}
\caption{CPM: April 1978- Oct. 1986}
\label{regress1.t}\end{table}




\begin{table}[ht]
\begin{center}
\begin{tabular}{r||c|c|c||c|c||c|c||}
\\ \hline 
    & \multicolumn{3}{c||}{Model 1} 
&   \multicolumn{2}{c||}{Model 2}
& \multicolumn{2}{c||}{Model 3}
\\ \hline
Dept. Var. &  Hard  & Soft &  Periph &    Hard  & Soft  &  Hard 
& 
 Soft+Periph
\\ \hline
\\ \hline
Const &  0.87 &  1.3* &  4.73** &  1.61 &  4.4  &   -0.57 &  6.9*
\\
      & (1.45)& (3.25)& (1.98)&   (1.18)& (2.7) &   (1.44)& (3.5)
\\ \hline
Lag Hard &  -0.25 &  0.09 &  -0.34 &   -0.18 &  0.40 & -0.29&
-0.23
\\
         &(0.18)& (0.41)& (0.25)&   (0.16)& (0.38)& (0.20)&
(0.49)
\\ \hline
Lag Soft &   0.49** & 0.58**& 0.29** &  0.51**& 0.70** & &
\\
         &  (0.08)& (0.18)& (0.11)& (0.07)& (0.18) & &
\\ \hline
Lag Periph &  0.10 &  0.44 &  0.69** & & & & 
\\
          & (0.12) & (0.27) & (0.16) & & & &
\\ \hline
Lag Soft+Periph & & & & &   &    0.35** &  0.97**
\\
            & & & & &   &     (0.06) & (0.14)
\\ \hline
\\ \hline
R-squared &  0.86 &  0.82 &   0.84 &    0.85 &0.80 & 0.82 &  0.89
\\ \hline
\end{tabular}
\end{center}
\caption{IBM: July 1981 - Oct. 1986}
\label{regress2.t}\end{table}

\pagebreak
 
\section{Conclusion}

In this paper we addressed the interdependent decision
problems facing buyers in choosing which of the early
microcomputers to purchase and when to make the purchase, and the
corresponding dynamic pricing problem for suppliers of those
microcomputers.  We find conditions under which price competition
among vendors induces consumers to buy early, despite the
uncertainty about 
the development of complementary
software. 

We also find conditions under which some consumers adopt
early whereas others wait for uncertainty to be resolved;
when these conditions are satisfied, it is possible that
late adopters purchase a different system than the early
adopters, leaving the latter stuck with an ``orphan" technology.
Our model suggests that orphaning will occur only when more and
better software than expected becomes available for a technology in
competition with that of the early leader.   Since the amount and
variety of complementary software cannot be predicted with
certainty, early adopters face some inherent risks, and orphaning
can occur.

An empirical implication of our theoretical analysis is that when
orphaning occurs, software is more likely
to precede hardware for the technology of the ``late" leader than
for the technology of the ``early"
leader.  The data we present support this prediction; there is
evidence from the early microcomputer market that the
pattern of adoptions and orphaning was associated with the later
adopters waiting for software  and other complementary
products to develop.  In particular, the advertising patterns
associated with
the DOS platform differ from 
those associated with CP/M, the leading operating system
among early microcomputers.  In contrast to CP/M,  there is
evidence that the success
of DOS depended largely on the entry of many
DOS-based software vendors and the associated increase in the
availability of DOS compatible complementary software.

\begin{thebibliography}{99}

\bibitem{aa} Arthur, B., 1989, ``Competing Technologies,
Increasing
Returns, and Lock-in by Historical Small Events," {\em The
Economic
Journal}, 99: 116-131.

\bibitem{ac} Bresnahan, T., and S. Greenstein, 1992,
"Technological Competition and the Structure of the Computing
Industry," Center for Economic Policy Research, Stanford
University, Publication No 315.

\bibitem{ac} Chou, C. and O. Shy, 1990, ``Network Effects without
Network
Externalities,  {\it International 
Journal of Industrial Organization}, 8: 259-270.

\bibitem{ae} Church, J. and N. Gandal, 1992, ``Network Effects,
Software Provision, and Standardization," {\it Journal
of Industrial Economics,}, XL: 85-104.


\bibitem{af} Church, J., and N. Gandal, 1993, ``Complementary 
Network
Externalities and Technological Adoption,"  {\it International
Journal of 
Industrial Organization,} 11: 239-260.

\bibitem{ba} Dixit, A., and R. Pindyck, 1994, Uncertain
Investment, Princeton University Press.


\bibitem{be} Farrell, J. and G. Saloner, 1986,  ``Installed
Base 
and 
Compatibility: Innovation, Production Preannouncements and
Predation, 
{it 
American Economic Review,} 76: 940-955. 

\bibitem{bf} Friedman, A., and D. Cornford [1989],
Computer
Systems Development: History, Organization and Implementation,
John Wiley and Sons, New York, NY.


\bibitem{gg} Gabel, L., 1991, ``Competitive Strategies for
Product
Standards," Mc-Graw Hill, UK.

\bibitem{dd} Katz, M. and C. Shapiro, 1986, ``Technology 
Adoption in 
the Presence of Network Externalities," {\it Journal of Political
Economy,} 
94: 
822-841.

\bibitem{ka} Katz, M. and C. Shapiro, 1992, ``Product
Introduction
with Network Externalities," {\it Journal
of Industrial Economics,} XL:55-83.

\bibitem{kn} Klenow, P., 1994, "New Product
Introductions," Mimeo, University of Chicago. 

\bibitem{la} Langlois, R., and P. Robertson, 1992,
"Innovation in Modular system: Lessons from the Microcomputer and
Stereo Component Industries," {\em Research Policy,} 21 (4),
297-313.

\bibitem{sa} Sanchez, R., 1994, "Strategic Flexibility in
Product Competition," Working Paper, University of Illinois.


\end{thebibliography}


\begin{center}
{\bf Appendix:  Low Basic System Valuations:}
\end{center}






Here we assume that marginal
costs are constant over time.  However, we suppose that
``non-techies" preferences are such that
$c- U_b < \theta^N < c < \theta^T,$ where, as before, $c$ is the
unit production
 cost which is both constant over time and with the level of
output.

  The first two inequalities mean that ``non-techies" have no
interest in a system without supporting services at any
price that covers marginal production costs, but would be willing
to pay
a premium for either system if software were available.  Three
outcomes are possible: (1)  All consumers
purchase the ex ante superior system in the
first period, (2) Techies purchase the ex ante superior system
in the
first period and Non-techies make purchases in the second period,
and
(3)Techies purchase the ex ante superior system
in the
first period and  Non-techies do not make any purchases in the
second
period.

Outcome (2) occurs if at least one of the systems experiences
innovation, while outcome (3) occurs if neither system
experiences innovation.\footnote{Outcome (3) will also occur in
the uninteresting case in
which $
\theta^N < c- U_b.$}
Under both outcomes (2) and (3), techies can get stuck with
orphan
technologies.
In particular, techies adopt the ex ante superior
system.  Non-techies who wait end up purchasing a system that has
experienced innovation.  Hence the groups may purchase different
systems.

The intuition for this result is to similar to the case of
falling marginal costs.  The only qualitative difference between
the cases is that in this non-techies will not make any purchases
in this case if they do not purchase in the initial period and
neither system experiences innovation.

We now provide the formal result.  In advance of the proposition,
let




$$ \tilde{\theta} ={ c(1- \rho_a \rho_b) +  U_b\rho_b( \rho_a - 1)
\over 2 - \rho_a\rho_b },$$


$$\hat{\theta} =
{N^Tc (1- \rho_a\rho_b) + N^Nc(1- \rho_a) - N^T \rho_bU_b(1-
\rho_a) \over N^T(2-
\rho_a \rho_b) + N^N(2- \rho_a)},$$


 $$ \grave{\theta} = {c(1 - \rho_a \rho_b)  - \rho_a(U_a-
\rho_bU_b) \over
2 - \rho_a\rho_b}, and $$

 $$ \bar{\theta} = {N^Tc(1 - \rho_b \rho_a) + N^N c (1 - \rho_b)
-N^T \rho_a (U_a -\rho_b U_b)
\over (2-\rho_a\rho_b)N^T + N^N (2-\rho_a)}.$$



\begin{prop}
(I) First Suppose that the ex ante superior system, A, is also ex
post superior
 system, that is $\Gamma
  = \rho_bU_b  - \rho_aU_a < 0.$
\vspace{2 mm}

\noindent (I)
Then there is a unique equilibrium in which:

\begin{enumerate}

\item  All consumers buy early from the ex ante superior
system,A,
if $\theta^N \geq \tilde{\theta}$.  Initial period prices are ${\bf
p}^0
= (- \Gamma+c,c).$

\item For $\theta^N < min[\hat{\theta},\tilde{\h}]$, techies
purchase
the
system A in the first period.  Non-techies make a
purchase only in the second period if at least one innovation
occurs.  The first
period prices are ${\bf p}^0 = (- \Gamma+c,c).$

\item  If  $\hat{\theta} <  \tilde{\theta}$, there is a third
region:
For
$\hat{\theta} < \theta^N  < \tilde{\theta}$, all
consumers buy system A in the first period,
the
first period price for system B is 0 and for
system A the first period price is $p_a^0(\theta^N)= \rho_a(U_a -
\rho_bU_b) +
 \theta^N(2 - \rho_a\rho_b) + \rho_a\rho_bc <
-\Gamma + c.$

\end{enumerate}

\noindent (II) Now suppose that  the ex ante superior system, A,
is
inferior ex post,  that is, $\Gamma > 0.$
Then there is a unique equilibrium in which:

\begin{enumerate}

\item  All consumers buy system A early
if $\theta^N \geq \grave{\theta}$.  Initial period prices are ${\bf
p}^0
= (c, \Gamma +c).$

\item For $\theta^N < min[\bar{\theta},\grave{\h}]$,techies
purchase
system A in the first period.  Non-techies make a
purchase only in the second period if at least one innovation
occurs.  The first
period prices are ${\bf p}^0 = (c,\Gamma + c).$

\item  If  $\bar{\theta} <  \grave{\theta}$, there is a third
region:
For
$\bar{\theta} < \theta^N  < \grave{\theta}$, all
consumers buy system A in the first period,
the
first period price for system B is 0 and for
system A, the first period price is
$p_a^0(\theta^N)= \rho_bU_b(1 - \rho_a) + \theta^N(2 -
\rho_a\rho_b) +
 \rho_a\rho_bc <
\Gamma + c.$

\end{enumerate}

\label{main3}
\end{prop}

The intuition behind this result is essentially the same as
Proposition
 (\ref{main2}).   The Techies buy early.  The price that the
Techies
pay, will, if
 the innovation is not so great, or its probability sufficiently
low, and the
 stand-alone value for the Non-Techies is high enough, also
induce
the
 Non-techies to buy early.  The main difference between
Proposition
\ref{main2}
 and Proposition \ref{main3} is the possibility of a third region
in which the
 initial price depends on Non-techies stand-alone values.  In
this
case, the
 firm with the ex ante superior system would prefer to sell to
both
the Techies
 and the Non-techies in the initial period than to sell only to
the
Techies in
 the initial period, and to the Non-techies in the later period
if
has the
 better system ex post.  The critical values of the stand-alone
values depend on
 the relative number of Techies and Non-techies.
Before we prove Proposition (\ref{main3}), we state and prove the
following
lemma.

\begin{lem}  Suppose that $\theta^N +
U_b > c.$  Further suppose that techies purchase in
the
initial  period and that non-techies do not.  Then there is a
unique equilibrium in the
final period, with the following prices:


\noindent (i) If $\alpha = (1,1)$ then $p_a^1 = U_a- U_b + c$
and
$p_b^1 =c.$
\vspace{2 mm}
\noindent (ii)  If $\alpha = (1,0),$ then $p_a^1 = U_a +
\theta^N$
and
$p_b^1 =c$.
\vspace{2 mm}


\noindent (iii)  If $\alpha = (0,1),$ then $p_b^1 = U_b +
\theta^N$
and
$p_a^1
=c.$
\vspace{2 mm}

\noindent (iv)  If $\alpha = (0,0)$ then $p_a^1 = p_b^2 = c.$



\noindent If non-techies wait, they receive an expected utility
of

\begin{equation}
\rho_a\rho_b(U_b + \theta^N - c).
\label{late}
\end{equation}


\end{lem}

{\bf Proof:}  The lemma follows immediately from Lemma 1, with
the
modification that when a single firm innovates, the maximum price
it can
charge non-techies in the second period is $U_i + \theta^N <
U_i$ + c,
since
$\theta^N < c.$
\hfill \rule{2mm}{2mm}



{\bf Proof of Proposition (\ref{main3}).}
\vspace{3 mm}

 We first prove the result for case
when the ex ante
superior system
is also superior ex post, that is,  for
$\Gamma =
\rho_b U_b - \rho_a U_a < 0$ and  $U_a \geq U_b.$
 Suppose that the
techies buy the ex ante superior system in the first period.  We
will show
later that this will be true in equilibrium.


Suppose the initial period price for system a is $p_a^0 =
- \Gamma +c,$
and the initial period price for system b is $p_b^0 = c.$  Note
that if all consumers buy early, the fact that there is price
competition and the difference in expected values of the two
systems is $\Gamma$ implies that these would have to be the first
period equilibrium prices.  If firm a were to raise its price,
firm b, which otherwise would not make any sales, could then
charge
a positive price and earn profits.

Given these prices and first period prices as described in
Lemma 2, the expected utility of  non-techies from buying early
is

\begin{equation}  \rho_aU_a + 2\theta^N -(- \Gamma + c) =
\rho_bU_b + 2\theta^N - c.  \label{early}\end{equation}
If the non-techies wait, from Lemma 2, they receive an  expected
utility of
$ \rho_a\rho_b(U_b + \theta^N- c).$

Comparing (\ref{early}) and
(\ref{late}), buying early dominates buying late for non-techies
at prices $- \Gamma +c, c$ whenever

\begin{equation}  \theta^N \geq {c(1-\rho_a \rho_b) -U_b\rho_b(1-
\rho_a) \over
2 - \rho_a\rho_b  } \equiv \tilde{\theta}
 \label{earlys}
\end{equation}
Note that $\tilde{\theta} < c$.  So for $\theta^N >
\tilde{\theta}$,
all consumers (techies and
non-techies) alike purchase system a, the ex ante superior
system,
in the first period.

Now consider the case $\theta^N < \tilde{\theta}.$  If firm ``a''
wants
to
sell to
both types in the first period, then it must set $p_a^0$ low
enough to attract non-techies.   From (\ref{late}) such a price,
$p_a(\theta) $ must satisfy


$$\rho_a\rho_b(U_b + \theta^N-c) \leq \rho_aU_a + 2\theta^N -
p_a^0$$
Let
\begin{equation} p_a^0(\theta^N) = \rho_a(U_a - \rho_bU_b) +
\theta^N(2 - \rho_a\rho_b) + \rho_a \rho_b c
\label{introp} \end{equation}


When $\tilde{\theta} > \theta^N$, the profits from selling
to all
consumers in the first period
are $N[p_a^0(\theta^N) -c]$ and the expected profits from selling
only
to the
techies in the first period are
$$-N^T \Gamma +
 N^N[\rho_a(1-\rho_b)(U_a + \theta^N) +
\rho_a\rho_b(U_a - U_b+c) -\rho_a c],$$ where the second term
represents the
expected profits from selling to non-techies in the second
period.
The profits to selling to both types are larger whenever

\begin{equation}\theta^N \geq \hat{\theta} =
{N^Tc (1- \rho_a\rho_b) + N^Nc(1- \rho_a) - N^T \rho_bU_b(1-
\rho_a) \over N^T(2-
\rho_a \rho_b) + N^N(2- \rho_a)}.
\label{lates}\end{equation}

It can easily be verified that $\hat{\theta}<c.$

When $\hat{\theta} \geq
\tilde{\theta}$,  (i) for $\theta^N \geq \tilde{\theta},$ both
types purchase
the
ex ante superior system in the first period at a price of
$|\Gamma|$, (ii)  for $\theta < \tilde{\theta},$ only the techies
purchase
the ex
ante superior system in the first period (also at a price of
$|\Gamma|+ c$.)  Non-techies make no first period purchases.


When $ \hat{\theta} < \tilde{\theta}$, there are three
regions:  (i) for $\theta^N \geq \tilde{\theta}$, both
type of consumers purchase system ``a'', the ex ante superior
system in the first period at the price of $|\Gamma|+c$,
(ii) for $\hat{\theta} \leq \theta^N < \tilde{\theta}$
both types purchase system ``a'' in the first period, but
at a price of $p_a^0(\h^N)$, (iii) if $\theta^N < \hat{\theta}$,
only techies  purchase
the ex ante superior system at the price $|\Gamma|+c$ in the
first
period.



Thus, assuming all techies purchase the ex ante superior system
in the first period we have shown the result for the case in
which $\rho_aU_a \geq \rho_bU_b$ and $U_a \geq U_b$.  We now
show that in fact techies will  buy the ex ante
superior system in the first period

There are three potential cases:  (i)  $\theta^N \geq
\tilde{\theta},$
(ii) $\tilde{\theta} > \theta^N \geq \hat{\theta} $, and (iii)
$\theta^N < \hat{\theta}.$    In case (i)  all consumers
purchase
system ``a'' in the initial period.  The prices are $p_a =
-\Gamma+c$ and
$p_b = c.$

In case (i), ``non-techies" are purchasing in the initial period,
so Proposition 1 shows that
techies will also purchase rather than wait.


In case (ii), ``non-techies" wait in equilibrium.  Thus,
regardless
of whether techies wait or
purchase in the initial period, equilibrium final period prices
are
given by Lemma 2.  Given
these prices the expected utility of waiting for techies is less
than $\theta^T + \rho_a \rho_b
U_b$.  The expected utility of purchasing in the initial period
is
at least as large as
$2 \theta^T + \rho_b U_b - c $, which is greater than the
expected
utility of waiting, since
$\theta^T > c.$


Finally, in case (iii) the initial and final period prices
are the same as in case (i), and so techies will have incentives
to buy the ex ante superior system in the initial  period in this
case too.
\vspace{3 mm}

\noindent We now prove the result for the case that the ex-ante
superior and ex-post
superior systems are different, that is, $\rho_aU_a <
\rho_bU_b$.
The proof is constructed in a similar  manner.  We now derive
$\grave{\theta}$ and $\bar{\theta}$, which are  analogous to
$\tilde{\theta}$
and
$\hat{\theta}$ respectively.

Suppose the first period price for the ex ante superior system,
system ``b", is $\Gamma = \rho_bU_b - \rho_aU_a+c$, and the price
for the other system is $c$.  Then non-techies who purchase
system ``b" early will derive expected utility of $\rho_bU_b +
2\theta^N - \Gamma -c = \rho_aU_a + 2\theta^N -c.$  Recall that
the
non-techies will derive an expected utility from waiting of
$\rho_a\rho_b(U_b + \theta^N-c)$.  Comparing these two
expressions,
non-techies will buy system a early whenever

\begin{equation} \theta^N \geq {c(1 - \rho_a \rho_b)  -
\rho_a(U_a-
\rho_bU_b) \over
2 - \rho_a\rho_b}\equiv \grave{\theta}.
\label{early2}\end{equation}
 
For $\theta^N < \grave{\theta}$ firm A can sell to both types in
the
initial period when the price it charges,
$p_b^0,$ satisfies
$$\rho_a \rho_b [U_b + \theta^N - c ] \leq \rho_bU_b + 2\theta^N)
-
p_b^0.$$
The most firm ``b" can charge and still sell to both types in the
initial period is denoted
$p_b^0(\h^N)$
and equals
\begin{equation} p_b^0(\theta^N) = \rho_bU_b(1-\rho_a)
+\theta^N(2-
\rho_a\rho_b)  + \rho_a \rho_b c.\label{introp2}\end{equation}

By selling to both techies and non-techies, firm ``b" will get
profits of $Np_b^0(\theta^N)$.  Firm A can set its first period
price
at $\Gamma$, sell only to techies in the first period, and earn
expected profits of $N^T\Gamma + N^N\rho_b(1-\rho_a)(U_b +
\theta^N -c)$,
where the first term is the first period profits from selling to
the techies and the second term is the expected profits from
selling to non-techies in the second period.
Selling to techies is more profitable than selling to both types
in the first period whenever
$  \theta^N < \bar{\theta}.$

The result then follows by showing that, analogous to the case in
which system ``a" is both ex ante and ex post superior, techies
always purchase in the initial period.  \hfill \rule{2mm}{2mm}

\end{document}





------------------------------------------------------------------------------
Neil Gandal					Fax: 972-3-640-9908
Assistant Professor				Tel: 972-3-640-9604
Eitan Berglas School of Economics
Tel Aviv University
69978 Tel Aviv
Israel

E-mail: gandal@econ.tau.ac.il
------------------------------------------------------------------------------


