Subject: a model of competition between free and proprietary software
From: Seth Gordon <>
Date: 20 May 2001 17:55:57 -0000

I've had this idea bouncing around my head for a while, and I hope
that people on this list can help me elaborate on it.

Suppose that F is a GPL'ed software package (e.g., Linux), and P is a
proprietary software package competing in the same market (e.g., SCO
Unix).  How will the quality of both these products change over time?

In their initial releases, P has a strong advantage over F: money.
The author of P can attract investors to provide seed capital (or
convince his or her employer to budget for the product's development)
with the prospect of sales revenue down the line, and use this money
to create something attractive to potential customers.  On the other
hand, the first release of F will probably be written in someone's
spare time, as a class project, or as an adjunct to another job; it
will have enough functionality to meet the author's needs, but it may
not have much more than that.  After the initial release, P's sponsor
will have revenue from software sales, and can plow this revenue into
further development.  Meanwhile, only a small number of people will
have the time or inclination to improve F.

The number of developer-hours that F can attract is roughly
proportional to F's quality, and if F's maintainer is competent, F's
quality is roughly proportional to the number of developer-hours
spent on it.  Therefore, if the first version of F is good enough to
attract a few good volunteers, F's quality will grow exponentially.

However, the number of developer-hours spent on improving P is *not*
proportional to P's quality, but to its revenue.  Furthermore, not all
of that revenue can be spent on developers' salaries.  Some of it must
be spent on salespeople, lawyers, and the other
accoutrements of a functioning corporation.  Most importantly, the
investors who supplied the original capital must be rewarded, and they
must be rewarded at an attractive rate of interest, so P's sponsor has
one *cost* that grows exponentially.

At a certain point, F's level of quality is so close to P's that if a
customer needs one feature from F that P does not have, it will be
cheaper for the customer to hire someone to extend F than to buy P,
and there are enough volunteers extending F that they can quickly
match any improvements to P.  Once F passes this point, the return on
investment for P's sponsors is no more than the ROI for a company
specializing in F-related services; that is, they may be able to stay
in business by providing support, maintenance, and consulting
services, but the copyright on P itself has no market value.

I know that the above scenario is missing a lot of details.  (For
example, I'm treating a product's "quality" as an attribute
independent of its market share, and assuming that a customer's
decision on which product to purchase is based only on "quality" and
price.  This is certainly oversimplifying things.)  However, if this
argument could be developed with more mathematical and economic rigor,
it might provide some insights into what situations favor free
software and what situations favor proprietary software.  (If the Fed
lowers interest rates, is that good or bad for free software?)  Also,
if a more formal analysis supports my theory that free will always
beat proprietary software in the long run, that analysis might appeal
to the CEOs and CFOs who wonder if "open source" is just another fad.

Unfortunately, my primary economics education comes from reading Paul
Krugman's columns, so I'm not sure how to develop my theory into
something that would convince the pros -- and I'm afraid that if I
tried, I would waste a lot of time reinventing wheels.  If one of the
business or economics gurus on this list could give me a list of
background reading, or even a background vocabulary ("the differential
equation that captures all of the variables involved in a business
reinvesting its profits is known as Mumblefrotz's Formula"), I would
be very grateful.

"Rav would never cross a bridge when an idolator was on it; he said, 'Maybe he
will be judged and I will be taken with him.'  Shmuel would only cross a
bridge when an idolator was on it; he said, 'Satan cannot rule two nations [at
once].'  Rabbi Yannai would examine [the bridge] and cross."  --Shabbat 32a
== Seth Gordon == == == std. disclaimer ==