(2200 words, very sorry, but I'm afraid that if I write a new shorter
version I'll get distracted before I send it out)
Zooko told me a little story at lunch one day. As I recall, it went
something like this:
You have two magic boxes. Each of them, when you put fuel
into it, consumes the fuel and produces some valuable
commodity, and it produces N times as much of the valuable
commodity if you put N times as much fuel in. But one of the
boxes produces an excludable commodity --- the box's possessor
gets to choose who benefits from the commodity --- and the
other produces a nonexcludable commodity, where everyone
benefits from it.
Which one produces more value?
I answered that it depends on a lot of things, such as the respective
ratios of fuel in to valuable commodity out, and the social
arrangements surrounding my possession of these boxes.
Zooko agreed that it depended on the efficiency issues, but argued
that the excludable box is self-reinforcing in a way that the
non-excludable box is not --- its possessor can trade its valuable
output for more fuel, which means that it's likely that a "machine
that runs of itself" will arise around it --- something that he argued
couldn't happen with the other box.
I have two rebuttals to this argument that I thought of at that lunch,
and a third rebuttal that only occurred to me more recently.
The first is that if the nonexcludable box is sufficiently efficient,
then you can set up the same kind of trading system around it. If you
are a potential customer, and you will receive value X in return for
paying Y, where Y is less than X, it is self-interestedly rational for
you to do so --- regardless of whether other people will additionally
receive some value from the transaction. (This works best if the good
is nonrival.)
There is potentially a prisoner's-dilemma situation, of course, where
every potential customer has an incentive to sit back and hope others
will pay for all of the nonexcludable commodity that they need. There
are several ways out of this:
1. If the commodity has increasing returns over the range expected to
be produced, rather than decreasing, then knowing that other people
may contribute as well is an incentive rather than a disincentive
to your own contribution. (That is, if it's unlikely that the
amount produced will be close to "all you need".)
2. If the commodity is fairly customizable, such that it is more
likely to fit your particular needs if you pay for its production
than if someone else does.
3. If the returns are sufficiently high that the amount you pay is
small in proportion to the value you receive.
All of these are frequently the case with free software: there are
increasing returns as software is more valuable when it can connect to
more things; its customizability is enormous; and the private ROI is
often enormous.
And of course people aren't purely self-interestedly rational, but
usually some part of their behavior is driven by such motives.
The second rebuttal is that the dependencies on the social
arrangements are quite extreme. If you are part of a clan with no
private property within the clan, for example, you won't be able to
trade commodities for fuel with other people inside the clan.
Instead, the people who are most considered most deserving within the
clan will get the benefits of the excludable box, and the fuel will
come from the clan's common supply. Or, if you are in an environment
where commerce is punished, or where swindlers are common, you may not
be able to set up the business relationships needed to get much of a
supply of fuel for the excludable box. Or, if I can use force to take
the box from you after you put fuel in it and get the resulting
commodity, or if I can merely take fuel from you, the excludable box
will still have little or no advantage.
If dominant assurance contracts work in reality, they represent
another set of social arrangements that could comfortably fuel the
nonexcludable box.
In short, the second rebuttal is that the social arrangements that
make the excludable box self-sufficient are fairly contingent --- a
system of self-interested rational agents who are nevertheless bound
to engage in only consensual exchanges based on well-defined property
rights --- and not that widespread in the real world.
These two suggest the third rebuttal, which is perhaps the most
interesting. If the box is possessed by a firm, the entrepreneur who
directs the resources of the firm will take into account the benefit
to all the firm's members --- not just those directly to the
entrepreneur. This provides the non-excludable box, as long as the
good it produces is also non-rival (i.e. it's a public good) with a
huge boost in its effective efficiency; perhaps 100, 1000, or 10 000
people's benefits are weighed against the cost of the fuel, rather
than just one. This allows the public-good box to become
self-sufficient at much lower efficiencies.
If we look at the existing world, this might explain why historically
most of the basic research done in the US has been done by
government-funded grants --- the US government is one of the world's
largest firms, particularly if you consider all of the citizens as its
employees. Much of the applied research has historically been done by
very large companies, although with the increasing power of the patent
system in pharmaceuticals and genetics, more and more of it is being
done by small startups instead.
Similarly, much of the work on large free-software projects has been
contributed by employees of very large companies like IBM and Intel.
If this principle holds water, it might be a second explanation for
the existence of firms, next to Coase's argument about the "cost of
using the price mechanism" to organize production, more recently
called "transaction costs". The problem here is not that the selling
of public goods is attended by unusually large marketing costs, risks,
or taxes --- in short, it is not a transaction cost at all, or even a
cost; it's that it's often in nobody's self-interest to pay the cost
to produce those goods, because they receive only a billionth of the
benefits, even when producing those goods would produce more benefits
overall than it cost.
It's one thing to say that a particular arrangement (in this case,
large firms) is more economically efficient under certain conditions
(in this case, the need for lots of public goods); it's something else
to show that people's individual incentives drive them in the
economically-efficient direction. For example, in the original
situation I was considering, of many independent selfish agents and an
efficient public-good box, it's economically efficient for all of the
agents to contribute fuel to the box; but only under some
circumstances do they have a selfish incentive to do so.
I've established that larger firms have more of an incentive to
increase production of public goods. But does the production of
public goods inside a firm create an incentive to make firms larger,
as do Coase's costs of using the price mechanism?
I'm not sure it does.
Consider the case of an independent consultant who uses Apache but
does not contribute to it. Everyone else will benefit if IBM hires
him and siphons off some of the value he produces to fund more Apache
development. But will IBM? Will the consultant?
Does the consultant benefit if she still produces the same value for
her clients as before? The clients pay IBM the amount they previously
paid her, and then IBM gives her, say, 50% of it. IBM's contributions
to Apache increase slightly, and this benefits the consultant. But,
by hypothesis, the benefit to her is smaller than the tax on her
paycheck --- or there's no need to invoke large firms, is there? She
could have just given IBM the money, or billed fewer hours and fixed
some Apache bugs in her newly spare time, without becoming an
employee. (I know it's not always realistic to tell your client you
want to work fewer hours, but sometimes it is.)
So it doesn't appear that, in the absence of increasing returns,
customizability, extremely high returns, transaction costs, or some
similar factor, there's a selfish incentive to go work for a large
firm on this basis.
Similarly, does IBM benefit? In the above scenario, they probably do,
since they're getting paid a lot more than they pay the consultant.
But they probably have to offer the consultant more money than she's
been making to come work there, and in that case, they're losing money
on her. However, they get to increase their Apache contributions a
bit, so that now the thousands of other Apache consultants they
already had on staff are producing a bit more value --- and there are
many thousands of them. So the value they capture by hiring this new
employee, even if she's not directly profitable, can be substantial.
This is a little dodgy --- I'm saying that by losing more money on a
new employee, they can afford to spend more on R&D. I think it's
actually correct, though.
Consider the case where IBM already had 1000 consultants and, say, 50
full-time Apache contributors on staff. Assume nobody else contribute
to Apache, and that the value of an Apache consultant is directly
proportional to the number of current Apache contributors, which
assumptions are pessimistic --- I think the real world can only make
this more profitable, not less. If all these people are paid 1 FTE,
then presumably the value-to-customers of each of the 1000 consultants
is something around 2 FTE. Increasing the number of contributors by 1
increases the value-to-customers of each of the 1000 consultants by
2%, to 2.04 FTE, for a total revenue of 2040 FTE. So IBM gets back a
40x return on that expense of one more contributor. (Maybe they give
some or 39/40 of that to the consultants.)
Suppose IBM hires 100 more consultants and 5 more contributors. Now
each consultant produces 10% more value (2200 FTE in total for the old
consultants, 220 for the new, total 2420 --- 21% more in total, or 42%
more profit for IBM if nobody's salary goes up) but IBM is still
taxing each contributor's salary with the same 5% R&D.
But suppose IBM was previously paying (and/or spending on office space
and sales and so on) all 1000 consultants 2*FTE (since that's what
they could get if they were independent) and therefore making a loss
of 50 FTE. Now if they hire the 100 more consultants and 5 more
contributors, they get 220 more FTE of net revenue but increase their
R&D expenses by only 5 FTE, so they're suddenly profitable by 220 - 5
- 50 = 165 FTE. They could split this profit with their consultants
(say, 164 / 1100 = 0.149 FTE each, for a new IBM consultant salary of
2.149 FTE), who are now making more than they could have made on the
open market beforehand.
Notice that these profit numbers are proportional to the square of the
number of consultants.
However, any one of the consultants can now quit and get 2.2 FTE
instead of 2.15 for their skills with the newly more powerful Apache.
So IBM has a very strong interest in getting more consultants, an
interest as strong as Metcalfe's Law would be if it were real, but
once they're there, each consultant has a small selfish incentive to
leave.
(This still works if you pay the contributors well; in fact, you can
afford to pay them more than the consultants as long as there are
fewer of them. If the contributors were also getting 2*FTE before,
then IBM was previously losing 100 FTE and afterwards is only
profitable by 220 - 10 - 100 = 110 FTE.)
So I think this effect is not strong enough to produce firms in the
absence of transaction costs, but it is strong enough to make them
much larger than a pure Coasian transaction-costs versus "costs of
organizing additional transactions within the firm" and "loss through
the waste of resources" analysis would suggest.
So to Coase's three factors, "a firm will tend to be larger:"
a. the less the costs of organizing and the slower these costs
rise with an increase in the transactions organized.
b. the less likely the entrepreneur is to make mistakes and
the smaller the increase in mistakes with an increase in
the transactions organized.
c. the greater the lowering (or the less the rise) in the
supply price of factors of production to firms of larger
size.
(I notice he actually left out "the greater are transaction costs",
although he certainly mentioned them in the rest of the paper)
we can add a fourth:
d. the greater the benefit derived from public goods.
Probably this is a well-known economic result, but I hadn't heard of
it before. It's certainly widely known that governments tend to
produce public goods in order to avoid underproduction due to the
free-rider problem; probably the extrapolation to large firms is not
as surprising for economists as it seemed to me.
