Is "increasing returns" a serious (logically consistent) concept that
we can use to refute the notion of perfect competition and -- on that
basis -- the relevance of general equilibrium? I don't know, but
"increasing returns" is not a logically consistent notion. (I am
alluding to the *theoretical* notion of "increasing returns," not to
some conventional definition used in empirical measurement.)
IMO, perfect competition and free markets are largely irrelevant, not
because of "increasing returns," but because of the very nature of
technology. Under constant returns to scale, the nature of technology
invalidates the hypothesis of perfect competition and with it the
results of general equilibrium theory.
This seems more fundamental to me, because technology is sine qua non
to production. And I mean "technology" in its broad sense, which
includes cooperation in general as well as one of its particular
forms, "division of labor," sometimes called "specialization."
How do economists conceptualize technology? As a relation that
transforms "physical" inputs into maximal outputs. (Quotation marks,
because -- if we stop to reflect -- they are not purely physical
inputs and outputs, mere physical objects, but *use values*, i.e.,
objects that relate to concrete, historically-evolved *human needs*.
But that's an aside.) So you have the inputs and, neatly
distinguished from them, a collection of basic recipes or "production
possibilities," that can hopefully be summarized in a transformation
function (not necessarily continuous or well behaved). That's
"technology," which lists feasible ways to mix up the inputs in order
to produce maximal outputs.
Conceptually, it is tricky to decide what's a regular input and what's
technology. That's so even if one ignores the fact that, often times,
technology is embedded in the inputs. Somehow the decision is made,
and a clear separation between inputs and technology is stipulated.
The issue of returns arises when you change the scale of input use.
Say, you multiply your inputs by k > 1. What happens to the ouputs as
a result? The static assumption is that technology is fixed. Only
the inputs change and they change proportionally.
How can you have decreasing returns to scale? You can't! Say k = 2.
If you are really doubling *all* of your inputs, then the least that
you can get is double your output. That should be obvious. The
typical textbook example of decreasing returns to scale is that too
large a productive unit becomes harder to manage or runs into resource
scarcity. Well, then you are not doubling your managerial input or
your raw materials along with the other inputs, are you?
But, back to increasing returns, can you get more than double your
output? Here the economists wave their hands conceptually. Yes, they
answer. And the typical example is the chemical industry. You square
the amount of aluminum input in the form of pipes or containers, yet
you cube the capacity. Well, yes, but you're not only squaring the
input. You are also changing the design of the pipes, their diameter.
So you are changing the technology, which violates the premise of the
analysis.
Jim Devine writes:
in theory, at least, there are increasing returns. One unit of labor
can produce an automobile in your garage. But 1000 units of labor you
can produce more than 1000 cars during the same time period. That's
because the larger scale of production _allows_ the use of assembly
lines.
If you multiply all the inputs by k = 1,000 in the garage and keep
technology fixed, how can you get more than 1,000 times the old
output? You'd have 1,000 garages, each with one unit of labor, each
producing one car. So 1,000 cars output. The only way you get more
than 1,000 cars is by violating the logic of the *scale* returns
analysis, adding new inputs deux ex machina or changing the
technology. Before, you didn't have 1/k-th of an assembly line in the
garage, did you? Now you have an assembly line out of nowhere. The
logic of the analysis says: multiply all inputs by k = 1,000; do not
add or remove inputs; do not improve or degrade the inputs (just
multiply them by 1,000); and do not change the technology. If you
accept the premise of an analysis and stick to the rules of logic,
then you have to follow through. You cannot change the premises in
the middle of the reasoning. I mean, unless you are writing a
textbook, in which case you're entitled to disregard logic.
Somebody may say, but technology is a collection of techniques. Not a
single technique. So you may switch to another technique, still an
element of the same technology. But that's mixing another layer in
the analysis. Techniques are chosen on economic grounds (cost min,
profit max). Not on technological grounds. So, think of returns to
scale as a shift in the whole transformation (or production) function.
Or, if it's more intuitive to you, pick a technique without yet being
committed to it economically and scale it. The point is that the
notion of returns to scale is separate from the economic problem.
Prices are not in the analysis yet.
Just to rivet this point: If the regular inputs are improved (workers
acquire additional skills via learning by doing or learning by being
trained or whatever, the quality of material inputs is perfected,
etc.), then you're not sticking to the premise of the scale returns
analysis. You are changing the inputs not only quantitatively
(multiplying them by k), but also qualitatively. So, if your outputs
more than double when you double your inputs, but the new inputs are
improved versions of the old inputs, then the extra output results
from the improvement on the inputs.
What clarifies things, IMO, is when this is viewed dynamically and
technology is taken as endogenous. Now technology is an output of a
prior process of production that uses up inputs. Thus viewed, the
concept of technology is broader. You may include, for example,
product innovation. In any case, current technology becomes just
another input to final production. And this leads right to the point
I was making, that technology -- viewed as an input or, more
generally, as a good -- has a nonrivalrous character. Nonrivalry, a
"physical" (use-value, actually) attribute of some goods, makes them
harder (more costly) to exclude, i.e. to appropriate (effectively, not
necessarily legally).
Moreover, socialization, cooperation, mutual coordination to
accomplish common tasks (whether through markets or directly) is
another input that needs to be produced. Its nonrivalrous properties
are transparent. But it must be produced and re-produced. Anybody
who has helped to coordinate a work team, build a family, or organize
a club, political organization, or listserv knows that fostering a
climate of cooperation is very input consuming. Without it, the
output is garbage.
Michael Perelman wrote:
Take the example of learning by doing. The
workers who make the 345th plane are different
from the workers who made the 344th plane --
the difference being the experience of making
the previous plane.
See my argument above. Here you make my point. It's not "returns to
scale," but the improvement in the input. Here technology exists as
worker knowledge and it is endogenous. The experienced worker is an
element in the list of outputs.
Tom correctly suggests that information represents
a form of increasing returns because the input
never disappears I agree with him.
My point is that we don't need "increasing returns" (an inconsistent
notion) to note the nonrivalrous nature of data, information,
knowledge, technology, etc.
Julio
