Economists know that specialization is important, and they
are good at enthusing about it eloquently, and briefly. Then they move on to
think much harder about topics they know to be narrower and less important. It's
an odd procedure, but it goes all the way back to Adam Smith, whose Wealth of Nations starts with three
chapters on the division of labor, then drops the subject and goes into great
detail about price determination, and never really circles back. Modern
undergraduate textbooks do the same.
Not spending much time on specialization makes sense if you
assume that although specialization is important, there’s no particular problem to be solved. If you believe
some breezy story like “people specialize, then trade for what they need, and
markets efficiently organize the trading,” then maybe economists have better
things to do than talk more about it.
But there is a
problem to be solved, and I plan to spend the next few posts proving that the
specialization problem exists, and is very serious.
There is, in fact, a fundamental tension between
specialization and competitive markets. Specialization tends to reduce
competition. It reduces the number of practitioners in each increasingly
narrowly-defined field. In the logical limit, it reduces it to one, as each
task gets sub-divided again and again until each sub-task is being performed by
just one agent. Yet markets rely on competition to set prices. The closer the
economy approaches to total specialization, the less competitive markets become.
I intend to illustrate that problem in several different
ways, in order to drive the important point home. My first example will follow
an old tradition by traveling to an imaginary desert island, where Robinson
Crusoe and Friday are stranded together. As there are only two people in this
simplified model, so there are only two goods—fish, and coconuts. Each person’s
utility is FC, where F is consumption of fish, and C is consumption of coconuts.
Specialization as a
Prisoner’s Dilemma
Crusoe and Friday allocate their time between fishing and
picking coconuts. Then, if it’s mutually agreeable to do so, they can trade. And
we may further assume that if they specialize,
with each one producing only one good, the total production possibilities are
expanded. There are a lot of reasons why this should be so. They may have
different talents, so that each is relatively more productive when doing what
he does best. There may be fixed (start-up) costs to each production activity.
Time spent walking to and from the fishing hole, or the coconut grove, is a cost
incurred just once for the activity and not tending to accumulate with the
number of fish caught or coconuts picked. Likewise, Crusoe and Friday may spend
time making tools, or mastering skills.
Let’s assume throughout that if both specialize, Crusoe can catch 10 fish and Friday can pick 10 coconuts, and that
this 10 fish plus 10 coconuts is the maximum the pair can produce, in the
double sense that (a) no Pareto-superior joint consumption bundle is technically
feasible, and (b) no feasible joint consumption bundle would push the utility
possibilities frontier out further. It’s not too important to fully understand
the last sentence. It basically just means specialization is the best outcome
for this two-person society, but not
necessarily for each of the agents involved.
If both agents specialize, so that Crusoe has 10 fish and
Friday 10 coconuts, it’s pretty clear how the trade should work out. They go
halves. Crusoe gives Friday 5 fish, Friday gives Crusoe 5 coconuts, and they
both get utility of 25. But the concept of the Nash bargaining solution is a way to formalize this result, and at
the same time, in a sense, to generalize it. Nash worked hard to figure out a
bargaining outcome for any game that is (a) symmetric, and (b) unaffected by
monotonic transformations of the utility function, and in that sense
non-arbitrary. We'll borrow the Nash bargaining solution to predict how Crusoe
and Friday will trade.
Now consider the case where one agent specializes while
the other does not. What happens then?
To keep the problem symmetric, let’s assume that Crusoe, the
better fisherman, can catch X fish and pick Y coconuts if he doesn’t
specialize, while Friday, the better coconut picker, can pick X coconuts and
catch Y fish. Further assume, for now, that X is 5 and Y is 4. If Friday
specializes and Crusoe does not, then Crusoe enters trade negotiations with a
consumption bundle of 5 fish and 4 coconuts that gives him a utility of 20,
while Friday’s 0 fish and 10 coconuts give him a utility of 0. That puts Crusoe
in a better bargaining position, and the Nash bargaining solution, by which terms of trade are set so as to maximize the product of the two agents' utility gains, provides a
way of making the resulting outcome concrete.
As simple as this problem seems to be, an analytical
solution turns out to be difficult (perhaps impossible, I'm not sure) to
achieve. But to solve it by numeric methods via the Solver tool in Microsoft
Excel is pretty easy. That's how I got the below results.
Under Nash bargaining (with X=5, Y=4, Friday specializing
and Crusoe not) Crusoe the
non-specialist will trade 1.48 coconuts for 5.84 of Friday’s fish. As a
result, Crusoe and Friday will consume fish and coconuts in equal ratios, but Crusoe will consume 2.37 times as much as Friday. As a
result, Crusoe will get utility of 34.6,
while Friday gets utility of 6.2.
We’ve now arrived at the counter-intuitive heart of my
argument. By specializing, Friday enriches Crusoe, but impoverishes himself. He
impoverishes himself by putting himself in a weak bargaining position. He has
lots of a resource, coconuts, that, thanks to his efforts, is relatively
abundant, and therefore relatively low in value at the margin. Meanwhile, his
complete lack of fish puts him in a wretched utility position, desperately in
need of trade in order to meet his needs. Crusoe enters negotiations from a
much stronger position, and can afford to walk away from them and still have a
well-balanced diet. So Friday gets quite disadvantageous terms of trade,
offering almost four coconuts for one fish, and ends up worse off than he would
have been if he had caught his own fish instead of trying to buy them from
Crusoe.
It turns out that Crusoe and Friday are playing a Prisoner’s
Dilemma game. The most appealing outcome is for both to specialize, and get
utility of 25. But it’s not in the interest of either to specialize. Each
player thinks as follows:
- If he specializes, I can get utility of 25 by specializing, or 34.6 by not specializing (and then trading at advantageous terms).
- If he does not specialize, I can get utility of 6.2 by specializing (and getting stuck with disadvantageous terms of trade) or 20 by not specializing.
Whatever you think the other player will do, you shouldn’t
specialize. Here’s the game in table form:
Table 1
Friday
|
|||
Specialize
|
Don’t specialize
|
||
Crusoe
|
Specialize
|
25, 25
|
6.2, 34.6
|
Don’t specialize
|
34.6, 6.2
|
20.3, 20.3
|
|
What a perverse outcome! Crusoe and Friday could increase
their utility by almost 20% if only they could specialize and trade, yet it’s a
dominant strategy equilibrium for Crusoe to go on picking most of his own
coconuts and Friday to go on catching his own fish, and trade remains minimal.
(Friday gives Crusoe half a fish in exchange for half a coconut.) Of course, it
seems likely that Crusoe and Friday could solve this problem somehow, but there
is a problem to be solved.
An Institutional Fix
Now, it seems reasonable to suppose that if Crusoe or Friday
specializes and the other doesn’t, the non-specialist will offer terms of trade
a bit more generous than the Nash bargaining solution predicts. Some reasons
for this are moral in nature, e.g., if people feel sympathy or value equality,
or if the non-specialist feels gratitude to the specialist for enriching him,
or is loath to seem to be “taking advantage” of his neighbor.
Yet it turns out that the moral sense does not need to be
invoked. There is what I call an institutional
fix, by which I here mean a set of incentive-compatible rules that can be set
up which mitigate the problem.
In general, the outcome of bargaining games is rather
underdetermined. The gains from trade might be almost completely captured by
either party if they can somehow make a credible ultimatum, and the other
prefers something to nothing. (In bargaining games, paradoxically, it can pay,
in a sense, to be irrational.) The Nash bargaining solution is a way to push
through the interminable bargaining puzzle with a result that’s general and
non-arbitrary, if somewhat inadequately motivated. But it can be just as
satisfactory to say that one party successful makes an ultimatum and captures
most, or for simplicity all, of the surplus resulting from trade, if you can
give any plausible account of why one player rather than the other captures the
surplus. And one reason why one player might be favored to grab the surplus is
that they have the "moral high ground."
To make this more concrete, suppose that Crusoe and Friday
agreed that they would specialize. Friday does so, and comes home with 10
coconuts. Crusoe, however, fails to specialize, and comes home with 5 fish and
4 coconuts. Now Friday has the moral high ground, so he might think he deserves
to get good terms of trade. He offers 3.5 coconuts in return for 2.3 fish, a
1.5:1 price ratio. This trade doesn’t help Crusoe at all, but it doesn’t hurt
him either. It leaves him indifferent while conferring a large benefit on
Friday. If Crusoe feels a bit ashamed at reneging on the deal they made
earlier, a trade like this should be a price well worth paying to partially
redeem himself. So Crusoe ends up with 2.7 fish, 7.5 coconuts, and utility of
20, while Friday gets 2.3 fish, 6.5 coconuts, and utility of 15.2.
While this arrangement is much better for Friday than Nash
bargaining was, he’ll still regret having specialized, since even after
capturing all the surplus from trading with Crusoe, he still ends up with less
utility than the 20 he would have received if he hadn’t specialized in the
first place. Crusoe and Friday are still stuck in a prisoner’s dilemma game. So
far, the institutional fix doesn’t seem to solve the problem.
But it turns out that for some values of X and Y, the
institutional fix does work. If a
non-specialist can produce 5 of good A and 3 of good B, and if a sole specialist
uses the moral high ground to capture all the gains from trade, then the
utility of a sole non-specialist turns out to be 15, and that of the
specialist, 17.6. The game then takes this form:
Table 2
Friday
|
|||
Specialize
|
Don’t specialize
|
||
Crusoe
|
Specialize
|
25, 25
|
17.6, 15
|
Don’t specialize
|
15, 17.6
|
16, 16
|
|
Now the dominant strategy is to specialize. If the other
player specializes, specializing gives you utility of 25 instead of 15. If the
other party does not specialize, specializing gives you 17.6 instead of 16, as
you use the moral high ground to insist on better terms of trade from a
reneging neighbor who, unfortunately, has impoverished you both. Either way,
you’re better off specializing.
The phrase “institutions” is quite popular nowadays in
development economics, and it’s used in what I regard as some quite unhelpful
senses. In particular, “institutions” is often a way of invoking the government
as a deus ex machina. When
development economists say that the West is rich because of its superior
institutions, they often mean little more than that the West is rich because
its government are somehow—there is little agreement about how or why—more
beneficent than governments elsewhere. (Probably they are, but I suspect the
degree of difference is greatly exaggerated, and anyway, quality of governance
might be—I think it probably is—more a result than a cause of the development
process.)
When I say "institutions," I don't mean
"government." There is no government on Crusoe and Friday’s island,
nor any coercion or violence for that matter. The rule “bargain hard if you
specialized and your neighbor didn’t; bargain soft in the converse case; and
trade on equal terms if both or neither specialized” is self-enforcing, once it
is established, in the sense that Crusoe and Friday each plays by that rule and
expects his neighbor to do so, and expects his neighbor to expect him to do so, etc.
The institutional fix is also not an ethical fix. It’s quite possible that Crusoe and Friday would
specialize because, instead of narrowly maximizing self-interest, each follows
the Golden Rule and loves his neighbor as himself, and specializes for the sake
of the social interest regardless of
what he perceives his individual interest to be, if he even bothers to think
about it. But that’s quite a separate story. In this case, the individuals are
acting in a strictly self-interested fashion.
To make this clear, it may help to integrate the Prisoner’s
Dilemma and the Institutional Fix cases together in a single game, which is
done in Table 3.
Table 3
Friday
|
|||||
Specialize, Punish
|
Specialize, Don’t Punish
|
Don’t Specialize, Fair
|
Don’t Specialize, Soft
|
||
Crusoe
|
Specialize, Punish
|
25,
25
|
25, 25
|
0, 15
|
17.6, 15
|
Specialize, Don’t Punish
|
25, 25
|
25, 25
|
7, 29.3
|
7, 29.3
|
|
DS, Fair
|
15, 0
|
29.3, 7
|
16,
16
|
16, 16
|
|
DS, Soft
|
15, 17.6
|
29.3, 7
|
16, 16
|
16, 16
|
|
Table 3 represents a game with the following rules.
- There are two stages, production and bargaining.
- At the production stage, players can choose to specialize or not to specialize.
- At the bargaining stage, players have three options:
- Hard: insist on capturing all the surplus;
- Fair: insist on capturing half the surplus;
- Soft: accept any terms of trade that hold you at least harmless.
- Players choose a single strategy before the game, which contains contingencies, such that play in the bargaining stage can depend on outcomes in the production stage.
Rather than show all the strategic possibilities, I simplify
by assuming that at the bargaining stage, players never play Hard except as
part of a Punish strategy, or Soft except to yield to an anticipated Punish
strategy by the other player after failing to specialization in the production
round. A Punish strategy consists in Fair bargaining when both or neither have
specialized, but Hard bargaining when one has specialized and one’s neighbor
has not (thereby giving the Punisher the “moral high ground”).
In this game, there are two Nash equilibria: one where both
players play “Specialize, Punish,” and one where both play “Don’t Specialize,
Fair.” If non-specialization will be punished at the bargaining stage, it’s not
worth it, and specialization will prevail. If non-specialists refuse to accept
punishment at the bargaining stage, and nix the deal instead, then punishment
backfires, and non-specialization prevails.
All other strategic combinations fail to be Nash equilibria.
If one of the players won’t punish, the other, rather than specializing, should
be a non-specialist and gain by exploiting advantageous terms of trade. But in
that case, the other player shouldn’t specialize either, leading to a
non-specialized equilibrium. If the players are non-specialized but one is a
soft bargainer willing to accept a hard bargain from an offended specialist,
the other player should specialize, in which case the first player should
specialize as well.
The institutional fix is self-enforcing, yet it still feels
rather fragile, because its stability depends on some belief about what the
other person would do under
circumstances that, in the Nash equilibrium, never arise. Thus, I think that my neighbor would be a hard
bargainer if I failed to specialize… but how do I know, if I never try it? Or, I think
that my neighbor would nix a deal rather than accept punishing terms of trade…
but again, how would I know?
Does society, then, depend on a whole array of such fragile
institutions, which induce cooperation only through threats that aren’t
ordinarily carried out? Could a wave of doubt cause such institutions to
dissipate, perhaps suddenly? It’s a disquieting thought, and the quintessential
worry of Burkean conservatives.
Specialization as a
Stag Hunt
If we change X and Y further in the direction favoring
specialization, the basic form of the game changes again, to what is called a
“stag hunt.” The charming name of this type of game is an allusion to a
practice of hunting a stag by first surrounding it, then closing in for the
kill. This hunting technique requires multiple hunters—but for simplicity we’ll
assume just two—to cooperate. Meanwhile, the hunters might be tempted to
abandon the stag hunt and just hunt rabbits, which they can catch without help.
The difference from the prisoner’s dilemma game is that if all the other hunters
play along, there’s so much more meat on a stag than on a rabbit, that all the
hunters are likely to be better off for having kept on task. But if one of the
other hunters goes off chasing rabbits, the stag gets away, and the other
hunters get no meat, and wish they'd hunted rabbits, too. So the stag hunt game
has two Nash equilibria: one where all
the hunters stay on task and catch the stag, and another where all the hunters
go chase rabbits.
Consider the scenario where a non-specialized Crusoe can
catch 4 fish and pick 2 coconuts, and a non-specialized Friday can pick 4
coconuts and catch 2 fish. Specialized, each can still get 10 of what he gets
best. Under Nash bargaining, if Friday specializes and Crusoe doesn’t, Friday
trades 5.58 coconuts for 1.47 of Crusoe’s fish.
Crusoe ends up with utility of 19.2, and Friday with 6.5.
Yet though Crusoe seems to get the better end of the deal, he still has
regrets. Since Friday specialized, if only he had specialized too, they could
both have had utility of 25. By not specializing, he impoverished Friday, as
before, but this time he impoverishes himself a little bit, too. But if Friday
hadn’t specialized, he would have been glad not to have done so himself. How
was he to know?
The payoff structure of the game is as shown below:
Table 4
Friday
|
|||
Specialize
|
Don’t Specialize
|
||
Crusoe
|
Specialize
|
25, 25
|
6.5, 19.2
|
Don’t Specialize
|
19.2, 6.5
|
9, 9
|
|
The lesson of Table 4 is a bit obscure. The game suggests
that you always benefit others by
specializing, but whether you benefit yourself
depends on others. If they’re trustworthy, if they’ll hold up their end, you
can all thrive together, and there might not be any sacrifice. Yet there’s a
danger of being left in the lurch, stuck as a specialist in a glutted market,
and regretting that you did the right thing. So whether to specialize is an
easy choice for altruists but a tricky choice for egoists. The game also
suggests that a society of altruists might be more prosperous than a society of
egoists, because they could more easily and reliably cooperate.
Lastly, it’s worth mentioning that all the production
specifications that give the game a Stag Hunt form under Nash bargaining are
also amenable to the institutional fix. If specialists can credibly threaten to
punish non-specialists at the bargaining stage, then specialization becomes the
dominant strategy at the production stage. I don’t know whether this holds over
all possible version of the Crusoe-Friday specialization game (e.g., varying
the utility function), but it holds for this one (at least for integer
productivities, which are the only ones I checked).
The Full Outcome Typology
in the Two-Person Case
I have been developing a typology of specialization
scenarios. There is a prisoner’s dilemma case; a prisoner’s dilemma with an
institutional fix; and a stag hunt case. There is one more: if one’s
productivity in the other good is sufficiently low, it’s not worth it, and one
should just specialize. Thus, if a non-specialized Crusoe can catch 4 fish and
pick only 1 coconut, his utility if he doesn’t specialize will be 14.7 if
Friday specializes, and 6.25 if he doesn’t. But if Crusoe specializes, he gets
25 if Friday specializes, and 7.8 if he doesn’t. Either way, Crusoe is better
off specializing, and specialization is a dominant strategy. This case might be
called spontaneous specialization.
Table 5 applies the typology to all the integer productivities
that can be imputed to Crusoe and Friday in their respective goods. It also
shows the utilities that accrue to the non-specialist (left) and the specialist
(right) under Nash bargaining.
Table 5
Non-specialist Good B
Production
|
||||||
5
|
4
|
3
|
2
|
1
|
||
Non-specialist Good A
Production
|
5
|
N/A
|
||||
4
|
34.6, 6.2
|
25.7, 4.9
|
||||
3
|
29.3, 7.0
|
23.5, 5.6
|
17.6, 4.2
|
|||
2
|
24.0, 8.1
|
19.2, 6.5
|
14.4, 4.9
|
9.6, 3.3
|
||
1
|
18.4, 9.8
|
14.7, 7.8
|
11.0, 5.9
|
7.4, 3.9
|
3.7, 2.0
|
|
In Table 5, mauve cells represent pure prisoner’s dilemma
cases; orange cells, prisoner’s dilemma cases where an institutional fix is
available; yellow cells, stag hunt cases; and green cells, spontaneous
specialization cases. I’m struck by how large a share of the cells are yellow
stag hunt cases. Often, it seems, both specialization and non-specialization
are equilibria. But the big, basic lesson is that there is a specialization
problem, that it’s common for specialization to be socially beneficent, yet not
automatically incentive-compatible for individuals.
Crusoe and Friday’s desert island may seem remote and
irrelevant, but I believe the specialization problem is applicable to many or
most situations where there is division of labor in a non-market context, such
as a family or an organization. A common phenomenon in large organizations is
the “turf war,” where different individuals or teams engage in a somewhat
surreptitious struggle to annex different functions to their scope of work. A
team looking for job security might start performing a bunch of tasks that lie
on the margins of their work. Another team has more specialist expertise and
could have done those tasks better, but it’s faced with a fait accompli. Meanwhile, the turf-grabbing team’s core functions
have been relatively neglected, yet they still need to be done, and the
turf-grabbing team is still best placed to do them. Management intervenes, and
maybe urges the turf-grabbing team to focus on its core tasks, but it’s
difficult to understand what happened, and when some compromise is reached in
order to settle the issue and move on, the turf-grabbing team’s scope of work,
and maybe its budget, has expanded at the expense of the other team, which now
faces an increased risk of redundancy. The interests of the organization would
have been better served if the turf-grabbing team had specialized in its core
functions, but the turf-grabbing team benefits by becoming less specialized and
grabbing more work.
That’s not to say that turf grabbing is always bad.
Sometimes the motive for turf grabbing is that a team is capable of doing more
than it has been tasked with, and its ambition and enterprise in expanding its
scope of work benefit the organization as a whole. An organization rife with
turf-grabbing might be doing well, expanding and innovating, and a lack of
clarity about roles is both a cause and a consequence of its culture of creativity
and change. But organizations should understand that specialists are
vulnerable, and tend to face incentives to broaden their functions so as to
improve their bargaining positions, and that it’s often contrary to the
interests of the organization for them to do so.
Two lessons that can be drawn from the specialization
problem of Robinson Crusoe and Friday are likely to become monotonous: we've
seen them before, and we’ll see them again. But they are so basic and important
that it’s worth insisting on them to the point where they become truisms.
First, virtue can often
achieve socially beneficent outcomes that self-interested behavior makes difficult
or impossible to achieve. A selfish and amoral Crusoe and Friday will face
some difficulty in reaping the full gains from specialization and trade, but
for a Crusoe and Friday who follow the Golden Rule and love one another as
themselves, or even a Crusoe and Friday who are merely scrupulous in keeping
their agreements, there is hardly a problem to solve. The altruists will always
specialize for their fellow’s benefit if not their own, and the promise keepers
will soon discern, and commit to, the optimal specialization pattern, then do
it.
Second, “institutions”—the words customs, protocols, and habits would do almost as well here—can
sometimes achieve socially beneficent outcomes even when individuals are
selfish, but they tend to have a certain fragility, and can be disrupted if
expectations change.
In the prisoner’s dilemma cases, where the specialization
problem is most acute, the gains from specialization and trade are apparently
rather small. At most, consumption increases by 20% as a result of
specialization, from 4 of each good to 5 of each good. This might suggest that the
specialization problem isn’t too severe and isn’t a candidate for explaining
the vast income disparities between, say, Bangladesh and the United States. But
the gains look small only because there are only two people and two goods. In
the next post, I’ll present an example in which the gains from specialization
and trade are absolutely enormous—and the specialization problem, in its acute
prisoner’s-dilemma form, is fully applicable.
