What's Wrong with the Edgeworth Box? (2)

(Part 1)

In Part 1, I explained my view that the Edgeworth Box is used to convince students and other consumers of economic theory that certain social arrangements are inevitable.  It's not so important itself as a pedagogical tool, since others have developed and the issues it was meant to settle have long ago become stare decisis.  But I think it's worth examining as an economic approach to describing reality.

ECONOMICS AS A HEURISTIC METHOD

The literature of economics is full of definitions of economics; readers are invited to use their preferred search engine and find a few.  In recent decades, economics has become much more pugnacious about being a science, with a (a) unique purview over the whole scope of political choice, and (b) comprehensible only to experts in the field.  In other words, as research project, economics have taken upon itself pretensions of universal authority, while pre-emptively rejecting the right of any outsider to criticize its positions.

Economists have implied, in doing so, a sort of motivational force-field around themselves, in which the doctrines they preach are impervious to the corrosive self-interest they impute to others.  While lawyers are quite open about the fact that they are paid to make arguments about legal doctrine by the expected beneficiaries of that doctrine, economists refuse to accept any such second-guessing.  "Markets" are presented as unimpeachably pure, sui generis, and uniquely fit to distribute wealth.  Economists may protest that they are merely engaged in abstractions of a reality too complex to present in fuller detail, but people should notice the bizarre implication that public choice is, ultimately, treated as insidious, while the power of business interests is presented as wholesome and self-policing.

So I propose to answer the question: as a research project, what does economics seek to do?

Economics is a process of binding decision-making to accounting.  Economics tries to explain and improve decisions by presenting them as causing, and caused by, conditions of scarcity, preference, and accumulation.  Humans have agency over their own access to wealth through the ability to produce and accumulate rather than merely hunt and gather.  Production and accumulation bring scarcity into the realm of something humans can control, leading to accounting and commerce, hence to the creation of markets.  This chain is not meant as a history, but as a heuristic.

The effort to link decisions specifically with certain objective, measurable conditions imposes a lot of simplification-by-average; while individuals are crammed with confusing idiosyncrasies, those particular quirks have effects that are much too small to matter with large groups. Likewise, confusion, doubt, and ignorance will cloud the decisions of individuals, but on average, the crowd is expected to know what it needs to know about objective conditions, and not make consistent errors about the future.

On average, preferences define a well-behaved utility function.  On average, expenditures are consistent for categories of goods, and not affected by unit price. And so on.  In most cases, these are not just simplistic, but unrealistically simplistic.  If you see a mountain from a distance of a meter, you see the grains in the granite and the twisted scrub growing out of cracks; back up 20 kilometers, and you see a massive peak that's generally triangular, probably with pale-lavender at the top and darker chiaroscuro near the base.  You do not see a polished cylinder or sphere.

This is justified as producing tolerably good predictions, but it doesn't.  It produces tolerably effective political justifications.

THE EDGEWORTH BOX IN CONTEXT

This brings me back to my abuse of the Edgeworth Box.  The idea was presented in Edgeworth's book, Mathematical Psychics (PDF; 1881), and later wedded to the concept of the Pareto Optimum: a condition where no one's utility can be enhanced without reducing the utility of another.  It's a somewhat nuanced view of conflict, because it implies human relations, even over the very short-run, are neither zero-sum nor yet nonzero-sum; in many cases, there may be distributional problems that can be resolved to everyone's benefit.

At the same time, though, an odd corollary is that, once the market has worked its magic and arbitrage opportunities are exhausted, then social factors are innately hostile to each other.  Solidarity plays no role in this; there is no chance for a group of people to get together and enhance their condition in the face of some powerful force, because the Edgeworth Box implies that they're as unified as they will ever be. Likewise, there's no scope for change.

To be clear: I'm not saying the Edgeworth Box needs to explain any change in the endowments of A and B, or suggest that A is really A₁, A₂,..., A_n, and these guys just need to get together and drive a harder bargain.  That's not for me to say, and I don't think it.  But the whole scheme excludes this as a concept.

(I need to pause here and mention that Frances Ysidro Edgeworth himself had a very sophisticated an nuanced idea, which is not closely related to the usual discussions of welfare economics where one is likely to find an EB.)

We can consider different contexts in which the EB applies:

1. Trade disputes: here, A and B are "rival" countries.  They are knocking out a trade pact, but the pact is very unpopular domestically.  Why?  Because A and B have at least three rival constituencies, specifically, those who are export-obsessed (workers and some business managers), those who are consumption-obsessed (households and investors), and those who are incentive-obssessed (activists for the environment, human rights, etc., who hope to use the trade pact to mandate some common policy in both countries).  While the three groups have massive membership overlap, they also can alter the final outcome.


2. Political disputes:  acknowledging that the USA is unusual in its bilateral polarization (C.f. most other OECD countries with four political poles, or Japan, with a single pole of varying valence), consider the problem of political disputes between Republicans and Democrats.  The absence of common ground is the result of experts and party caucuses seeking a new constituency to recruit for either side, until there are no loose interest groups. The purpose is not some new modus vivendi; it's the permanent eradication of the rival's potential for control.    The conflict is asymmetric because the Democratic Party itself consists of a huge number of constituencies that are watchful, if not positively enraged, with each other.


3. Labor disputes: Again, mine is a US-centric view, but the lengths to which management will go to prevent unions from being organized not in the realm of economic behavior.  Unions have been a successful partner of management in Scandinavian countries and postwar Germany; one can dispute the purity of company unions in Japan, but they are prone to actually showing a flicker of independence.  I suspect this has to do with the evolution of the large American industrial corporation into a quasi-sovereign entity, often with its own (de facto) law enforcement and court system,

Here are three common conflicts that attract a lot of attention, They are modern and plausible. Readers of this blog are unlikely to find themselves in an actual shooting war, and pay negotiations are pretty much random confusion or else unilateral decrees on the part of the employer.  The Edgeworth Box is, in that sense, not applicable to anything real. 

What's Wrong with the Edgeworth Box?

In this post, just this one time, I'm going to eschew the footnotes and sources because I don't think they'll be necessary.  Edgeworth boxes are probably familiar to students of economics because they are used to present the idea of Pareto Optimality (on that subject, I'll say more later).

On the right is an example of an Edgeworth box. The two axes represent amounts of a finite good; let's call the horizontal axis good H and the vertical axis good V.  There's two parties, person (or group, or firm) A and person B.  Party A gets an amount of good H that will be h_a. Party B gets an amount of good H that is the total amount H - h_a = h_b.  Obviously, the same applies to good V.

Starting with the point of view of A, we can see a succession of dark blue curves labelled a₀, a₁,.. a₃. These are indifference curves, or trade-off curves. They represent possible combinations of  h_a and v_a  that, together, are of equal benefit to A.

(I've posted on Edgeworth boxes before, and here's a post where I used plots of actual indifference curves generated by a computer.  The concept is the same as a production possibilities curve.)

We can see that A's utility improves quickly as it acquires/consumes larger and larger amounts of both H and V.  This cuts into B's maximum possible utility, though. As one can see, if the two parties are at one of the two points where a₂ and b₂ intersect, they can both improve their well-being by negotiation and exchange.  By "moving" to the intersection of v* and h*, the two parties will be consuming the same total amounts as before, but they'll be at a* and b*, meaning they'll be at a much higher level of satisfaction.

In this particular version of the chart, one could sketch a more-or-less straight line from A's corner to B's, and this would roughly correspond to the points where A and B have distributed H and V between themselves so they are as satisfied as they can be, given their respective endowments.  You might have a situation where A consumes almost all of both H and V, but if the distribution is a point on that line, it's Pareto-Optimal.  This line is called the "contract curve," because the original purpose was to explain contract negotiations between workers and business managers.  Not that it matters, but the curve is often estimated to be squiggly or logistic-shaped.

At this point, I'd like to sum up some criticisms of the Edgeworth Box that I think are invalid:

1. It's too simple in that it only allows for two goods. This is not a valid criticism because the idea could be extended to a lot more goods (i.e., more dimensions), and represented mathematically.  It doesn't change very much if you accept a manageable mathematical expression of utility.
2.  Utility functions aren't real.  Economics is about using logical reasoning from analogies. In other words, individual people are likely to have intransitive preferences, bliss points, and other anomalies, but those are peculiar to individuals.  At this point, I don't expect to say anything original about the "realism" of utility functions.  
3. Pareto Optimality permits gross unfairness (income inequality).  Yes, it does.  There are a lot of valid moral criticisms of economics, but attempting to identify a point of failure is not one of them.  There is a meaningful distinction between unfairness and inefficiency when it comes to bad distribution.  
4. The Model is actually very boring once it is understood.  To be sure, this is totally true: once you grasp the idea that the characters need to be able to truck and barter in order to reach optimality, then what is left to say?  The 

When it comes to arguing with the solution to a thought experiment in economics, it's not unusual to find yourself up against the terms of the model.  In an Edgeworth Box, the availability of goods is zero-sum, for example; if A gets more of a good, B gets less of it.  If A and B negotiate a contract freely, then, short of a violent revolution in which the workers and peasants—Party A—liquidate the ruling class—Party B— there will be no change in the overall distribution of goods.  

In this light, the Edgeworth Box is a polemical tool.  The professor can argue with a radical student that there is no alternative.  Perhaps the student expects a revolution [offered up sarcastically]?  Revolutions do occasionally happen, but the whole box will shrink in the next period because of the disruption to production.  Striking won't adjust the distribution because the employer will just find other workers.  If the strikers win, the distribution of goods will be off the contract curve because the new contract will remove the ability of workers to choose an employment arrangement they prefer.  Eventually the radical student just gets frustrated and gives up.

Grad students and professors propose thousands of models, or mathematically representations, of social conditions each year.  Many are probably very good, but only a tiny number will become entrenched as a pedagogical tool, eventually being adopted by economists because they frame a particular problem a particular way.  The strategy is to impose a solution a priori.   Granted, this is difficult to avoid, since economics involves a nexus of choices with accounting; that one fact, in isolation, requires economics to have a process of making mathematical analogies to reality, and those analogous require inputs and outputs of factual information to be useful: exchange rates, inflation, rates of investment, and so on.  But the Edgeworth box is especially egregious as most contexts to which it could apply are, in fact, three-party or more.

(Part 2)