Coase defenestrates Knight on firms

Coase dismisses Knight's view that firms exists to serve the purpose of concentrating income uncertainty to the owners of the firm, not the workers.  He does this by hypothesising precisely the opposite - a firm which presents a fixed income service interface whilst internally paying workers on a profits basis.  While I agree that this isn't an essence of the firm, I do disagree that Coase's argument challenges that - just because it is possible to create a firm which pays its workers on a profits basis assuming fixed income service costs, this isn't a convincing argument against the idea.

After all, in a sense, all companies create a fixed income cost base with a view to making variable (and hopefully excess) profits.  Just like marketers, in fact.  Though with marketers, the uncertainty is even lower due to the reduced complexity in not having a firm and employees.

I think Coase is right that firms aren't the sine qua non of providing fixed income for workers - financial contracts can do this, in theory, which you can pick up in a market, independent of firms per se.  Insurance policies do this kind of thing.  These could, in theory, exist in a pre-firm world.

The simplest model of the firm

Coase highlights, as did Adam Smith, that the firm makes sense in only in a wider economic environment.  Let me immediately jump to the situation of firms in a wider economic context.  There's a fairly easy, though not initially very useful way to model them.

How many companies are there in the world?  That's clearly a temporally bounded question.  Right now (April 2014) a casual search on the web reveals that there are 120 million companies in the world, of which 45,000 are listed on various exchanges, and, separately, about 65,000 are classed as multi-national.  (I got this from Quora).  Forbes tells us that there are 147 companies which 'control everything'.  While I appreciate the journalistic hyperbole, it isn't going to be too much of a surprise to me that there's a power law distribution in ownership of the companies in the world, and in their size.  This is based on research at the Swiss Federal Institute of Technology, which performed an ownership analysis of 37 million of the hypothesised 120 million and discovered that 147 companies owned 40% of the net value represented in the 37 million.  Apparently 737 companies in their research owned 80% of the value.  

There are N humans and M companies.  Companies can be owned by humans or other companies.  The final owners of all value in all companies are always humans, though in specific cases, the mth company is owned by a number of humans and a number of other companies.  The only constraint at the individual company level is that a company cannot own itself.

A single 32 bit word in a computer can represent over 4 billion distinct things.  This would be more than enough to represent distinct companies.  But let us be generous.  Let us say we are looking to capture the ownership relationship.  With 7 billion people on the planet (a large fraction of whom own nothing), together with our 120 million companies, we'd like more than 4 billion distinct things.  We could just represent each human or company by a 64 bit word, and we'd be good to go for millennia.  If we plan to model it on computers, we might want to economise.  We could do this by assuming that no more than 4 billion people own shares.  This is eminently reasonable for this year.  That's 4 bytes per human/company.  Pew research recently (2013) claimed that 53% of Americans have no stocks, even including retirement account holdings.  This from the world's leading stock owning nation.

Let's embed 120 million companies as a series of 120 million 32 bit words, and worry about the ownership identities later, knowing that our 32 bit word is probably more than capable of capturing this.  That's 457 megabytes.  This can model all the companies in the world.  With 27 Gigabytes of memory I can start to model all the people and all the companies in the world, just in the memory of a computer costing less than £1,500.

What, in addition to its identity, would we like to minimally model with a company?  For me, two things which jump out above all others are who owns it, and how valuable it is.  Or put another way, what the company does isn't being modelled at this stage.  Let me get a handle on this.  Upper limits first.  The current high water mark was Apple, a while back, which topped $463,000,000.  Companies are said to be bust if their net equity is negative, so I could imagine again a 32 bit word could capture this number, just about.  Precise values are not needed.  Nor negative numbers.  So make it integral, giving values from 0 to 4,294,967,295.  If we say the number represents the value in thousands of dollars, this is a fair compromise to getting small values but capturing larger ones.  The maximum value in any one company would top out at 4.2 trillion dollars, which is plenty of headroom above 0.4 trillion.  That's another 457 Mb for the value of each company.  

Finally, the ownership relation.  This has the possibility to be a big one. For example, Apple has by implication of its market cap divided by its share price about 890 million shares of a free float.  Clearly, at worst, this could be distributed to 890 million separate individuals.  Times 120 million companies, worst case, this is quite intractable if your goal is to have it all in RAM.  In a couple of years it ought to require no cleverness and we will be able to model each share as a separate object.  I think it might be useful to own fractions of a share, a share of course already being a fraction of ownership of the value of the company.

In the real world, a company has a register of holders of shares, and from the individual perspective, an owner of a collection of shares has their own list of the things owned and their amounts.  Having both is redundant information, though it might allow faster two way lookup (what companies does this person own and who owns this company).  Also a company can be modelled as a unitary whole, with fractional ownership.  That is, the number of shares per se is not essential.  All companies are fully owned by someone.  Transformations of the ownership unit will be applied if a dilution event occurs.

The company will have a list of N owners, together with their fraction.  Ownership can change.

Later, I think it is possible using techniques for automatic classification to encode the similarity between companies as patterns in the 32 bit word.  This will allow industry modelling.  Finally, it is possible to imply a power law distribution of company value and distribution of ownership using real data.  

Firm Storms

Right at the outset, as Coase sets up the seeming paradox: if prices can direct production, who needs a co-ordinator to direct the production process (someone he identifies as the entrepreneur, the essential part of the firm, as he conceives it).  My first thought is to notice how Coase's approach takes you from zero entrepreneurial participation (the pre-firm world) to some participation and to jump ahead to that final destination point, where all production is directed and co-ordinated by one class of actor, and in the limit, one actor.  That is, there are two possible post-markets end points to Coase's story - the first is the existence of a number of companies which purchase all their factors of production not from any market, there being none, but from each other, in bilateral (or indeed multi-lateral, for that matter) contracts.The second is that there is just a single co-ordinator - why bother calling it a firm, as that word surely at this level loses its common meaning.  That unitary co-ordinator is probably maximising something - the happiness of the proletariat, the utility of the citizens, depending on your politico-philosophical bent.  

A physical metaphor springs to mind.  The illusion of the institution-lite free markets are like a gas, the frozen centralised singular co-ordinator being like a solid singular object and the existence of companies being like the formation of droplets of liquid out of the gas.  This metaphor has its flaws, but the thing I like about it is visual image of the formation of a certain kind of structure out of the homogeneous, isolated particles of gas.

But Coase, for me, is not describing any state transition which has any resemblance to reality.  It is a story he's telling.  The creation myth of the firm.

Market places, and money, and the firm are clearly not as old as our species itself.  We had 70,000 years of homo sapiens spreading around the globe, making dramatic inventions and discoveries, all in the context of an agriculture-free, essentially nomadic lifestyle.  Then we invented farming about 15,000 years ago and, when that idea spread around the world also, rather like a gas, we reached a point where marketplaces, money, trade, the firm became possible, indeed, happened.  That it happened to an already geographically diverse set of populations of homo sapiens around the planet was to have significance in the story of money, currencies, economic and political borders.  That the need for a minimal-trust form of inter-regional money is embedded in our geographical diversity.  That our planet allows different kinds of farming in different regions.  That some plants and animals existed in some and not other regions.  That some farming techniques were better than others, that their implementation also varied. All of this formed the material basis for the possibility of trade, markets, and in time companies. Provided the variety upon which temporally stable rules of supply and demand could operate.  Rather as the process of condensation happens randomly here and there in a gas, droplets being formed at a multiplicity of 'places' in the gaseous space, and so too for the same 'reasons' (these temporally situated stable rules of supply and demand).