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.

Everyday lower prices!

One advantage which Coase explicitly mentions in his classic paper on why a firm might provide a lower cost solution to direct bilateral markets contracts has to do with long term contracts.  It may be cheaper to replace a series of spot or futures contracts with an in-house longer term one which fixes in the costs of the factor of production.

Is this a real advantage?  Assume for the moment that the futures price of the factor of production in the market place is the fair value of the factor.  

The argument goes like this.  We need some factor F to make one of the corporate products.  There is a spot price $S_t$ for this product right now.  We need it for a series of t periods in the future.  We might look to buy it on the futures market for expiry t.  There we assume (naively) a fair value of $S_te^{rt}$, using the risk free rate.  But, the futures market isn't infinitely deep - it peters out after a number of months or quarters or years.  Wouldn't it be better, more possible, cheaper, for a firm to internally charge for this?

My first thought is if those longer term contracts are needed by companies, then one of two things would happen. First, there might be a deeper (temporally) futures market.  Second, there is an OTC market which can (and does) service those needs which might exist, as it does currently for financial derivatives.  

My second thought: even ignoring that point, how does the company achieve a better price, all costs considered, than the market?  What is the company doing, other than taking a chance.  The hurdle it has to overcome is the cost of that futures contract, assuming it exists, for the corresponding time period, including all costs.  Companies in general can't take a chance and persistently win, on average.  The efficient markets hypothesis would see to that.  So on average, the average company will be no better and no worse off than the futures market would imply.  Otherwise the company is merely subsidising that particular factor of production within the the corporate balance sheet.  If this is persistent, how can that company survive long term? Luck is not on the side of the average company, so if it is internally charging $S_te^{rt}$ minus some benefit based on reduced contract costs, isn't this just putting the extra cost on the firm generally, socialising the cost within the firm?  Doesn't this just put the firm at a disadvantage, at the margin, to the degree that this is an economically significant benefit?  All this assumes that the average company can't produce the factor any cheaper than the spot price $S_t$ implies.

It leaves untouched the general argument for the deal costs - contract creation costs, the costs in general of getting the deal to 'the market'. 

Also with large corporates there's a real internal communication problem.  It is a version of the search cost all over again.  Large companies are a bit like 'the world out there' insofar as finding the right internal market has its own costs. And the larger the firm, the larger these costs.  This would be a drag in general on the size of the firm.

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.  

Walking in a firmless land

A classic in the field of economics which attempts to answer the question:  what function do firms serve is Ronald Coase's 1937 The Nature of the firm.  Just as barter served for Adam Smith a pre-monetary assumption of how the world works, so for Coase there exists a world where no firm exists, and all products are made through direct purchases with participants in pre-existing direct markets. This kind of 'creation mythology' is probably not wrong in itself, but I must pause at the outset to look at how unrealistic it is.  Coase in that paper opens up by making a claim that the creation myth of the firm he's about to espouse is not only tractable to a marginal analysis, but is realistic.

There are two points I'd like to make.  The first is an anthropological one.  Coase specifically doesn't talk about the other pre-firm possibility - where goods and services get produced by friends, family members, slaves.  This must be surely how the thousand year old Japanese company did it.  Just what is it when a family decides to run a family hotel for over a thousand years?  Well, there must be many parts to that particular story - the value placed in the business, the family tradition inculcated in all the descendants which encouraged some family members to continue, the lack or abundance of alternatives available to offspring, the number of offspring being produced, both to serve as workers and as mouths to feed, the desirability of the service offered (the hotel was by a hot spring which clearly must have had some value to people in the neighbourhood).  

Given what we now know about economics as a subject (post-Kahnemann and Tversky, post-Becker, post-Lucas) it must be clear now in a way it wasn't to Coase that a marginal analysis could be possible even to the non-markets, familial, slaves and friends firm.  This would be even more realistic than Coase's pre-firm landscape.

Second, how realistic anyway is this Coasian pre-firm landscape?  Not very.  Putting well functioning markets prior to the emergence of a firm seems to me rather fraught with too much difficulty.  So-called free markets are clearly the product of a particular policy environment which implies a well developed cultural landscape.  Rules over property, enforcement, resolution dispute, probably a monetary environment, tools for discovering the best and most correct market, and so on.  That particular constellation of desirables, whilst not specifically demanding a large governmental infrastructure, certainly needs a supporting framework of institutions.  Jumping to the end of his paper, we're going to find that the marginal value of adding the firm into this mix is 'worth it'.  This positive value is the value, in general, of the firm.  But if the pre-firm world is a figment, or at least unrealistic, then the 'value' of the firm is in question.  Underlying this pre-firm fantasy world is the implicit mechanics of a well functioning and pervasive set of elastic supply and demand curves in a fairly institution-free context. 

What economics needs at this point is a new creation myth, one which doesn't assume the existence of a barter and creditless economy pre the invention of money, nor the existence of a well evolved set of free markets pre the invention of the firm.  Why not have an anthropologically informed creation myth, which resonates more strongly with the way our economic systems did in fact emerge.