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).

How much is this really going to cost me?

The single most essential pre-requisite of the Coase paper where he gives birth, economically, to the firm, is the idea of a transaction cost.  I wanted to do a posting on this.  Transaction costs have been long understood in economics.  I personally remember first discovering the existence of a bid and an ask in a market.  It was shockingly late in my life, since I have until then no direct relation to any market.  My first thought was that it seemed quite unfair, like somebody somewhere was making free money on this.

Ok, the set up is this.  A couple of participants wander into a market.  The market is a market for a some particular good.  One participant comes to sell this good, and another comes to buy it.  Let us pretend that they both are happy to take the price, $p_t$, which the market tells them the good is worth right then.  So the buyer hands over $p_t$ to the seller at the same time as the seller hands over the good to the buyer.  They exchange pleasantries and head home.  Deal done.  Simple, right?  Well, that's how I used to think how it worked.  But it is more complex than that.

Let me spell it out with some questions.  How did the buyer know where to turn up?  They didn't just accidentally wander in there together, did they?  If they really did wander, that could entail in general a lot of wandering.  And a lot of turning up at dodgy sub-optimal markets where they would get some sub-optimal price $p'_t$.  Was that market advertised?  How did they get to hear about it?  Who's funding that?  What kind of good am I looking for?  All of these are referred to as search and information costs.  

Second, when engaging in a discussion with the seller, how did that proceed?  Did bargaining happen?  If so, how expensive were those costs?  Did they result in anything more formal than a verbal agreement to pay $p_t$ for the good?  Was it written down anywhere in the form of a contract?  Are they evenly onerous for the buyer and the seller?  How did the goods turn up here?

Third, who pays to chase up the issue when something goes wrong?  Who pays for the policing and enforcement that all parts of the contract are maintained.  This is important in situations where one (or both) sides of the good/payment are to be delivered at some point other than 'right now' - something which happens a lot.

This trio of costs are generally what is meant by transaction costs.  Could this all happen with just two transactors?  If that is possible, then surely we can consider transaction costs as merely rolled up into the single price we transacted at, $p_t$?  That certainly would reconcile my naive thought that there just was a price to be agreed.  Imagine a world where the seller advertises and pays for this advertisement, and will set his price based on this cost.  That contracts are standardised and again funded by the seller, who embeds the ongoing legal costs into the ongoing price $p_t$.  And that all markets are only for the single current time, t, where the buyer is expected to perform the range of quality checks which will satisfy them when they purchase from the seller, and therefore that there's virtually no need for enforcement costs.  This is probably itself unrealistic in its own way.  But in that world, it might be possible to imagine a single seller and a single buyer, and a single agreed price with the transaction costs burned in.  It is a bit of a stretch, but for simple goods where quality is easy to ascertain, has low value, etc, it is just about imaginable.  

If there literally was a single seller, then it isn't really a market, is it?  That seller could set his price with not many competing pressures on them to make it any lower.  But then this isn't a point about transaction costs per se but just about the price in general.  The competition introduced by a healthy market may cause the price to come down in general.  How does a multitude of sellers affect our trio of transaction costs?

Well, all along I've pretended we start with just one buyer and one seller - clearly this isn't sustainable - if we now imagine a marketplace of sellers, surely this can't exist in any sense with just a single buyer - no, we need a set of buyers.  But still, we have two types only, the buyer type and the seller type.  

Implicit in this market place is the assumption that some sellers are going to be different from other sellers - in terms of the price, and maybe in terms of the trio of transaction costs too.  Otherwise is a market of cloned sellers really any different from a single seller with exclusive pricing advantage?   If each seller sells differently, then the possibility exists that some markets will have better and worse prices for the good.

I'm trying to think of this in the context of a world with no firms.  So there is nobody to go out of business.  Just a set of sellers with different prices.  Buyers now have higher search and information costs - who to buy from?  Surely there would be variability in the bargaining costs but I wonder if I could hold on to the possibility that the average bargaining cost remained the same?  Let's say yes.  But to the average buyer, this isn't any good since he doesn't know that this seller has better or worse than average bargaining costs associated.  This variance in the bargaining costs, represents one element of the search and information costs.  So I'm thinking search and information costs may be more fundamental than bargaining costs.  Again, I'm hanging on to the thought that enforcement is minimal for the same reasons.  So I want bargaining costs to be negligible too, even in the presence of variability, which is an element of search costs.  And enforcement to be negligible.  The presence of a marketplace for the good increases the informational/search costs for the average buyer.  

Well, the average buyer, that non-existent person, maybe doesn't care about the search cost?  They get the averagely good deal.  A bit like the passive index fund investor. But his non-zero embedded search cost is a function of how much searching individuals actually do.  Imagine no-one bothered finding the best deal.  They walk into the market place and randomly pick a market.  This wouldn't be a healthily running market.  No competition would be possible to drive down average prices.  

What I've been trying to do here is embed the so-called transaction costs in a pre-firm world into the price a single seller and a single buyer set, with a view to seeing this as a kind of mental accounting.  In a firm, you'd like to know how much your legal and finance departments cost you, how much your marketing and operations departments cost you, how much your compliance department costs you.  And maybe even express this as a fraction of the unit cost of your product.  But pre-firm, this is less relevant and becomes a kind of mental accounting in a seller's and a buyer's head for setting an individual price.  As well as trying to imagine that the seller and the buyer could 'own' these costs, I've also been trying to find ways to imagine these costs being negligible, in a so-called free-markets context, since if I can do this, then it would weaken the Cosean theory for the birth of the firm. 

I notice in passing there is a natural narrative order to these transaction costs - the approach, the deal, the delivery.  Imagine, wrongly, that all these costs were equally burdensome across a buyer and a seller.  If that really were the case, then these sunk costs would net out and become irrelevant to the price.  There is clearly an asymmetry in this relationship, but still, some fraction of the gross costs residing in this two participant world resides with one party and the remainder with the other. If, on the other hand, some of those transaction costs were due to some set of third parties, T  then this netting would not be possible.  The degree to which I can equalise and minimise the differences between B and S in a two participant world, then the more I can claim that the Coasean justification for the birth of the firm to be weaker.

Clearly, you look to reality to see likely candidates for T.  The host for the ground on which the market takes place.  Agents for the ground who advertise its presence and value. Third party contract enforcers, creators of contracts, the list could go on.  If the lion's share of the transaction costs reside with T then there's less opportunity for this netting and equlibration of transaction costs.  T  is nothing other than cultural institutions, practices, participants with structural  and supporting roles in the market event. And given that our starting point is this rather fantastic and unreal institution-lite free market, I feel justified in seeking a kind of Coasean world where T's role is minimised.

To summarise, I've looked at the case where there is no market making, no promise to buy back, an institution lite world of seller and buyer trading goods on the spot market with negligible transaction costs which partly net off as a way of making it difficult for Coase to justify the firm as a 'solution' to the phony problem domain he sets up in his classic paper.  Now on to the paper itself.

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.