crescet and titubit

The speed with which one's wealth grows, and its absolute level, are tied to one's life style (one's consumption of one's income).  A useful simplification is to assume one's income derives largely from one's wealth.  Economically, this is almost completely unreasonable, since it applies only to a vanishingly small fraction of humanity.  One then needs to spend to live from this wealth.  There are however minimal quality of life spends which may imply several modalities in the relation between the wealth growth process and the spend process.  I assume for simplicity that wealth is sufficiently large that the income spent can be made in a way which still leaves wealth growing.  Put another way, there is an assumption that the wealth process grows faster than both inflation and the daily consumption of your lifestyle.   A second critical threshold is for now also ignored - as with the case where the lifestyle spend significantly impacts the wealth process, transaction costs also can incur a third hurdle to overcome.  These assumptions clear away much of the thrust of the Darst book on asset allocation.

Next, an implicit starting assumption is that wealth at time $t$ may be considered as residing in one or more currency (short term fixed income) buckets.  One then imagines that the mean value theorem can be applied to the act of taking financial risk above this risk free (globalist) position.  That is to say, in equilibrium, the entirety of the job of strategy allocation and capital deployment can be waved away as solved for now, and modelled as a single 'bet' over an appropriate time frame, whose outcome can be a win or a loss.  One then determines the ideal bet size, per unit of time, based on the mathematics of Gambler's Ruin.  That is to say, that the average bet size can be no bigger than some fraction $\delta$ of wealth at point $t$ if volatility (and long term, ruin) is to be avoided.

Of course, in reality, the complete opposite applies with titubit.  Bet sizing is often ignored and instead one's lifestyle generates the major driving constraint to investment returns variance tolerance.  In short, our lack of funds makes us bet too big - this together with transaction costs, destroys our wealth.

The billionaires' t-shirt

A story.  Off the coast of some fantasy country are a thousand tiny islands, owned by a thousand owners.  On each island was a single shop selling t-shirts, each one with a different message: "I came to Tikka Moa and all I got was this lousy t-shirt" or "I came to Tima Takkoa and all I got was this lousy t-shirt".  Each t-shirt costs $1.  The shop owner on each island owns the single ship which takes you from the mainland to the island.  Return tickets vary from $1,000,000 to $10,000,000.  When you arrive, along the path to the shop you are offered a series of increasingly costly admittance tickets and legal proofs each of which entitles you to move on up the path.  You then hand over your pound for the t-shirt and make your way back, again enduring a costly series of checks and duties.

You get to hear about the islands only by virtue of being a member of one of a small number of exclusive members clubs which have high entry fees.  These island owners employ a vast number of quasi-policemen on the mainland who vet and confiscate and pursue anyone who tries to wear one of their t-shirts without the appropriate documentation.

The t-shirt operates as some kind of ridiculous Veblen good.  Well, assuming you take the total cost of the the transaction, and not the sticker price.  The sticker itself is also sold with the t-shirt, at a cost of $100.

At a rough approximation, the cost of the t-shirt is neither here nor there, yet still you need to be a millionaire to pay for all of the ostensible transaction costs.  In short the full price is nothing but the transaction costs.  How would the story change economically if the seller had rolled up everything into the t-shirt cost, making all the so-called transaction costs seemingly 'free'.  Well, not much.  The members' clubs would probably not be so exclusive.  There would be a lot more phony trips.  But a simple 'show me the money' rule could cut most of that out.

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.