Broken Symmetry

The Coase Theorem as the Harmonic Approximation for the Macroeconomy

In the last post, I showed how a market could be approximated as a simple harmonic oscillation in number of transactions per unit time (and price per unit time).

In the second to last post, I elaborated on how coupling between these markets could be analyzed with Feynman-style diagrams.

It's worth mentioning something else that just falls out of this analysis, which is very interesting.  Coupled simple harmonic oscillators are used by physicists to describe crystals in the so-called "harmonic approximation."  In this model, the lack of dissipative forces and the corresponding coupling dynamics lead to the result that energy, when added to any part of the system at a moment in time, will eventually be evenly distributed througout the system.

Not coincidentally, there is already a theorem in economics that describes the same effect in markets: the Coase Theorem.  If markets are modeled as simple harmonic oscillators with no dissipative forces of transactions costs interfering with their dynamics of oscillation or coupling, then regardless of where energy (see the last post for how "energy" shows up in markets) is added to the crystal, it will eventually be spread out evenly throughout the entire macroeconomy.

The Coase Theorem is the harmonic approximation applied to the dynamics of the crystal that is the macroeconomy.

The Hamiltonian for Markets in the Absence of Transactions Costs

We already know that supply and demand can be derived from underlying periodic patterns of consumption and production measured for a given population within a given window of time.

From the existence of these frequency distributions, we can infer that there must be some Hamiltonian that applies to the dynamics, a Hamiltonian that will end up producing the equations of motion.

In the absence of the dissipative force of transactions costs, it's not hard to guess what form the Hamiltonian will take: the Hamiltonian will assume the form of a simple harmonic oscillation in price per transaction.

Let q be defined as the discrete time-varying quantity that represents the number of transactions that must occur within a market within a particular window in time. q can be measured from the frequency distributions that characterize patterns of consumption and demand for various populations within different windows in time.

Then dq/dt is the derivative that represents how the number of transactions changes in time.

Let c be defined as a fixed quantity that equals the spread between the quantity of goods available for sale and the quantity of goods demanded at each moment in time.

Then let price p be estimated as proportional to the spread c between the quantity of supply and the quantity of demand at a moment in time, i.e.:

p = q / c

Then because we know that the total number of transactions that will occur within the market within the time window from which q was measured is a conserved quantity, the current (or time-varying volume of transactions per unit time) is:

i = -dq/dt

Let L be defined as a fixed quantity that represents measured liquidity, or the amount of time it takes to complete a transaction at a given price level within a unit of time.

In the absence of transactions costs, the market "energy" (a/k/a intrinsic value) can be represented by the following Hamiltonian:

H = L/2(dq/dt)^2 + q^2/2c

Physicists will recognize this as the Hamiltonian for a simple harmonic oscillator.  I have deliberately chosen the notation to match the notation familiar to electrical engineers who study LC circuits.

In reality, neither c nor L may be entirely independent of q or its time derivatives. This will introduce nonlinearities into the dynamics that make things difficult.  Nonetheless, good estimates of L and c can be used to predict bubbles.

Feynman-style Diagrams for Illustrating Cross-Elasticity of Supply and Demand

I'm still playing with different dynamic models that could be used to build up the observable frequency distributions of consumption and production (from which I have already shown the supply and demand curves of introductory economics can be derived).

But it is obvious already that whatever dynamic model is adopted will apply only to price in a discrete market.  In practice, however, no market is completely isolated from all others.  The traditional method for analyzing the relationship between the supply and demand for two different types of goods or services is to measure the cross-elasticity of demand.

Here's another far out idea, which is going to take months to develop: there are probably Feynman-style diagrams that could be used to demonstrate the coupling between supply and demand cycles that are observable now as cross-elasticities in supply and demand.

Basically, we could treat price of good A as an electron and price of good B as an electron, with the value of the underlying supply of these goods being equivalent to the electromagnetic field in which both are bathed.  Thus, cross-elasticity of demand or supply is simply an interaction between two different particles, which is mediated by the electromagnetic field of intrinsic value.

I've already noted in earlier posts how, once such formalism has been developed, the phenomenon of spontaneous symmetry breaking could be used to model Schumpeterian waves of creative destruction.

On Why Improving Dynamic Economic Theory is Important: Schumpeter v. Arrow

Lately I've been exploring dynamic economic theory on this blog, and I'm spending more time than I originally intended fleshing out a dynamic model for market prices.  I wanted to take a brief moment to explain to the readers of this blog why I'm doing that, since it probably won't be obvious for everyone.

As far as most economists are concerned, state of the art mental models for dynamic economic theory revolve around two positions most famously articulated by economists Josef Schumpeter and Kenneth Arrow.  Schumpeter emphasized how innovation required temporary monopolies.  Arrow emphasized how monopolies were counterproductive to innovation because monopolists had costs associated with both their existing market and any new market that emerged through innovation.

A few scholars have already figured out that there was really no argument between Schumpeter and Arrow.  In fact, they were looking at the same economy of innovation, but within different windows of time.  In particular, Schumpeter had in mind R&D and early-stage commercialization.  As Arrow knew when he wrote about what would later be called "the Arrow effect," neither R&D nor early-stage commercialization are likely to take root or grow within the environment of a large-scale corporation focussed on manufacturing, marketing, and distributing consumer products.  Schumpeter, for his part, would have agreed that we don't want large-scale corporations to have monopolies that permit them to ignore innovations that consumers want.

The simple fact is that Arrow and Schumpeter probably don't have as much of a disagreement as some lawyers and economists seem to think.  In fact, both would probably have agreed that were it possible, it would be in the best interests of both inventors and entrepreneurs to have a division of labor between inventing and entrepreneurship, with separate sources of financing and services.  Inventors need entrepreneurs to take their ideas to consumers.  Entrepreneurs need inventors to inspire them with big new ideas, the kind that lead to the waves of creative destruction that Schumpeter described and that we have lived through in the last few decades.

Which brings me back to my explanation for why I've been thinking and writing about dynamic economic theory.  My belief is that most arguments over these issues would be resolved if economists had better mental models for understanding the life cycle of technology markets.  I'm trying in a humble way to chip away at the problem by proposing some fundamental new ways of thinking about supply, demand, and market price.  My hope is that these new mental models will put us back on the right footing for tackling the most complex issues we face in setting policy and designing institutions, both public and private, that will promote innovation and growth.

A Simple Proof that Innovation Requires Inventors

Over at the blog for Techdirt (an unfortunate misnomer), my evil-initial-twin Mike Masnick has in a series of posts been arguing, in summary, that ideas are cheap and that execution is what matters for innovation.

To Mr. Masnick (and whomever agrees with him) I present the following proof that his argument is incorrect:

If it is true that execution is what matters to innovation, then it should be possible, in principle, to build a Turing machine capable of innovation.  No such Turing machine exists.  Therefore, an inventor is required for innovation.

Incidentally, this proof also explains why Malcolm Gladwell is mistaken to distinguish between inventing and artistry on the grounds that inventions may be reproduced independently whereas artistry is unique.  He observes, inter alia, that the claims of multiple patent applications have often overlapped. This is true.  But the specification and drawings of a patent merely describe in words and with pictures the work of each inventor, which remains unique.

Certain readers may recognize in this proof the general strategy followed by Goedel in proving his incompleteness theorem.

The Fundamental Hypothesis of Periodicity

I've posted an excerpt of a longer paper that I'm working on to SSRN here.

But you can also download it right here.  Download Periodicity.pdf

In a nutshell, I argue that a new fundamental hypothesis should be added to economics, the fundamental hypothesis of periodicity.  I show how the supply and demand curves from introductory economics are cumulative distribution functions that may be derived from the more fundamental frequency distributions that characterize patterns of consumption and production for a population of people, within a window of time.

The longer paper that I'm still working on starts with this hypothesis, and then develops a time-domain model for market prices that can reproduce the frequency distributions (and hence supply and demand curves).

Update: In the draft posted, I refer to the distributions as gaussian.  They are only gaussian by crude approximation.  They are better approximated as poisson distributions.

How to Improve Accounting and Financial Statements

The last three posts give an insight into how accounting and financial statements could be made more accurate and useful in assessing the health of a firm: both time and frequency should be measured to capture the dynamics of people.

Consider the status quo:

• Income statements are the time-integrated stream of earnings and expenses, adjusted with non-cash items to reflect earnings or expenses that will occur later in time.
• Balance sheets are a snapshot of assets, liabilities, and equity and a moment in time.  The assets and liabilities are often organized by liquidity, which serves only as an extremely crude measure of frequency of turnover.
• Cash-flow statements are really a revision of the income statement that makes clear more information about exactly how much cash was generated and spent.

Except by taking several financial statements -- i.e., either a series of quarterly or annual financial statements -- and comparing them, there is no way to reconstruct from the bare financial statements the frequency of supply and demand for the firm.

For example, it is impossible to know from the currently standard financial statements how often inventory turns over, how often cash turns over, how often, investments turn over, how often employees turn over, &c.  Yet this information is every bit as relevant as how much the earnings or expenses that resulted.

With a more accurate economic picture of how value is created within a firm and market in mind, it's easy to see that requiring a separate statement of the average frequency of financially important events would be very useful in understanding the current health of the firm.

By the way, although changing financial accounting standards is hard, changing the way internal accounting is done is easy.  Given the fact that most accounting is already done by a computer, only a very simple, crude algorithm is needed to process the journal entries in order to produce a separate set of numbers that show the frequency distribution of various events.  I know that Quickbooks already has such a feature for showing the aging of accounts receivable.  The same feature could be slightly modified to reflect the frequency distribution of a host of other events.

Let me put it a different way: if the Bear Sterns CEO had known exactly how much the frequency in client-turnover had increased over the few months leading up to March, would he still have been reassuring everyone that the market's falling confidence in Bear Sterns was "a whole lot of noise"?

Endogenous Growth results from Divisions of Labor and Learning in Supply Cycles

Now that I've shown the connection between frequency and phase distributions for supply and demand cycles and the supply and demand curves from Econ 101, I would like to revisit a point made a few days ago in a post in which I explored how supply and demand cycles would look in a two-person economy.

Specifically, the observation was that dividing a complex task (such as meal preparation) into a sequence of simpler tasks that could be synchronized would have a multiplying effect on the aggregate supply available within a window of time.  With the connection between aggregate supply and supply frequency and phase now clear, we can see this more easily.

Part of the increase in aggregate supply results from the increase in frequency made possible by synchronizing and amplifying supply cycles.  Specifically, if the cook doesn't have to wait around for the ingredients before cooking, and the speed of cooking or gathering ingredients doesn't slow down too fast with the quantity of meals cooked or gathered for, then the frequency of the supply cycle will increase, and along with it aggregate supply within a window of time.

Part of the increase in aggregate supply, however, results from learning that occurs after the cook and gatherer have specialized in cooking and gathering, respectively.  Specifically, all else being equal, the longer the cook cooks and the gatherer gathers, the higher the quality of the supply.  This is a natural results so long as quality is part of the supply signal that couples with demand.

In a future post, I will explain how information asymmetries at the point of coupling between supply and demand can result in systematic (and potentially catastrophic) deviations between price and what the load that the supply or demand cycles can realistically bear over a period of time.  The lack of negative feedback to subprime mortgage buyers can be viewed as one example of the larger problem with deviations between price and sustainable load.

How Dynamic Prices Result from the Frequency and Phase Distributions of Supply and Demand

As explained in my last post, the demand curve familiar from Econ 101 can be derived from a frequency distribution of how often people want a particular good or service.  Specifically, the demand curve can be derived by looking within a particular window of time, counting the number of people who want the good or service with a given frequency within that period, and then binning those counts from minimum to maximum frequency.

The supply curve from Econ 101 can be derived in a similar manner from the frequency distribution that is characteristic of production for a given good or service.  Supply, like demand, has a characteristic frequency associated with its production.

Going back to the example of meals, assuming certain raw inputs are available* meals can be prepared with a distribution of frequencies.  The fastest chef in the world might prepare a meal within 15 minutes.  The slowest in 3 hours.  In any case, like the frequency distribution for demand, there will be a frequency distribution for supply.  That distribution will have a mean and will be roughly normally distributed.

And again if we recount the frequency distribution by binning the number of chefs that can cook no more than one meal per day into bin one, no more than two meals per day into bin two, no more than three meals per day into bin three, and so on -- if we recount the distribution this way we end up with the familiar supply curve from Econ 101.

The last logical step needed to connect supply and demand cycles to market price is the connection between the number of people in each bin and price.  The relative scarcity of goods or services provides this connection.  In other words, assuming the opportunity costs of the goods or services is fixed, then there is a connection between the number of people in each bin and price.  The connection arises from two rather abstract, but undeniable observations: the larger the total number of people that want something, the more other things each of those people must be willing to give up in order to get that something.  Similarly, the larger the total number of people that are willing to provide something, the more that each of those providers must be willing to forego doing in order to provide that something.

With that connection between number of people in the bins and price complete, the mathematical relationship between frequency distributions for supply and demand and the supply and demand curves from Econ 101 is complete.  Having shown the connection, it should be obvious to any economist that there is a whole research program that could be pursued of analyzing supply and demand distributions rather than supply and demand curves.

At this point, some readers may we wondering why, if supply and demand are cyclical, do we not observe price cycles more often?  The answer lies in a characteristic of cycles that has not been discussed before in this or the previous post.  That is the characteristic of phase, or the relative position of peaks in the supply and demand cycles.  When the phase of the cycles is randomly distributed in time -- as they probably are most often -- then the cycles will tend to cancel one-another out to zero.  Although the cycles are always fluctuating in the background, when they're aggregating over a period of time and across many people, they will tend to result in a steady price.

The exception is for when the supply or demand cycles that are usually randomly distributed in phase refract off of something that tends to selectively cancel out only cycles with certain phases.  This would cause the aggregated demand or supply cycles to bubble up to much higher prices.

Relatedly, if the supply or demand cycles were not wholly independent, such that an earlier demand cycle fed some of its price into a later demand cycle, or an earlier supply cycle into a later supply cycle, then the price of supply or demand would tend to increase.  This would result when the cycles were not superposing linearly, but were aggregating nonlinearly due to some external perturbation.  A change in the money supply or a change in liquidity could have such an effect.

Business cycles (such as the bubbles observed in technology and real estate) could thus be predicted from changes in the phase and frequency distribution of supply and demand.

In future posts, I'll elaborate on how supply and demand might not aggregate linearly or have randomly distributed phases.

* We have to make this approximation for the same reason we have to assume a steady-state equilibrium for the Econ 101 supply and demand curves to make sense.  In mathematical terms, time and frequency are Fourier pairs.  To get a perfectly accurate static picture, you have to give up on measuring time with arbitrary precision.  To get an accurate dynamic picture, you have to give up on measuring frequency with arbitrary precision.  In effect, economists have been doing the former forever.  I'm the first I know of to propose doing the latter.

The Shape of the Demand Curve follows from the Natural Rhythms of Life

The shape of the familiar demand curve is a mathematical consequence of the natural rhythms of life. 

Over time, everyone consumes goods or services with some characteristic frequency.  For example, on average we eat three meals a day.  But some people (fashion models) eat only one.  Others (body builders) eat six.

Thus, the frequency of meals eaten by everyone in a market for meals can be represented as a distribution.  The distribution will be a roughly bell-shaped, normal distribution.  We call such distributions "normal" because they occur so often when lots of independent variables are at work in determining the shape.

But what will the shape of a plot of the distribution take?  That depends on how I decide to count people. 

First, imagine that I count according to the frequency of meals eaten.  Specifically, I could count up the number of people in a market that eat one meal per day, and put them in bin number one, the number of people who eat two meals per day, and put them the next bin, the number of people that eat three meals per day, and put them in the third bin, and so on.  Eventually I could build up a curve, the y-axis of which reflects the number of people with a given frequency of eating, the x-axis of which reflects the frequency of eating.  As suggested above, this curve would probably have the familiar bell-shape if it were a large enough population.

Second, imagine that I don't care how often people are eating, but instead want to know how many meals are being eaten by the population of the course of a day.  In that case, I would bin people differently.  I would count everybody who wants at least one meal per day in the first bin, everybody who wants at least two meals per day (or less) in the second bin, everybody who wants three meals per day (or less) in the third bin, and so on.  I'd actually be recounting some of the same people when I counted this way.  But now the x-axis shows the number of meals likely to be demanded within a day, and the y-axis the number of people corresponding to that demand.

And notice that the shape of this second curve is downward sloping, and will tend to accelerate downward as the number of meals increases -- the difference between the number of people who eat six meals per day and the number of people who eat three meals per day is larger than the difference between the number of people who eat nine meals per day and the number of people who eat six meals per day.

If you don't recognize it by now, this second curve is simply the familiar demand curve from Econ 101.

The demand curve is the mathematical result of selectively recounting the frequency distribution of meals eaten over a specified period of time.

Germany Leads the Way

Today on the IAM blog, Broken Symmetry's favorite IP investment management journalist Joff Wild blogs about new IP-focussed investment funds in Germany.

IP Bewertungs AG (a/k/a IPB) stands out from the pack.  According to an executive at IPB, IPB doesn't merely aggregate patent rights.  IPB is actually spending time and money after acquiring IP rights on pre-commercialization development.

Without hearing more, it's difficult to know exactly what kind of development they're doing.  But it's easy enough to imagine that they've got a team of scientists or engineers assigned to each portfolio of IP that they've acquired, working to further refine the inventions patented into product or service concepts that are more susceptible to early-stage commercial development.  Without the know-how of these scientists and engineers mixed in, naked IP is far less valuable to prospective transferees.

Coupled with the earlier article on IPB published by IAM magazine, which laid out some facts about the comprehensive diligence process that IPB goes through prior to acquiring a patent portfolio, IPB is beginning to emerge as a thought leader in this market.

Antitrust and IP: Revisiting Microsoft Antitrust Liability

I just found a link to this editorial from Charlie Munger on the Reflections on Value Investing blog.

Charlie argues that corporations with market share should not be held liable under antitrust law for adding improvements to products or services that were pioneered by smaller competitors.

He's partly right, but he leaves something out.  Microsoft had already spent billions and billions of dollars setting up manufacturing, marketing, and distribution channels.  How could it benefit consumers to demand that a new firm rebuild the same infrastructure whenever an improvement to the existing product or service was demonstrated to be valuable to consumers?

Except for the IP.  The small competitor that comes along has done something important and valuable for consumers by inventing and demonstrating the commercial viability of the improvement.  Without these Schumpeterian upstarts snapping at its heels, Microsoft would have little incentive to make such improvements.

So he's right that antitrust liability doesn't make sense.  But he's silent on the corollary, which is that IP infringement liability probably does make sense.  There's no way to ensure that these Schumpeterian upstarts have incentive to keep snapping at Microsoft's heels without strong IP.

Vacant Lots, Four-Legged Tables, and Patent Trolls

Today I visited Telegraph Avenue in Berkeley for the first time in about a year.  Although I've been there several times over the past few years, for some reason today I started noticing some of the changes that have taken place on Telegraph Avenue since I use to hang out there in high school in the mid-1990s.

Cody's is closed.  The Internet, most likely.  Rasputin and Amoeba are still alive, but not looking quite as healthy somehow.  There are still plenty of street vendors.  But one was setup in front of an Adidas store, with its front window covered with photographs of graffiti-covered walls (and Adidas wearing youth).  I don't really believe that whatever used to be there offered superior culture.  Yet I still missed it.  On the plus side, the staff at Shakespeare & Co. is as surly as ever.

What caught my eye also was a vacant lot.  That vacant lot, at the corner where Amoeba is located, has been there for at least fifteen years.  It clearly could be put to better use.  There's a high fence up around it, which I think conveys something of the owners' attitude toward the people who have probably suggested selling.

I started thinking about how that vacant lot is evidence of how strong private property rights are in the United States.  Even on Telegraph Avenue -- which at least used to be a bastion of Marxist ideology -- the owner of that vacant lot could not be compelled to sell to a developer.

We can say that that's inefficient.  And it is.*  But inefficiencies of this sort should be tolerated if we are to avoid the low-probability catastrophes, the perfect storms of public opinion that blow down the houses that we build for ourselves and our families.

In a way, those vacant lots are like the fourth leg on a table.  If you design a table with only three legs, the table won't wobble.  But it will topple more often.

Patents are never far from my mind.  So naturally, I wondered what any of this might mean for patent reform.  I think the analogies make the prescription quite plain.  I think we may need to learn how to tolerate a few trolls and holdups in order to ensure that inventors get a fair shake in bargaining with transferees.

*Here's a whole 'nuther argument: I distinguish sharply between the vacant lot and the historic preservation scenario that has unfolded at a new development down in Cupertino.  There the local historic preservation society managed to prevent a building that had been the home of a nursery for decades from being torn down for a new shopping center.  The fools who sit on that board have shown themselves incapable of distinguishing a physical place from the memories of the people who made it special.  How do you deal with well-coordinated minorities that have a loud voice in politics?

Reconstructing Dynamic Price from the Rhythms of Life: the Phase Problem and How to Solve It

Fourier taught us how to understand the mathematical relationship between time and frequency.  When we know how a function changes in time, we can calculate what frequencies are carried within the function, and vice versa.  There are limits, as I shall explain below.  But the "Fourier transform" is an incredibly powerful mathematical tool when dealing with dynamic systems.

For example, if I know the distribution of frequencies that characterize a particular human activity, such as eating, I may be able to reproduce the function of meals consumed over time by performing an inverse Fourier transform.

The catch is that I need to know more than simply frequency to reconstruct the time varying function.  If I know only that a person eats three meals a day, I know that the time domain structure will include three peaks -- one for each meal.  But I do NOT know when those peaks will be distributed throughout the day.  This is "the problem of phase" -- phase being the measure of relative position of peaks.

Fortunately, economists are not the first to have to deal with this problem.  It turns out that the same mathematics apply to the conversion of x-ray diffraction patterns back into three-dimensional crystal structures.  And the physicists, chemists, and biologists who determine molecular structures using x-ray diffraction have devised a number of strategies for solving the phase problem.

First, we can tell from the inverse Fourier transforms the relative position of the various peaks.  If the frequency is small enough -- i.e., if there are only a small number of peaks, we may be able to deduce fairly easily where each peak occurs with respect to one another.  That helps.

Second, we have the ability to test our hypothesis about time-domain structure by observing how the frequency domain changes with known variations in diet.  So if we know that a certain group of people are fasting, and we can measure their frequency-domain behavior, then we may be able to more easily reconstruct the time-domain for other frequency-domain measurements.

Finally, and related to the second point, we can look at the frequency of eating meals in markets in which meals were more scarce and less scarce, and by comparison make some guesses about what the time-domain structure of meals looks like.

In any case, economists have an advantage over physicists in deducing time-domain structure in that the behavior of their "molecules" can be observed directly.  I can simply go out and watch lots of people and record when they eat.

Dynamic Price in a Two-Person Economy

Economic analysis has been hobbled by its ignorance of a simple fact of nature: change.  Time is missing from the mental models that most economists use to study most economic problems.  To remedy this problem, some part of economic analysis will have to be rebuilt from scratch.

If we started from scratch, what would be the most sensible atomistic unit to choose for our analysis of markets and firms?  I suggest that it should be individual people.  Others will object that people are difficult to model with numbers.  This is true.  The success of economics as a theory can largely be attributed to the success of the fundamental rational hypothesis as a description of the behavior of aggregated groups of people over long periods of time.  What other hypotheses could be as fundamental?  Here I propose one:

The needs of a person change in time according to rhythms that, in the aggregate, and over long periods of time, have a characteristic frequency.

Examples will help illustrate my point.  Although not all of these rhythms will have a Gaussian distribution in frequency, there will nonetheless be a mean time that people need to sleep every day, a mean amount of time people may go without eating, a mean amount of time people may go without drinking, a mean amount of time people may walk without resting, a mean amount of time that people may live without dying.

When we talk about the market for a good or service in economics, we're talking about the aggregate supply and demand for that good or service across an economy of people.  Yet the supply and demand curves taught in introductory economics are static.  It is true that good economists have the ability to understand how supply and demand curves change in time in response to changes in supply and demand for other goods and services.  But the simple model of supply and demand taught in introductory economics does not include time as a variable.  What I have been arguing in the past few weeks is for an alternative means for modeling market prices that takes into account the rhythms of people in supplying and demanding goods and services.

Let's take as an example one of the very simplest models possible for a market -- two people in a market for food during the waking hours of one day.  We need at least two for there to be a market.  We can ignore for now the fact that our two people will sleep before and after.

Each of these people needs to eat about three meals per day.  So the demand cycle for each person has amplitude = one meal, and frequency = 3 per day.  As an aside, the demand cycle is not sinusoidal.  It probably looks more like an exponential growth from zero followed by a precipitous drop back to zero shortly after each meal.  A transaction needs to take place for the drop back to zero to occur (i.e., a meal needs to be eaten).  If not, the demand cycle will continue to increase exponentially until the person starves to death, at which point it will again drop back to zero regardless of whether any transaction takes place.

The supply cycle for food has a different amplitude and frequency.  Gathering raw ingredients might take each person an hour per meal.  Cooking raw ingredients into a meal might also take about an hour for each person.  Thus, the amplitude and frequency of the supply cycle for each person working alone is amplitude = one meal and frequency = 6 per day -- i.e., (12 hours awake/day) / (1 hour gathering + 1 hour cooking).

Consider now what happens when we put the two people together:  Both have a demand cycle of 3 meals / day.  Both have the ability working alone to supply up to 6 meals / day.  But so long as the quantity cooked or gathered doesn't much affect the frequency of the supply cycle for the respective activity (a crucial assumption), it makes sense for one person to do the cooking while the other does the gathering.

First, by phase shifting the two supply cycles and increasing their respective amplitudes -- i.e., by timing the gathering of twice as many raw ingredients to be finished just before the cooking of two meals begins -- the two people can synchronize their supply activities such that each spends at most six hours meeting the total demand for both (of 6 meals per day).  More likely, each spends far less than six hours because it doesn't take twice as much time to gather or cook for two meals when you're already gathering or cooking for one.  In fact, it's not at all unreasonable to guess that gathering for two meals would take only 50% longer than gathering for one and that cooking two meals might take approximately the same amount of time as cooking one.  So the amplitude and frequency after a division of labor might be one meal / 45 minutes (gathering) and one meal / 30 minutes (cooking) for an aggregate one meal per 1 hour 15 minutes -- 45 minutes faster than would be possible for each working alone.

This explains how divisions of labor work.  When supply activities are synchronized into an assembly line, divisions of labor multiply the rate of supply while decreasing the total required labor.  So long as the amplitude for each supply cycle can be increased faster than frequency decreases and successive supply cycles can be kept synchronized, divisions of labor multiply the rate of supply.  Without a division of labor, added units of labor lead only to proportional additions to supply.

Second, over longer periods of time, by specializing in either gathering or cooking, we can reasonably expect that the frequency of the supply cycle may be still further shortened.  Instead of the gatherer taking an hour and a half to gather two meals and the cook an hour to cook two meals, the gatherer might learn how to gather for two meals in an hour, and the cook to cook two meals in 45 minutes.  This observation helps in understanding the relationship between divisions of labor, learning, and endogenous growth.

Within this simple model of supply and demand, "market price" is a function of the supply and demand of each person at a moment in time (the time of the transaction), and is measured in the same units of meals per day.  The demand cycle requires 3 meals per day per person.  The supply cycle permits at least 6 meals per day per person (as explained above supply cycle frequency may be increased by divisions of labor and learning).  What shape should the function of market price take?

First, supply must exceed demand and demand must be above some threshold level before a transaction takes place.  If there isn't any meal to eat or nobody is hungry, then no transaction can take place even if someone is hungry.  Thus, if we want market price to be a positive number, then it should be a function of supply minus demand.  In addition, supply should reflect the cumulative supply that hasn't been consumed in earlier transactions.  I'll ignore the possibility of spoilage since we're looking only within a one-day time window.

A corollary to this first point is that price will be undefined in an economy in which each person gathers and cooks for herself.  No transactions take place so long as each human can rely upon herself to synchronize and meet her own supply and demand.  No market will develop until there is a division of labor.

Second, the phase and frequency of supply and demand -- i.e., the relative position of peaks and relative frequency of cycles -- will affect market price.  For example, because meals can be prepared before eating and at a rate faster than demand for them increases, the supply cycle doesn't need to be running continuously to meet the demand cycle.  If the supply cycle runs twice as fast as the demand cycle, the supply cycle can be idle for at least 50% of the time and both humans will still get enough meals.  But the supply cycle does need to lead the demand cycle on average in order to ensure that meals are ready when people get hungry.

Third, averaged over long periods of time, voluntary transactions will tend to occur at a price that both humans agree fairly represents the respective contributions made to the supply cycle.  For example, all else being equal, if I've spent two hours gathering and you've spent one hour cooking the same two meals, I might reasonably expect you to give me more than one of the meals you've cooked.  I can't expect to get two.  You wouldn't agree to that because then you'd go hungry.  But over time, surplus or leftovers will be transferred to the person who is mutually perceived to add more value to the supply cycle.  And the supply cycle will naturally tend to that amplitude and frequency that matches output to the mutual perceptions of value.

This explains the principal of diminishing marginal utility.  Given a demand cycle, the closer that each person gets to matching their share of aggregate supply to personal demand, the less incentive each actor has to continue learning and increasing the amplitude and frequency of the supply cycle.

The model also explains market failures.  If I ask too much, you may tell me to cook for myself.  At worst if you don't already have the raw ingredients, you go hungry for a few hours while you go out and gather for yourself.  Although I won't have to gather again until tomorrow, I still have to spend two hours cooking.  By tomorrow, I may miss your cooking and lower my asking price.  If not, we'll be back where we started, with no division of labor, spending twice as much time scrambling around and cooking as we would otherwise need to.

Last, notice that although the relative amount of time spent on supply is a good starting point for estimating value of each person's contribution, the market price might also reflect a variety of other things, such as the quality of the ingredients gathered, the timing in which they were supplied to the cook, along with past track record of and future expectations for similar transactions.  Even in a two-person economy, price is a complex, multivariable function, which is nonlinear in time.

Let D1 and D2 represent the demand functions for person 1 and person 2.  Both are a function of time with amplitude 1 meal and frequency 3 / day.  Let Di represent either D1 or D2.

Let S1 and S2 represent the individual supply functions for person 1 and person 2.  Working alone, these functions have amplitude 1 meal and frequency 6 / day.  Working together, the functions will shift so that S1 (gathering) leads S2 (cooking).  Frequency and amplitude will increase by the division of labor, and (over many days) learning.

Let t* equal the moment in time when a transaction occurs.

Let Sum(S1)dt and Sum(S2)dt equal the integrated sum of S1 or S2 individually over the period of the single demand cycle immediately preceding t*.

Let Sum(S1 + S2)dt equal the integrated sum of S1 plus S2 over the period of the single demand cycle immediately preceding t*.

Given that Di(t*) > 1 meal and S12 - Di > 0 (see the first point above):

Let P1 and P2 represent the price paid by person 1 or person 2, respectively.

On average,

P1(D1,S1, S2, t*) = Sum[(S1/S2)*(S1+S2)]dt/(period of single D1 demand cycle) - D1(t*)

and

P2(D2, S1, S2, t*) = Sum[(S2/S1)*(S1+S2)]dt/(period of single D2 demand cycle) - D2(t*)

As a result,

P1 = P2 when D1(t*)=D2(t*) and Sum(S1/S2) = Sum(S2/S1) = 0.5

More later.

A Dynamic Model for Market Cycles

I have posted a draft paper elaborating on the model of market prices as the result of coupled, damped, driven oscillations in supply and demand.

Send me your negative feedback.  (No pun intended!)

Update: I've pulled the paper to revise and elaborate.

Schumpeterian Competition

Two weeks ago I read about University of Chicago professor Lee Fennell's work on rebundling real property, and noticed that her theory sort of implies a cycle in the housing market.  This is obviously true post-subprime bubble.  But what has slowly dawned on me since then is that economists do not yet have any simple models to describe bubbles.  Reading in the Wall Street Journal about Bernanke's team, I went to their Princeton home pages and discovered that at least some of the models used in their papers require a theory of psychology.  Psychology is of course important for investors and regulators to understand; but I believe that a theory of psychology is not required for modeling market cycles.

Fluctuations in the market price for a particular good or service can be modeled in time as a relatively simple function of scarcity in an older good and its newer substitute.  (Think of how IBM PCs were replaced by Macs in the 1980s.)  The simplest mathematical model to associate with Schumpeterian creative destruction of price as a function of time and demand for the older good is the simple harmonic oscillator.

The most useful observation about market cycles that can be drawn from Schumpeter's work is that creative destruction will reverse increases in price over time -- even as supply remains steady or decreases.  When a new substitute for an existing good becomes available, the price of the old substitute will decay over time as consumers switch from old to new.  The result is growth, then decay in price, even as supply remains stable. 

To add some phenomenological richness to the simple oscillator model, one can model in variables for transactions costs, liquidity, and external money supply.  These additional variables change the simple harmonic oscillation predicted by Schumpeter into a damped, driven harmonic oscillation.  RLC circuits and tuning forks are other systems that can be modeled as damped, driven harmonic oscillators.  In my analogy to the RLC circuit, price is a voltage signal that varies in time, which is in turn a function of the aggregate demand for the older good.

A time varying price signal will behave considerably differently after taking the effects of liquidity, external money supply, and transactions costs into account.  For example, when demand (and hence price) swing rapidly, a resonance response (i.e., bubble) may occur when transactions costs are not too large and liquidity and external money are not too small.  These were the conditions that obtained in the subprime mortgage market recently.  A corollary is that the period of the cycle could have been estimated by looking only at the magnitude of liquidity and external money supply (this is the "resonant frequency" for the bubble).  Another corollary is that the "quality factor," which is equivalent to the liquidity divided by the transactions costs, tells us how big a bubble effect we might see.  And indeed the subprime market could fairly be characterized as having very strong liquidity and very low transactions costs as it approached its peak.  (We sort of blew the circuit at that point.)

Yet another useful observation that can be drawn from the model is that bundling supply without including a proportional bundling of demand or other negative price effect will lead to an unsustainable exponential growth in price.  Actually, there are many such lessons that could be drawn from Control Theory, which physicists now routinely use to design and monitor dynamic equilibriums in other systems.

Finally, I note that no physicist would attempt to design or monitor such a system without first getting comfortable with the accuracy of her tools of measurement.  In the case of markets, our tools are not working too well for the moment because the accounting rules do not make any sense in view of the actual relationship between price and value, which is a function (ultimately) of the value that everybody in a market places on a particular good, not simply the value placed on a good by the two parties to a transaction at a moment in time (which is what most people think of when we talk about "price").  Increasing transparency into what company managers see is useful and important in preventing fraud on shareholders.  But adopting rules that are consistent with reality in terms of how economic growth and decay occurs is equally important.

It's also worth mentioning that in some sense, all of these price cycles are coupled, either weakly or strongly.  Hence the entire economy could be modeled as a chain of coupled damped, driven oscillators.  This is actually a theoretical model from which quantum field theory and non-equilibrium statistical mechanics depart.  Among other useful results, these theories have permitted physicists and chemists insights into how and when to expect phase transitions in what would otherwise be considered unstable thermodynamic states.  This in turn suggests another insight into the problems economists and accountants have been having dealing with bubbles.  Like the static models of supply and demand, thermodynamics is successful in making forward-looking predictions about how a physical system will behave in response to changes in temperature, volume, and pressure.  But it still took a mathematical model of molecular dynamics to understand exactly how and when transitions would occur: thermodynamics, like static economics, provides little insight into how long unstable equilibriums will persist.

Conflict and Cooperation: Another Thing the Founding Fathers Knew that We've Forgotten

Culture and law intersect at the personal level. Everybody lives in the two worlds simultaneously. But lawyers often behave as if there is no world but law.

This was not a mistake made by the Founding Fathers of this nation. To be fair to us today, except for one day in September of 2001, we have not had much visceral experience with how legal and cultural conflicts may result in violence. But the Founding Fathers lived much of their lives in such conflict. And their fathers had lived much of their lives in conflict (that between church and state).

And how did the Founding Fathers choose to act when faced with the question of how man should be governed? I submit that their answer was to build a government that requires people to cooperate. Our systems of checks and balances are so valuable not for their salutary effect on law, but for their salutary effect on culture. To give but one example, freedom of speech has not helped us by permitting a man to say what he likes; rather, it has helped by forcing a man to listen to what he hates.

It is the cultural norm of cooperation that forms our constitution, both literally and figuratively. It is the cultural norm of cooperation that has permitted the United States to grow and prosper to a scale beyond all nations in the history of mankind. It is the cultural norm of cooperation that is most threatened at times when we choose sides, commit ourselves to theories, and refuse to listen and see facts that might lead us to change our theories, and later our actions.

Among many others in this once great nation, the culture of patent law has devolved into a norm of conflict because of a great misunderstanding about what intellectual property is. In the spirit of cooperation that helped forge our constitution, let us learn to cooperate in promoting the progress of science and the useful arts by granting to authors and inventors fair value for their work. There has never been a time in our history in which the fate of patent law has been more in question.

Update: See this latest example of communication breakdown in action.

What are the Existing Best Models for Business Cycles?

Readers:

Can anybody tell me what models academic economists right now consider the best for explaining business cycles?

Applying Control Theory to the Subprime Mortgage Supply Cycle

In an earlier post, I explained how transactions costs, liquidity, money supply, and scarcity can be modeled as the resistance, inductance, capacitance, and voltage of an RLC circuit.  When Schumpeterian creative destruction causes a demand voltage to spike, the coupled supply circuit will damp the spike at the "resonance frequency."  Oscillation will still be observed if the demand spike is large enough, but the resonance or bubble effect will decay to zero over longer time periods unless an active element is included in the supply circuit.

To show how the resonant frequency for this RLC filter can be calculated, let's apply some actual numbers to the supply cycle for subprime mortgages.

Because of MBS, CDOs, and CDO^2s, the liquidity in the subprime market was actually much larger than ever before.  How many orders of magnitude is hard to say.  I'll estimate that the rebundling and sale of mortgages increased the scale of supply by a few orders of magnitude, and also increased the number of days / sale as the bundling, rebundling, etc. takes longer to accomplish than a simple mortgage.  If it takes 100 days to do the bundling, but by doing so you get up to $10,000,000 scale, the measure of liquidity becomes:

L = (100 day / sale) / ($10,000,000 sale) = 1 x 10^(-5) days / $

Money supply (capacitance) should be measured in units of days / $ -- i.e., the number of days that each $ loaned from an external supply spends in the market before being paid back.  I'm going to estimate that about $1,000,000,000 of the entire money supply (on average) was locked up in mortgages, MBSs, CDOs, or CDO^2s.  And banks were probably holding onto these funds for about 100 days before going back to the Fed.  Of course the government kept messing with money supply by increasing and decreasing the cost of lending, but I'm ignoring that.  I'll repeat, however, that if the money supply obeyed something like Taylor's rules, we'd have a more determinate system.

C = ($1,000,000,000 * 100 days) = 1x10^11 $-days

Solving the differential equations for the frequency of the resonant peak for this cycle, we find that:

Resonant frequency = 1 / square root (L * C) = 1 / sqr ( 1x10^-5 days / $ * 1x10^11 $-days ) = 0.001 cycles / day.

In other words, according to these estimates of liquidity and money supply, we can predict a peak in the subprime mortgage market to occur about once every three years.  And that's roughly how long it seems to have taken for us to reach a peak once bundling of mortgages started.  In general, when you hit a damped harmonic oscillator (like an RLC circuit) with a signal spike, it will ring at a particular resonant frequency.  The resonant frequency is like the "sweet spot" on a baseball bat, whereby  an incoming spike at that exact frequency will be damped to zero at exactly the length of one period of oscillation.  If the demand spike has a longer or shorter frequency, then the damping will either occur in less than the period of the resonant frequency (overdamping) or the spike will continue to oscillate but at lower amplitude (underdamping).

When the liquidity and money supply effectively underdamp the incoming demand spike, the RLC supply circuit will continue to oscillate at the resonant frequency, but at successively lower amplitudes.

Beyond Econ 101: Modelling Supply and Demand Cycles as Coupled, Damped, Driven Harmonic Oscillators

The supply and demand curve (x) taught in introductory economics represents the aggregate state of the supply and demand for a particular good or service at a moment in time.

In the real world, supply and demand do not rise or fall with gentle de-accelerations or accelerations.  Rather, with demand held constant, as supply passes a certain price threshold, suppliers will stop producing the good or service, and begin producing a substitute that can be supplied at lower cost.  Similarly, with supply held constant, when demand reaches a certain floor of zero gains in value from increased quantity, demand will begin to rise in the market for a substitute as consumers begin to substitute lower cost substitutes.  Thus aggregate supply and demand will oscillate in time rather than remaining static.   Schumpeter was the first to observe  this effect when he observed how innovation in a market would lead price to decline as consumers switched from an old to a new good or service, even as supply for the old remained steady.

Schumpeter gives us a theory that explains how price will fluctuate in time.  If we next add in transactions costs (resistance), liquidity (inductance), and external money supply (capacitance) we have enough variables and enough understanding of their interaction to develop a fairly rich description of the observable behavior of price over time in various markets.

For example, supply and demand can seldom be approximated as decoupled from one another (and therefore constant with respect to one another).  The coupling of real supply and demand cycles is better approximated as two coupled, damped, driven harmonic oscillators.  The strength of the coupling will be a function of the "stray impedance" of the market, which arises from any coupling between the independent elements of the "circuits."  Usually, however, transactions costs are the mechanism for coupling.  Beyond a certain threshold, transactions costs will grow nonlinearly, and introduce the effects of non-linear coupling into the system.  When the coupling is weak, fluctuations in supply and demand will merely add or subtract linearly to produce a relatively steady price -- i.e., a steady-state market price that is observed in most markets, most of the time.

The mathematical model is simple.  Undergraduate physics majors could work out the dynamics on paper.  The static (x) model drops out by measuring each cycle within a window in time.

Here are a few predictions from the model.  When the coupling between the oscillators is weak, they'll simply superpose linearly -- i.e., one frequency will simply constructively and destructively interfere with the other.  I.e., the supply cycle will run smoothly regardless of whether demand is blowing up or stagnant; and vice-versa.  When the coupling is strong, however, non-linear effects emerge.  The frequency of the two cycles will "beat" and to produce "envelope frequency" = supply frequency + demand frequency, modulated at "beat frequency" = supply frequency - demand frequency.

How To Improve Price Signals

The intrinsic economic value of a good or service is ultimately a function of the value that everybody in society places on that good or service.  Value is a function of scarcity.

Market prices, however, are often a function of only the value estimated by the parties to a transaction at a moment in time (i.e., the value placed on the good or service by the buyer and seller at the time of transaction).

Price could be modeled as a Taylor expansion of terms, each term reflecting the addition of more people to the approximation of price.

Current market prices are linear approximations because market transactions are bilateral (i.e., two-body problems).

For price to more accurately reflect the intrinsic value of a good or service, higher-order terms must be included in the expansion (three-body, four-body, etc.)

Physicists and physical chemists who study non-equilibrium statistical mechanics know how to do these calculations with small molecules.  You need them to model phase transitions, i.e., dynamic changes in physical state (such as melting or evaporation).

Most of the time, markets behave as simiple harmonic oscillators (i.e., linearly), and the difference between price and value is small.  This is the business cycle.

Occasionally, however, the higher-order terms in the expansion can dominate, producing a stagnant or bubble market (i.e., an overdamped or underdamped harmonic oscillator).  Incidentally, a strongly positive higher-order term in the price expansion could be the mathematical equivalent to what Charlie Munger calls "febezzlement."  His example of febezzlement is the wealth effect caused by increased spending by money managers during the upswing of an economic cycle.  Febezzlement is short for "functional equivalent of bezzlement," bezzlement being the term coined by Galbraith to name the wealth effect caused by government increases in the money supply, which he noted were not unlike the wealth effects caused by ordinary embezzlement.  Wealth effects are a non-linear term in the price expansion.

Berkshire-Hathaway has produced critically damped harmonic oscillations by making a habit of giving negative feedback, thereby damping the upward effect of valuations to a level that stabilizes oscillation.

Libertarians need to understand better the relationship between market price and externalities.  Government should not be the only entity that forces buyers and sellers (through taxes) to take into account the long-term, low-probability effects that each transaction will have on non-parties.

Again, Berkshire-Hathaway has forged a new path by selling 20-year term puts on the market.  Selling insurance on long-term, low-probability events is one way to limit the need for taxation and public regulation.

The difficulty is always in finding people who can accurately calibrate the coefficients in the price expansion.

Whom does the Constitution say IP is For?

"To promote the progress of science and useful arts, by securing for limited times to authors and inventors the exclusive right to their respective writings and discoveries;"

I'll be in attendance at the Law & Econ of Innovation Conference tomorrow.  Come say hello if you're there too.

Editorial Note: Cross-Posts to Patent Prospector

Due to non-overlapping audience interest, I will no longer be consistently cross-posting patent-related posts to Patent Prospector.  For the time being at least, Broken Symmetry is the best venue for finding my commentary, including patent-related commentary.  I will continue to enjoy reading the commentary from Gary and Jordan at Patent Prospector.

I consider blogging a collaborative enterprise.  Please let me know in a comment or email if there are topics that you would like to hear more (or less) about.

Our Blind Spot for Inventors ...and How Universities Can Remove It

United States Secretary of Commerce Carlos M. Gutierrez, among other things, is in charge of the Patent and Trademark Office.  Yesterday the San Jose Mercury News published this piece by Gutierrez identifying three specific areas for Congress to focus on in considering patent reform:

• Damages Apportionment
• Post-Grant Review
• Patent Application Quality

In two previous posts, I have blogged about Damages Apportionment.  Lately, I have been working through a very good paper by J. Gregory Sidak, which gives some convincing responses to the Lemley and Shapiro arguments that damages apportionment is a necessary response to the problem of Cournot complements.  In a nutshell, asymmetric bargaining power between patent owners and groups of potential licensees may more than make up for the inefficiencies of negotiating with multiple complementary input suppliers. 

This is a complex problem, and it makes sense for us to be very careful about making changes in this area of the law.  Nobody really knows how damages apportionment will prospectively affect the value of patents.  Nonetheless it seems reasonably certain that implementation of damages apportionment would effect a net redistribution of wealth from inventors to licensees.

Post-grant review, by driving up the cost of the patenting process, is also likely to favor large applicants over small ones, especially independent inventors.

Improving patent quality is probably the only reform item proposed by Gutierrez that does not definitively cut against smaller entities and independent inventors.  This is because the quality problem in terms of raw numbers must be more the fault of large entities than small.  My personal experience suggests that startup companies put far more resources into putting together good patent applications than the larger, publicly-traded corporations that are often interested more in having a huge portfolio for defensive/cross-licensing problems with other large publicly traded corporations.

In all of these discussions of patent reform, who's looking out for the dispersed group of small entities and inventors?  Only the universities that are the home for many of these inventors have the resources to get a chair at the table in negotiating patent reform.
 

What the PTO will look like in a few years?

The NYT on Sunday carried this article on the USA National Innovation Marketplace, founded by inventor Doug Hall.

First, this is more evidence of how the shortage of patent lawyers is forcing inventors in many technical fields to find new ways to attract private funding.  I discussed other consequences of the shortage in an earlier post on Stranded R&D.

Second, I wonder: How much more effective would the National Innovation Marketplace be if we had patent lawyers draft a set of claims, and put that up with the other materials offered on the website?

Isn't that what the PTO should look like in an era in which the costs of offering multimedia and social networking services through a website have dropped so low that even teenagers can launch new companies?

UPDATE: On a conference call today (5/13/8) I hear from Patent Commissioner John Doll (a fellow former p-chem grad student!) that the PTO is working on a social network for Examiners.  Why not offer a social network for both inventors and Examiners?  Why not work with Planet Eureka, which has already built one?  The idea of software engineers hired by the PTO reinventing this particular wheel is particularly troubling to me.

Summing Up: Feathering the Nest for Inventors

Sensible patent reform should focus on feathering the nest for inventors in the United States.  There is nothing more important to our long-term prospects within the global economy.  To summarize the posts made this week:

IP is a limited exclusive right to an inventor's time, not a limited exclusive right to a thing.  I.e., IP is Not an Asset.  Lawyers, business people, and politicians should consider how the patent law will affect the activities of inventors.  A plugged R&D pipeline can lead to Stranded R&D and an exodus of inventors from the United States.  We would promote the progress of arts and sciences better by building legal and financial institutions that recognized the benefit of a division of labor between inventing ideas and building things.  This is What Adam Smith taught the Founding Fathers.

Editorial Note: Broken Symmetry and the Lollapalooza Effect

When I was in graduate school at the University of Chicago I took a graduate level physics course on non-equilibrium statistical mechanics.  I struggled in that course.  There were some kids in there that were just off the charts.  I ended up with what one might call a "gentleman's B."  But I did spend quite a bit of time thinking about and visualizing what was happening in the systems we studied in that course.  A few years later, when I started learning about the economic analysis of law, I started thinking about how, with lots of simplifying assumptions, markets could be modeled as physical systems.  And this got me to thinking about how non-equilibrium statistical mechanics might have some interesting applications to the study of economics.

Earlier this year, I started reading Charlie Munger, another ex-physicist who has spent some time thinking about markets.  I read about what he describes as the "lollapalooza effect," which sometimes occurs in markets, and realized that it was basically a description of spontaneous symmetry breaking.

To see the connection, you have to make a lot of simplifying assumptions about how people behave.  Charlie's strength as an investor is probably due to his ability to sense inarticulately when his simplifying assumptions are strong enough to be trusted and when they should be kept under watch.  But here's how one physicist has come to visualize the lollapalooza effect of broken symmetry:

People can be modeled as particles in a potential.  The contours of the potential are determined by the opportunity costs of engaging in various activities (driving, working, playing, everything).  So you have a manifold that includes a variety of local equilibria corresponding to various states of the world.  It gets messy fast determining the shape of these contours because the contours of the manifold (i.e., the opportunity costs of various activities) are themselves a function of the previous activities of the particles.

There's enough energy (capital) in the system to keep the particles bouncing around in one local equilibrium, but not enough for many (or any) of them to bounce out into a new equilibrium.  But every once in a while, there's a perturbation to the system (an exogenous shock), which drives enough of the particles into a particular direction at a high enough energy to move them into a new local equlibrium in which they have different and new local symmetries.  Local symmetry just means what you would see if you were an ant in the particle's position on the manifold.  If the particles can store information and communicate (this is where we completely lose the physicists if we haven't lost them already), they've now got a larger map of their system.

Scale invariance (a tool used by physicists to describe transitions between equilibria) occurs in political or economic revolutions when so much energy gets added to the system that local symmetries are no longer important.  The particles just bounce around so fast that they don't even notice the contours. Once things settle down, they'll tend to settle into new and different local equlibrium.  But it's often difficult to predict with certainty which local equilibria the particles will fall into. Revolutions are messy and difficult to control.  The exception might be for a catalyzed phase transition in which one particle or small group of particles act as "seed crystals," so that everybody ends up moving with them into a new local equilibrium.

Firms and even governments are spontaneously self-assembled organizations of particles that result from the symmetries of particular local equilibria given the amount of energy (capital) available to sustain the organization.  Just like water can take the form of a solid, liquid, or vapor given the amount of energy (measured as a temperature distribution) and its interactions with surrounding molecules (including other water molecules), people will self-assemble into different kinds of private and public institutions in order to minimize the amount of capital required to sustain their assembly.

Incidentally, the concept of allocative efficiency in economics (i.e., the principle of maximizing utility over the manifold for every particle) corresponds pretty closely to the extremization of hamiltonians and lagrangians in physics.  But the transactions costs of engaging in social and economic transactions between particles are dissipative forces (i.e., stickiness to the manifold) that have to be assumed away to do the calculations and find the most efficient equations of motion (i.e., institutional design).  So it's no surprise that the Coase Theorem has to assume away transactions costs in order to say that the default local equilibrium assigned by government doesn't matter.

The Most Important Role of Public and Private Regulators?

Libertarians struggle with the question of how and when any government or private regulation is proper.  In the wake of the subprime mortgage market collapse and in view of the existing problems with the patent system in the United States, I have come to a few more general conclusions.

The most useful role for regulators is to ensure that the consumers whose transactions constitute the smallest units of demand within a market are required to internalize at least part of both the positive and the negative externalities (i.e., social costs and benefits not otherwise priced into the bilateral transaction) of subsequent comparable transactions.  This will require at least the cooperation of the individual or firm that is counterparty to the smallest unit of demand.

In the housing market, a bubble developed because at each stage in the cycle from homebuyer to bank, to larger institutional investors, and back to buyer, no accounting was made for how an increase in home prices was going to increase the price and decrease the volume of transactions in other goods.  In other words, the opportunity costs of increasing prices in homes was not sufficiently internalized by homebuyers in the subprime mortgage market.  This problem could have been avoided by requiring homebuyers to buy insurance covering the risk of declines in home price due to off-site factors.  (Thanks, Lee Fennell.)

Taxes are probably the most impactful way that government regulators have ensured that the negative externalities of an individual engaging in particular activities are internalized by the same individuals in some measure.  (Thanks, Pigou.)  In the sense I'm thinking about them, taxes are like an insurance premium we pay to the government to ensure that somebody is worrying about (and will bail us out from) major catastrophes that are too large in scale or too long in time horizon for the market to accurately price into transactions with consumers.  Please note that this does not mean that I am in favor of raising taxes!  A corollary is that the role of government may be rationally more limited in places and times when private institutions are able to more accurately price low-probability and long-time horizon (i.e., major) catastrophes.  Requiring insurance and reinsurance against catastrophes is probably healthier for everyone than building labyrinthine bureaucracies (like FEMA) that aren't going to do much work on preventing disasters, and won't be much help when they inevitably occur.

Here's one piece of evidence to support this theory.  Warren Buffett and Charlie Munger have almost made a religion out of including negative feedback in every financial statement, probably even in every transaction.  The result?  Longer time horizons and more accurate pricing (through negative feedback) have permitted them to run what is perhaps the most efficient conglomerate in the history of humanity.

"How is it organized? I don’t think in history of world has anything Berkshire’s size organized in so decentralized a fashion. Net amount of bureaucracy is tiny, costs are low, autonomy in subsidiaries is vast, no common culture shuffling people around. How far can this go? This system has gone farther than any other system. Low cost, not a lot of envy effects – where everyone compares everything. People in subsidiaries have a feeling – whereby there is less fealty to headquarters. If you want an imperial headquarters which exacts a big overhead charge on the provinces – they will resent it. Net number of intra-subsidiary transfers is tiny. It has worked well. It can go a lot farther. No one else has been here before."

Berkshire-Hathaway is one of the first private regulators to make negative feedback a priority, and look at what they have accomplished.  What would the world look like if we redesigned legal and social norms to encourage negative feedback (i.e., accountability).  And Berkshire-Hathaway did it without any government telling them that they had to.  They were seed crystals in this sense.

Update: The characteristic slope of the Taylor Rule for monetary policy (which requires that the magnitude of changes in target rates always exceed the magnitude of changes measured in inflation) could be viewed as an embodiment of the negative feedback principle.  A control theorist might say that the Taylor Rule leads to more stable economic cycles by requiring a decrease in money supply in response to increases in inflation.  Assuming the measurements were accurate, in the limit in which the lag in time between the decrease in money supply and the increase in inflation approches zero (i.e., assuming adjustments could be made instantaneously) the money supply rate and the rate of inflation should be equal.

Thus, the best known approach to matching the money supply rate to the real rate of inflation is not unlike the approach followed by Buffett and Munger in their attempts to match the price of Berkshire-Hathaway stock to their estimates of its intrinsic value: negative feedback works.

IP is not an Asset: Patents and Inventors Need to Stick Close

Earlier this week, Peter J. Wallison argued that conventions in fair value accounting may in part be the cause for the recent bubble markets.  Specifically, Wallison pointed to the convention (implemented under FASB 157) that requires assets to be carried at "market" values, even when those assets are not being held for trading purposes.

Almost any scientist or engineer would immediately have recognized the truth of this argument.  Our understanding of any system -- chemical, electrical, mechanical, or financial -- will be limited in part by the accuracy of our tools of measurement.  When one considers how FASB 157 required banks to report the values of MBSs, CDOs, and CDO^2s on their balance sheets far above what the banks would themselves have been willing to give away for the same assets, one understands how the financial markets quickly lost track of the intrinsic value backing the securities traded.

This wisdom has direct relevance to the secondary markets for IP.  Most of the firms now in the secondary markets for IP have taken the view -- and are conducting their businesses -- as if IP were an asset.  This is because IP does bear some characteristics of an asset.  Namely, like real and personal property, IP can be protected through exclusive rights.  The analogy to property has thus come to dominate our understanding of the nature of IP.

Although accountants often treat IP as an asset, IP is not a commodity.  IP is more like equity, although it is not like other equity.  IP is a limited exclusive right to human capital (namely, to inventors' time solving a technological problem).

Maybe part of the reason that Abraham Lincoln understood the importance of patent law is because he understood that human capital cannot be owned.  The photograph shows the Emancipation Proclamation, whereby Lincoln did more for the cause of freeing human capital than many other men together have done in the course of human history.  Lincoln loved the patent system because he understood that it too could lead to more freedom.  Scientists and engineers work best free from the immediate demands of business people and customers.  The idea of a patent system carries within itself the promise of more innovation and more freedom.

POSTSCRIPT: Please note that I do not believe that inventors are literally enslaved right now.  There are obviously huge differences between the enslavement of millions of black Americans and the metaphorical enslavement of inventors who are now forced to do work other than inventing because of the broken patent system.  I do, however, believe that making people more free leads always to a multiplicity of unanticipated social benefits.

Slicing and Dicing Insurance and Property Risks

I see that Charlie Munger has come out against slicing and dicing insurance risk.

I'm going to make a simple observation based on a couple of posts from earlier this week.  The problem with slicing and dicing insurance or property is not the slicing and dicing -- which respectively serve only to amplify the positive or negative externalities of ownership.  The problem is that the source of price signals -- i.e., the individuals who decide whether to buy property or insurance -- are not generally forced to buy both.

Each individual within our society should be required to accept some measure of both the positive and negative consequences of her actions.

Charlie, if you're out there, don't you agree?

What the Founding Fathers knew about R&D that we have forgotten