Outrageous Texting Charges and "A Beautiful Mind"

Congress is all bent out of shape over outrageous charges for text messages via cell phones. That provides a hook for a discussion of Nobel Laureate John Nash whose work was dramatized in the book and movie A Beautiful Mind. (I've just published a Google Knol on the Nash Bargain concept that earned Nash his fame.)

OUTRAGEOUS TEXTING CHARGES

I believe it costs the cellphone company only a fraction of a cent per text message. They are making excessive profits by charging 20 cents each. Some kids have run up multi-hundred dollar monthly bills by doing hundreds of texts a day.

OK, I agree the per text charge is obscene, so what should Congress do about it?

IMHO, (ALMOST) NOTHING!

I would favor a law or regulation that requires the cellphone companies to charge no more than the package plan cost in any given month. They have unlimited text plans that cost $30 and up a month, so the breakeven point is about 150 text messages a month. If an account uses less than the breakeven number of text messages (or air minutes, etc.) in a given month, they should be charged the per-unit amount. If they use more, the bill should be capped at the lowest available package plan rate. Beyond that, so long as consumers are made aware of the charges in advance, and have the ability to block text messaging if they don't want it, I think the cellphone companies should be allowed to charge whatever they want.

Let the market and a "Nash Bargain" (see discussion below) set the prices according to what the consumers are willing to pay. Texting is not a necessity of life!

(Phone service and text communication -e.g., email- are not monopolies anymore. My wife and I have a T-Mobile cellphone plan where we share 400 minutes per month with free weekend and evening calls. We blocked text messaging since we don't use it. Our landline phone was costing around $35/month so we cut our connection. Our home phones are now connected via the Internet to T-Mobile at Home for which we pay less than $13/month, including taxes and fees, for unlimited calls in the US including caller ID and voicemail.)

AMERICAN PUBLIC HAS TOTAL MISUNDERSTANDING OF COMPETITION IN AN "ELASTIC" MARKET

Our school systems do not teach anything about how prices are set in competitive markets - or even in a monopoly situation. Yes, if some item is a "necessity of life" and there is only one supplier, they can charge whatever they like, which is why we need protection from natural monopolies. If competitors in some market illegally collude to set prices, limit quantities, and divide markets, the government needs to intervene to protect citizens.

However, if people can live without some product or service, the market is "elastic" - meaning the price will vary with the quantity available, according to a "Demand Curve".

Did you ever learn about a Demand Curve in school? Even college? Most people think products and services should be sold at a price that is some reasonably small percentage above the cost of production and distribution. They think that any mark-up in excess of that reasonable percentage is immoral and should be illegal. They think that producers and retailers can inflate their profits as much as they'd like by increasing prices.

They do not understand that, in an elastic market, even a monopoly supplier can often INCREASE profits by DECREASING prices! Indeed, the best way to set prices in an elastic market is to match production quantities with consumer demand. It turns out that both maximizes consumer value and producer profits.

EXAMPLE OF A MONOPOLY IN AN ELASTIC MARKET

Say a company is the only supplier of a unique product that is nice to have but not a necessity of life. What should they charge for it? Should they set the price as high as anyone is willing to pay? Should they set the price to make their profit per unit as high as possible?

It turns out the answer to both questions is NO! They can actually maximize their profits by producing and marketing a quantity of product that is more than the quantity that would yield the highest per-unit profit.

The figures (from my Nash Bargain Advisor Excel spreadsheet) illustrate the situation. The heavy black line is the Demand Curve that indicates how the market price declines from about $12 per unit to $4 when the quantity on the market increases from 10 million to 100 million units. The thin red and blue curves indicate the production Cost Structures per unit for two alternate production facilities, as a function of the number of units produced. A producer (whether a monopoly or not) has to decide the optimum level of capital investment. Capital investment in more automated production facilities will increase initial, non-recurring costs, but may reduce incremental production costs by a sufficient amount to pay back the investment -or not- depending upon the number of units eventually sold and the market price when they are sold.

The heavy red and dashed blue curves indicate the profit per unit as a function of the number of units produced. You might think the maximum overall profit occurs when the profit per unit is maximized, but you would be wrong! The figure below illustrates the overall profit (or loss) for Alpha and Beta alternatives as a function of quantity produced. It turns out that, up to a point, lower market prices lead to greater sales quantities and lower per-unit production costs and that is what yields the maximum profit.

The overall profit for the alternative Cost Structures is maximized with a market quantity of 65 million for Alpha and 62 million for Beta, assuming each is a monopoly in a given market. This corresponds to a market price of $7.20 to $7.36 per unit. If the monopoly produces too few units, say 10 to 14 million, it will get $11.68 to $12 per unit, but will lose money overall. On the other hand, if produces too many units, say over 70 million, there will be a glut on the market and overall profits will go down substantially.


A COMPETITIVE MARKET AND A "NASH BARGAIN"

The insight John Nash brought to Economics and that gained him the Nobel in Economics for 1994 is that the situation is the same for multiple producers in a competitive marketplace. If two or more companies produce the same or similar products in an elastic market, such as Burger King and McDonalds or HP and Acer, it is to their advantage to collectively produce a certain number of units, neither too few nor too many.

If there are too few fast-food restaurants in a given geographic area, they may be able to charge a bit more per burger, but they will sell fewer as potential customers choose to eat at home or to go to full-service eateries. On the other hand, if there are too many fast-food places, they will have to reduce prices drastically to attract customers and their overall profits may decline or turn into losses.

The same is true for PC makers. As production quantities have multiplied, prices have come down sharply and features have improved dramatically. This, in turn, has increased sales to the point of nearly 100% market penetration in the US and other westernized countries. More and more people have at least one PC and some have a desktop plus a laptop, and other families have one for each member of the family. (My wife and I have one desktop plus three laptops between us.) With the economic slowdown, however, there may be too many units on the market and prices may drop to the point where some producers face losses and have to cut back production or drop out of the market.

So, how can competitors in an elastic market adjust production quantities such that they can each make a fair profit? Well, they could collude and fix quantities and prices and divide markets to increase their profits. However, that would be totally illegal!

Using game theory, John Nash came up with a way to reach "equilibrium" without illegal collusion. His solution is for each competitor to use their own Cost Structure and estimate the Cost Structures of competitors and calculate the quantity they should produce, assuming others are rational and will do the same. (The highlighted part of the previous sentence is the most important part. If competitors are not rational, or if they try to "cheat" by producing too many units, the Nash Bargain will not work.)

The Nash Bargain Advisor (see my Knol) calculates the optimal quantities each competitor should produce to maximize their own self-interest, assuming others "cooperate" by doing the same in a rational way. The Nash Bargain Advisor also calculates the consequences if one or more producers "cheat" and over-produce more than their optimal quanitiy, or, if one or more producers under-produce due to miscalculation or disruption in supplies or production facilities.

Ira Glickstein

Bet on Google for Solar Power?

A Reuters story today says "Google Inc is closing in on its goal of producing renewable energy at a price cheaper than coal..."

That is GREAT news! I'd bet that Google and other profit-making enterprises, spending moderate amounts of their own money, are much more likely to hit "pay dirt" that all the government investment in the world.

"Google's Green Energy Czar Bill Weihl said the odds of success had gone up in the last year or so from a long shot to a real possibility of demonstrating working technology in a few years. 'It is even odds, more or less, I would say,' he said in an interview with Reuters. 'In, you know, three years, we could have multiple megawatts of plants out there.'"

Google plans to use "solar thermal" technology that generates steam to drive electrical generators, rather than photo cells that turn sunlight directly into electrical power.

Wikipedia has a fine item about solar thermal and they include a number of photos. The first photo above shows a parabolic trough of mirrors. They reflect sunlight to a fluid pipe that is most likely inside an evacuated tube to reduce convective heat loss. The second photo above shows an array of flat mirrors that reflect sunlight to a central collector. In both cases, the collected heat is turned into steam to drive electrical generators.

A SOLUTION TO GLOBAL WARMING?

As readers of this blog know, I am a "realist" on global warming. I acknowledge that we have had significant actual warming of about 0.5ºC over the past 150 years and I am concerned about the rapid increase in atmospheric CO2. While I do not believe human activities are responsible for more than about 0.1ºC of this warming, and I do not think we can do much about that 0.1ºC on a practical level, I do believe we should take conservative actions to reduce the continuing rapid rise of CO2. Solar energy (along with nuclear, wind, and biomass) is one carbon-free avenue we should explore.

I commend Google for their work in this area!

Ira Glickstein

Super Ethics

[From John] Ira previously wrote the following, “All animals, including we humans, are wired with an emotional system that has been "designed" (by evolution and natural selection) to serve as an ombudsman for the long term survival and reproduction of the society we have been socialized in. Absent a properly socialized emotional system, we would focus on our own short-term and short-sighted interests and our society would fail.”

I accept Ira proposition as far as he takes it. The problem as I see it is that his expression, “for the long term survival and reproduction of the society we have been socialized in” does not provide for the long term survival of humankind as a whole, rather it provides for the midterm survival of the strong, who, ultimately are overthrown and fade into history. There seems to be no inherent evolutionary (natural selection) process that assures the long-term survival of mankind as a whole. History bears this out, dynasties have continually risen and fallen since cities and nations were formed. Towns, cities and nations were sacked, men were enslaved if not killed outright, man warred against man. Today is no improvement, in the last century we have had the two most destructive wars in history. It also included the largest mass genocides in history – the Holocaust Stalin’s purges and the murders of the Pol Pot. Today we are confronted with terrorism and the constant wars in Africa. Nuclear war threatens us. There seems to be no end.

With the rise of the world economy man may find in his own individual selfish interest the need for stability throughout the world; this may lead to a form of super-ethics applicable to all mankind. Mini steps have been made with the Geneva Convention and the United Nations but they are very weak. While there is a general consensus amongst the developed nations that such super-ethical standards are necessary, national interests often over ride this consensus.
We have a long way to go.

Optimal Span - Why YOU Should Care

Howard agreed to do his new Topics on Biosemiotics and Language (with some help from Joel's Topic on Memory) with the expectation I would do one on Optimal Span. He was Chairman of my PhD Committee. My dissertation, Hierarchy Theory: Some Common Properties of Competitively-Selected Systems, centered on Optimal Span. (Howard is the author of an excellent book Hierarchy Theory - The Challenge of Complex Systems.)

Why should you care and how does this affect you?

Most obviously, it affects your employment experiences, but also (according to my thesis) the hierarchical structure of things from your ability to discriminate sights and sounds and tastes to written language to how proteins, RNA, and DNA fold! As recenty as 2006 a Dutch scholar I do not know wrote Organizational Structures for Dealing with Complexity and cites my PhD dissertation and a draft paper I wrote for my students at U. Maryland (see Bart A. Meijer, pages 6, 104, 106, 107 and 204).

MANAGEMENT SPAN OF CONTROL

Management experts have long recommended that Management Span of Control be in the range of five or six for employees whose work requires considerable interaction. That's why corporate hierarchies usually have around six employees (sometimes a few more than six) in each first-level department and around five (sometimes a bit less) first-level departments reporting to the next level up and so on. (If the lowest level consists of service-type employees, there may be a dozen or two or more in a department, but there will usually be one or more foremen or team leaders, etc.)













The above diagram shows three different ways you might organize 49 workers. In (A) you have ONE manager and 48 workers, which is a BROAD hierarchy. Management experts would say a Management Span of Control of 48 is way too much for anyone to handle! In (B) you have THIRTEEN managers in a three-level management hierarchy and only 36 workers, which is a TALL hierarchy with an average Management Span of Control of only 3.3. Management experts would say this is way too inefficient with too many managers! In (C) you have SEVEN managers and 42 workers in a MODERATE hierarchy with an average Management Span of Control of about 6.5. Management experts would say this is about right for most organizations where the workers have to interact with each other. Optimal Span theory supports this common-sense belief!


HUMAN SPAN OF ABSOLUTE JUDGEMENT

George A Miller wrote a classic paper in 1956 The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information that showed that human senses of sight, sound, and taste were generally limited to five to nine gradations that could be reliably distinguished. Miller's paper begins as follows:

My problem is that I have been persecuted by an integer [7 +/- 2]. For seven years this number has followed me around, has intruded in my most private data, and has assaulted me from the pages of our most public journals. This number assumes a variety of disguises, being sometimes a little larger and sometimes a little smaller than usual, but never changing so much as to be unrecognizable. The persistence with which this number plagues me is far more than a random accident. There is, to quote a famous senator, a design behind it, some pattern governing its appearances. Either there really is something unusual about the number or else I am suffering from delusions of persecution.

Miller's paper is well worth reading!

WHAT DID IRA DO ?

Miller's number also pursued me until I caught it. I showed, as part of my PhD research, that, based on empirical data from varied domains, the optimal span for virtually all hierarchical structures falls into Miller's range, five to nine. Using Shannon's information theory, I also showed that maximum intricacy is obtained when: The Span (optimal) for single-dimensional structures is, So = 1 + 2e = 6.4 (where e is the natural number, 2.71828459). My "magical number" is not the integer 7, but 6.4, a more precise rendition of Miller's number!

Hierarchy and Complexity

As M. Mitchell Waldrop observes:

[The] hierarchical, building-block structure of things is as commonplace as air. (Complexity - The Emerging Science at the Edge of Order and Chaos, Touchstone, 1992.)

Howard H. Pattee, in his seminal book that I mentioned above, was one of the early researchers in hierarchy theory and he personally challenged me to find:

a simple theory of very complex, evolving systems [and] common, essential properties of hierarchical organizations (Hierarchy Theory - The Challenge of Complex Systems, Braziller, 1973.)

Most complex structures are compositional or control hierarchies. An example of a compositional hierarchy is written language. A word is composed of characters. A simple sentence is composed of words. A paragraph is composed of simple sentences, and so on. An example of a control hierarchy is a management structure, where a manager controls a number of foremen or team leaders, and they, in turn, control a number of workers.

Ira's Hypothesis

The hypothesis at the heart of my PhD dissertation is that the optimal span is about the same for virtually all complex structures that have been competitively selected. That includes the products of Natural Selection (Darwinian evolution) and the products of Artificial Selection (Human inventions that competed for acceptance by human society).

Weak Statement of Hypothesis

In what I call the "weak" statement of the hypothesis, I showed that it is scientifically plausable to believe that diverse structures tend to have spans in the range of five to nine. I did this by gathering empirical data from six domains plus a computer simulation. The domains are:

1. Human Cognition: Span of Absolute Judgement (one, two and three dimensions), Span of Immediate Memory, Categorical hierarchies and the fine structure of the brain. These all conform to my hypothesis.


2. Written Language: Pictographic, Logographic, Logo-Syllabic, Semi-alphabetic, and Alphabetic writing. Hierarchically-folded linear structures in written languages, including English, Chinese, and Japanese writing. These all conform to my hypothesis.


3. Organization and Management of Human Groups: Management span of control in business and industrial organizations, military, and church hierarchies. These all conform to my hypothesis. NOTE: Hierarchy means rank or order of holy beings. I showed that the hierarchy of the angels of the heavenly host, as recounted in Jewish and Christian scriptures and later mystical writings are not typically in the range five to nine and therefore do not comform to my hypothesis. That is a good result because these hierarchies are not competitively selected! They are either the product of human imagination -or- the Creation of God who is not bound by the laws of information theory!


4. Animal and Plant Organization and Structure: Primates, schooling fish, eusocial insects (bees, ants), plants. These all conform to my hypothesis.


5. Structure and Organization of Cells and Genes: Prokaryotic and eukaryotic cells, gene regulation hierarchies. These all conform to my hypothesis.


6. RNA and DNA: Structure of nucleic acids. These all conform to my hypothesis.


7. Computer Simulations: Hierarchical generation of initial conditions for Conway's Game of Life. (Two-dimensional ). These all conform to my hypothesis.

Strong Statement of Hypothesis

What I call the "strong" statement of the hypothesis is that Shannon's information theory, and Smith and Morowitz' concept of the intricacy of a graphical representation of a structure, can be used to derive a formula for the optimal span of a hierarchical graph.

This work extended the single-dimensional span concepts of management theory and Miller's "seven plus or minus two" concepts to a general equation for any number of dimensions. I derived an equation that yields Optimal Span for a structure with one-, two-, three- or any number of dimensions!

My equation for Span (optimal) is: So = 1 + De. (where D is the degree of the nodes and e is the natural number, 2.71828459.)

NOTE: For a one-dimensional structure, such as a management hierarchy or the span of absolute judgement for a single-dimensional visual, taste or sound, the degree of the nodes, D = 2 . This is because each node is a link in a one-dimensional chain or string and so each node has two closest neighbors. For a two-dimensional structure, such as a 2D visual or the pitch and intensity of a sound or a mixture of salt and sugar, D = 4. Each node is a link in a 2D mesh and so each node has four closest neighbors. For a 3D structure, D = 6 because each node is a link in a 3D egg crate and has six closest neighbors. Some of the examples in Miller's paper were 2D and 3D and his published data agreed with the results of my formula. The computer simulation was 2D and also conformed well to the hypothesis.

OPTIMAL SPAN IN MY NOVEL

In Chapter 6 of my novel, Jim and Luke wonder about the control structure for the 1600 scepter-holders:

After a period of silence, Luke spoke up. “Sixteen hundred people are way too many for there not to be a hierarchical structure,” he began. “If the scepter-holder system was properly designed, according to system science theory at least, there would have to be several grades above the lowest class of scepter-holder.”

He took out his read-WINs and put them on.

“Luke,” I observed, “There’s no WIN coverage in this area …”

“Right,” answered Luke, “But there are processors and software in my read-WINs that allows them to operate independently. I’ve got a program for ‘optimal span’ – you know the ‘magical number seven plus or minus two.’”

“What the heck is that?” I asked, “And why would I care? Where are we going here?”

“Well, back about a century ago, a psychologist named Miller discovered that human perception, such as sight and smell and taste and memory and so on, is limited to five to nine gradations. He called it 'the magical number seven, plus or minus two' or, more scientifically, the 'span of human perception'."

“Another guy, an engineer named Glickstein, about sixty years ago, proved the optimal span for any structure is one plus the degree of the nodes times 2.71828459, the natural number ‘e.’ For a one-dimensional string, the degree is two and the formula comes out to be around six and a third, or a little more. He also showed with Shannon’s information theory that the range five to nine was, at least theoretically, over ninety-six percent efficient and four to twelve was over eighty percent efficient. And that’s not just for control hierarchies like a management chain, but also containment hierarchies in all types of physical systems and even software systems like …”

“You just told me how to build a clock,” I laughed, interrupting Luke. “All I want to know is what time it is! Please, tell me why I give a hoot about the range five to nine or the number six and a third or a bit more?”

“About forty years ago,” continued Luke, “A management expert rediscovered the optimal span theory and proclaimed that all management structures must adhere to it! Did you ever notice how nearly all departments at TABB have either six or seven workers to each manager? How each second-level manager has six or seven first-level managers working for him or her?”

“Yeah, come to think of it,” I replied, “That’s how it is. On the other hand, when I worked in a factory as a college summer job, we had about a dozen guys and gals in our team.”

“Well,” replied Luke, “The lowest level, like a platoon in the military, can have ten or twelve or sometimes a bit more. The theory only applies when the workers have to interact with each other in complex ways, not when they’re doing grunt work.”

“OK,” I replied, “So, as I asked before, where are we going here?”

“If you’d quit interrupting, I’ll tell you,” Luke said good-naturedly, “According to the optimal span program in my read-WINs, sixteen-hundred scepter-holders would break down into about two-hundred-fifty first-level ‘departments,’ each with six or seven scepter-holders and one higher-level scepter-holder ‘managing’ them. The two-hundred-fifty second-level scepter-holders would report to thirty-six third-level scepter-holders who, in turn, would report to six fourth-level scepter-holders who would report to the top dog scepter-holder if there was one.”

“OK,” I replied, “So the scepter-holders are hierarchically organized … Wait a minute, did you say thirty-six?”

“Yeah,” replied Luke, “There should be thirty-six scepter-holders at the third level. What about it?”

“Well,” I began, very seriously, “We have a tradition in Judaism that there are thirty-six ‘tzadikim’ or ‘righteous ones’ for whose sake the world exists. No one knows who they are. When one dies, he, or she I guess, is replaced by another, chosen by God. They are sometimes called the ‘Lamed Vovniks’ because, according to gematria, which we discussed some months ago, the Hebrew letter Lamed stands for thirty and the letter Vuv for six, which adds up to thirty-six.”

“So,” replied Luke with a level of interest that surprised me at the time, “There would be thirty-six especially powerful scepter-holders who would regulate the rest! And they do need regulation. I’m not one-hundred percent pleased with Stephanie’s ethics ...

Ira Glickstein