Monday, June 29, 2009

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.)


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?


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.)


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.


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.


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


Howard Pattee said...

The problem is that the basic assumption of rational markets is demonstrably false. As our current financial situation demonstrates, people are not rational and therefore the market is not rational. Frauds, fallacies, fads, credulous consumers, deceptive advertisers, and greed rule the market. Many psychological studies (one example)show human bondage is emotional.

Ira Glickstein said...

I agree emotion plays a greater role than most people realize as demonstrated by Dan Areily in the link you provided (and discussed here at TED-Irrational Decision Making).

Was it a mistake to award John Nash the 1994 Nobel in Economics for his work that assumes competitors will behave rationally?

According Nash's "equilibrium" theory, if competitors "cheat" and produce more than the "Nash Bargain" their profits go down and they may go out of business. Such creative destruction is a necessary component of free markets. It serves, on average, to reward rational behaviors despite our human tendencies to the contrary.

If, as you claim Howard "Frauds, fallacies, fads, credulous consumers, deceptive advertisers, and greed rule the market" what is the solution? More regulation by the Congress administered by civil servants? Is there any evidence they are any more rational spending other people's money than individuals and profit-dependent companies spending their own money?

Ira Glickstein

Howard Pattee said...

In a democracy by our votes individuals have some influence over how the government uses our money, although big business lobbying largely perverts this influence. We have little influence over how profit-making businesses use our money except by laws enacted by government. There is some optimum governmental control between communism and anarchy that prevents the excesses of both extremes. I do not agree with your simplistic view is that government is bad and business is good at spending our money. Currently most voters feel the same.


Ira Glickstein said...

Our influence on government comes every few years when we vote. We never get to vote on the army of faceless civil servants who actually administer and provide government services.

We influence profit-making businesses every day of our lives when we vote with our dollars to eat at our choice of dozens of restaurants -or- buy food at our choice of many markets -or- grow our own vegetables, etc. We do the same when we choose where to buy our clothes -or make them- and our cars and appliances and entertainment. We vote with our time and skills when we choose our jobs (I quit two jobs over a three-year period before I ended up at IBM for decades.)

Yes Howard, big business and big labor and other special interests pervert our government. They use their influence to get subsidies and bailouts and loopholes.

Limited government responsible only for essentials (national defense, domestic tranquillity, adherence to contracts, and welfare for the aged, ill and disabled) would offer less opportunity for perversion by the politically-connected. The government that governs least is the government that governs best.

Businesses that cannot keep good employees happy and/or fail to satisfy their customers go out of business. (That is, unless they are politically-connected and get a bailout.)

Government agencies hardly ever go out of business, no matter how poorly they perform.

Employees at private firms get fired if their performance falls below a norm. Civil servants have a job for life.

Ira Glickstein

Q: How many people work for the government?

A: About half of them!