Fairness in Exchange

Evaluating the Mutually Beneficial and Zero-Sum Components of Exchange

Last update: April 2012


Introduction: Visualizing Exchange

Popular discussions in economics contrast mutually beneficial exchange to zero-sum games. In mutually beneficial exchange we both win. The traditional example involves a farmer and a tool maker. The tool maker gets food from the farmer. The farmer gets tools from the tool maker. Both are better off. In zero-sum exchange one person's gain comes as a result of another person's loss. The standard example is gambling. In gambling no wealth is created; wealth is merely transferred from one person to another.
Now, if we create a graph to show how exchange impacts me and impacts them it quickly becomes visually obvious that perfect mutually beneficial exchange or pure zero-sum exchange is highly unlikely. An entire plane of partially equitable and partially inequitable exchange is possible.

Let's review the graph. The black diagonal in the first quadrant represents perfect mutually beneficial exchange. The line represents both parties gaining equally. The purple in the second quadrant represents zero-sum exchange where I lose and others gain. The green line in the fourth quadrant represents zero-sum exchange where I gain and others lose. The red line in the third quadrant represents negative sum exchange where both parties lose. We should also note that the x-axis represents gain or loss for me that has no impact on others and the y-axis represents gain or loss for others that has no impact on me.


I can sell you a used car. We agree to a price of $1000. But I know and don't tell you that the transmission is bad and it's about to seize. Thus the car is only worth about $400. The positive sum part of our exchange is $400, the real value of the car. The remaining $600 is the zero-sum part of our exchange, where my gain comes totally from your loss.

I have a yard sale. I offer an old relic I had in the attic for $20. You recognize that the relic has collectors value, so you buy it for $20 then immediately resell it to a collector for $300. Your knowledge was of value to me, but your failure to share your knowledge allowed you to make a zero-sum gain. (You added no value to the item being resold.) The mutually beneficial part of this exchange was $20. But most of the $300 was zero-sum gain for you, where you profited from withholding information from me, just as the seller of the junk car profited by withholding information about the car from the buyer.

We should quickly recognize that there is no reason to expect the actual measure of exchange to be limited to any of the diagonals or the axes. Intuitively, we know this already. We know that sometimes we get paid less than we should for the work we did or risks we took. We all have stories or know stories where others have profited more from our work than they contributed or supported. We know that when we get a bargain we paid the seller less than he could have received for his goods. If we could measure the gain or loss that each party got in these exchanges we know that we would not have perfect mutually beneficial exchange - the point would not be on the perfect exchange diagonal.

We should note that deviations from perfect exchange usually result from imperfect information or coercion. Somebody involved in the transaction doesn't know what the real cost or value of his actions are. Many economic theories are based on the assumption that people make well informed decisions where perfect information can or does exist. The theories assume either sufficient laws or sufficient ethics to prevent coercion in the transactions.

Estimating the Mutually Beneficial Exchange and Zero-sum components

No real human exchange is purely mutually beneficial exchange nor pure zero-sum game. Thus, we can evaluate all exchange as being composed of both a mutually beneficial part and a zero-sum part. We can break the value of each exchange into its parts; we can estimate what portion of the exchange is mutually beneficial and what portion is zero-sum. The zero-sum gain part of any transaction will be the difference between the gains of the two parties. The mutually beneficial part is the twice the lesser gain. In a perfect free market with perfect information and no coercion both parties would receive a profit equal to the average of the two profits.

Parts to this discussion

  1. Introduction: visualizing exchange
  2. Evaluating the components of exchange
  3. Recognizing Externalities
  4. Estimating the Ponzi portion of profits
  5. Implications and conclusions



Related pages at this site


Estimating zero-sum elements





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Externalities: Unintended Consequences to Third Parties

We must remember that our choices affect others. Our actions and exchanges will affect people who were not privy to our agreement. In economics the impact on uninvolved third parties is termed externalities. To develop an analytical means to review how profits are made from impacts on third parties we need to work with three dimensions - two parties involved in the exchange, plus the uninvolved third parties who are affected.

We can borrow the three dimensional graphing system used for soil science to guide us visually here. We will first plot what percent of the costs each party contributed to the exchange. We then plot the profit that each party made from the exchange. The zero-sum part of the exchange is the vector from the cost point to the profit point. The direction the vector points shows who received the profit and who suffered the loss of the zero-sum part of the exchange.

For our example, we represent a mining company. The owners & executives provide 5% of the total cost of running the mine through buying the equipment, mineral rights, and managing the operation. The workers contribute 75% percent of the operating costs through their labor and personal risks. The community absorbs 20% of the operational costs by accepting the cost of the impact on their water supply, breathing the particulates, and dealing with subsidence and other property damages. The workers receive 70% of the revenues and the owners and managers receive 30% of the revenues. We see this on our graph with the red dot C representing the distribution of costs, and the blue dot P representing the distribution of revenues or profits. The green vector shows that one group, the executives, took a larger share of the profits than they contributed in costs and risks.

Here again, we diagram an imperfect market where part of the profit is derived from mutually beneficial exchange and part from zero-sum gains.

Estimating Ponzi Element of the exchange
Two essential features make up a Ponzi Scheme. 1. A zero-sum exchange occurs. 2. The number of people paying in is larger than the number of people taking out. There are many ways to decorate these features to make the scheme appear different and exciting, but these two elements together make a Ponzi scheme regardless of the decorations. As we have reviewed above, all real human exchanges have a zero-sum portion. All that is needed to complete a Ponzi scheme is a means of having a large number pay while a small number profit.
We can informally evaluate where Ponzi schemes occur by comparing who pays in, and how many pay in, to who profits, how many profit, and how much they profit. Formally, analytically, we can use the vector in the three dimensional graph. If the vector points from a large number paying in to a small number profiting, we have a Ponzi scheme embedded within a beneficial exchange. Formally, we could estimate the size of Ponzi portion of the exchange by comparing the size of the group paying in to the size of the group benefiting and measuring the portion of the profit that is derived through zero-sum gains (green vector in our graph.)

More Examples:

Environmental Ponzi Scheme: A gas company gets permission to "frack" an area to extract the gas. After ten years have passed five company executives have each pocketed over $2 million. But the fracking has contaminated the ground water. 1000 local residents have to buy and maintain water filters at a cost of about $100 per year for the next 30 years. Five people at the top of this scheme have taken a total of $10 million but only by making 1000 people pay in a total of $3 million. In short, at least 30% of their profit was the result of an environmental Ponzi scheme.
Transfer of Risk Ponzi Scheme: Executives at an investment firm create a plan to sell debt to high risk borrowers. The ten executives each pocket $5 million derived from interest and fees charged to 500,000 borrowers. When the economy weakens 100,000 borrowers lose their investments to foreclosures and a government bailout rescues the bank by giving the bank $10 billion derived from 300 million taxpayers. In this example, all of the profit made by the bankers was derived transferring the risk of the decisions to borrowers and taxpayers.
Leveraged Position Ponzi Scheme: Executives at one company believe that a smaller company is undervalued. They buy controlling shares of that company, merge the smaller company, eliminate a product line, close a facility, and lay off workers. A few months later stock values decline. The executives each take a $1 million bonus for their actions. In this example, the executives added no value to the smaller company. Their profit was totally derived from losses suffered by the former company's workers and investors, as well as their customers. Nothing mutually beneficial occurred during this exchange.

Each of our examples is derived from well documented scenarios that have been in the news over the last 30 years.

Implications & Conclusions
Imperfect information within an economic system combined with coercion (leveraging) can and will lead to zero-sum gains being part of nearly all human transactions. Mutually beneficial exchange is a free market ideal that, like democracy, is never perfectly realized.
It is important to remember how the uncompensated costs of externalities contribute to the profits of large organizations. In large organizational transactions the zero-sum gains can develop a Ponzi scheme characteristic. The Ponzi nature of situations becomes so evident with these graphing tools one is led to suspect that a formal analysis will show that large corporate profits and executive salaries are frequently derived through the Ponzi nature of externalities and leveraging.
This has implications for tax fairness. It is justified to tax unearned income at a higher rate than earned income. Portions of incomes, particularly incomes that are significantly larger than the other involved parties (e.g.: executive salaries) are effectively unearned as they are derived from zero-sum gains.


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