This hubpage is inspired by a lecture of Tatsuya Kameda given on 3/23/09 in the colloquium of the Indiana University Cognitive Sciences program. The lecture concerned the question of whether and why people work in groups. The problem which was envisioned was that of hunting and gathering. The issue was what was the best way for hunters and gatherers to decide where to hunt and gather. They could work as a group by each going off separately to do reconnaissance, share their info and then decide where to forage as a group.

Apparently, empirical studies show that bees do this sort of thing conscientiously, but when humans try to do it, only a few members of the group are doing any work while the rest shirk their duties. Nevertheless, this system is more efficient than just having the most intelligent human dictate where the group will go based on only his own reconnaissance.

Kameda tried to explain this disparity of behavior between bees and humans. He attributed the difference to bees' only being aware of a hive interest while humans pursue their individual self-interest. Kameda worked out a mathematical model that explained human behavior. The production curve (describing the amounting of hunting and gathering achieved as a function of the number of people doing their duty) was concave. (That is there was declining marginal production/ person, the more people were conscientious.) [The concavity is quite natural. When many people go out information gathering, often they will uncover the same facts.] People would only perform their duties as long as the marginal contribution to their individual share of the group take was greater than the cost of their participation.

There is some value of the number of people at which marginal contribution equals cost and this is the number of people that would work. It is a stable equilibrium. If fewer people were working, the pay-off would be greater. If more people were working, the pay-off would be smaller.

All of this started sounding very familiar to me. I tried to reconcile it with my rather limited knowledge of Economics.

 I really know only one theorem in microeconomics. It is this: The price of a commodity will equal the cost of the marginal producer. Let us see why this is.

The law of supply and demand dictates that the price of a commodity is decreasing with increased supply. This corresponds to the concave production function in Kameda's argument. Any producer who is able to produce at a cost less than the price will do so. The fact that production changes the price doesn't matter much. The equilibrium is stable. More production lowers the price which lowers the payoff for production while less production increases the price which increases the payoff for production. It is good, classical economics.

The law of supply and demand seemed very similar to Kameda's argument. Both rested on a stable equilibrium arising from a concave production function. However, there is an important difference. In Kameda's model, the payoff to an individual from his effort is merely his share of the payoff to the group. We can set up a similar model in the setting of production of commodities.

Suppose there are N steel mills of a given capacity with varying costs. Let Pbe the price of steel. (You can imagine it declines with the amount of steel produced.) Suppose that each mill receives an equal share of the revenue generated by all N mills together regardless of whether or not it produces any steel. Thus the benefit to any mill of the steel it produces is P/N, its share of the price. Thus the price is now N times the cost of the marginal producer. Only those steel makers efficient enough to produce steel at 1/N th of its price will produce any. There is again a stable equilibrium. It is essentially Kameda's stable equilibrium.

Aside: In the final chapters of Ayn Rand's novel Atlas Shrugged, a proposal is made very similar to this. The efficient steel maker Rearden and the  inefficient steel maker Boyle will pool their resources and each be paid not according to his production but to his number of furnaces. The parameters are set so that Rearden has a negative incentive to produce. (But they could have been set differently.)

Often when economists deal with this example, they only consider the case in which N goes to infinity. Then there is no production. This is quite a challenge to the traditional Marxist view of things. Marxists like to imagine that the physical means of production determine how much production there will be. But here we have an example where by keeping the means of production constant but by altering the incentive structure, there is a radical change in the amount of production.

Incidentally this paradox for Marxists is a triumph for economists. It shows that changes in apparently abstract things like the supply of money, or the incentive structure can create concrete changes in the real economy, in the amount of production, for instance. Economists aren't concerned with anything like the morality of an economic arrangement. They are merely (dismal) scientists trying to figure out what might happen in any given arrangement.

However more needs to be said. It is not necessary that N be infinite. There might be fixed costs associated with maintaining an unproductive steel mill even in a communist system. This will keep down the number of mills N. Thus even in the communist system, there will still be production. It will be entirely carried out by the more efficient largely for the benefit of the less efficient. Nevertheless, it will still benefit the efficient enough to make it worth their while to carry it out.

Largely the utilitarian argument made by economists against communism boils down to this argument. Under communism, there is less production. But one could also see advantages to communism. No one goes without. Only the best and brightest work. The rest have plenty of leisure time to twiddle their thumbs.

A final important point I'd like to make is that often those issues which are actually economic issues, are quantitative and not just qualitative. It isnot just important whether or not there is a stable equilibrium. It is not important just what happens when parameters go to zero or infinity. It can be important to know where the stable equilibria are when the values of the parameters are moderate.

Ideologues who venture into economic theory often err because they have heartfelt beliefs which intefere with their consideration of subtle issues. Marx may have missed the role of incentives in economics because incentives were not physical, but rather a human convention. Rand claimed that N goes to infinity case showed that looters were never practical and her ideas were. Her idea was that Rearden should run away in the dark of night to Colorado carrying only the bar of gold a visiting pirate had given him.

Empirical evidence that Ayn Rand's ideas were not entirely practical may be found in the dearth of disappearing industrialists in the more than fifty years since her novel was published. Perhaps a mathematical model could be set up to explain this which takes account of the costs of resisting the government.

Economics is a science. It is neutral and may serve consumers, producers, and looters alike. When the looters establish their laws, these laws have parameters and they will try to set these parameters, using, they hope, sound economics, in order to maximize their take. (The optimization process is sometimes called suply side economics.) It requires leaving the producers some incentives to produce. Ayn Rand was wrong in at least one respect. A society can exist that is half free and half loot. For good or ill that is the world in which we are living. Moreover, the parameter "half" can be varied.