First Mathematical Model of a Gift Economy
Economist’s mathematical formulation of a gift economy suggests that it should function like a conventional market
One of the founders of modern economic theory was the French mathematician Leon Walras. In the late 19th century, Walras laid down the fundamental ideas behind equilibrium theory which has gone on to have profound effects on economic thinking, on wealth creation and ultimately on the nature of 21st century society.
Equilibrium theory is the idea that in any market the forces of supply and demand will push prices towards an equilibrium. It’s great advantage is that it can be precisely formulated mathematically which allows economists to make specific predictions about the way markets should behave.
This mathematical predictability is like a drug for economists, locking them into certain patterns of thought that they have struggled to move beyond. In particular, equilibrium theory does not allow for the kinds of dramatic collapses in prices that various markets have repeatedly experienced throughout history.
Consequently, since the 2008 financial collapse (which ought not to have been possible under equilibrium theory), there has been a growing sense that economics needs to be drastically reformulated. Understandably, equilibrium theory has come under particular attack.
But alternative economic systems are hard to find and those that are known have been largely ignored by mainstream economists. Today, Peter Weijland at the University of Amsterdam in the Netherlands takes a small step towards changing this by developing a formal mathematical theory describing a gift economy. Weijland’s conclusion is that such an economy is not so different from the market economy that dominates today.
Weijland’s key insight that makes the gift economy mathematically tractable is that when Albert gives Brenda a gift, this is not a one way transaction. Granted, Brenda immediately benefits from the gift but Albert also has a reasonable expectation that the gift will be returned at some point in the future.
In other words, Albert exchanges his gift for a kind of social credit that has particular value now and in the future. “We develop a mathematical model for such economies by means of a system of social credit instead serving as an alternative money of account,” says Weijland. “Every individual keeps track of a mental bank account of social credit in relation to every other person individually.”
When thought of in that way, social credit becomes a form of currency, just like dollars, yuan or euros. And it immediately becomes amenable to the same kind of mathematical treatment that economists use to model conventional transactions.
That makes this approach interesting. It implies that, in many ways, a gift economy should function just like a money-based economy.
Weijland immediately turns to the economists’ traditional favourite: equilibrium theory. He shows that the value of goods in a gift economy should naturally tend towards an equilibrium. “We analyze how a moneyless market eventually comes to an equilibrium similar to the ones found by Walras,” he says.
That’s promising because it’s the first time an economist has created a formal mathematical description of a gift economy and opens the way to more detailed study.
But it’s also a concern. The big problem with equilibrium theory is that it assumes that humans are perfectly rational agents that always make decisions that maximise their return.
But a growing body of evidence is revealing what any school child could have told economists long ago: that humans aren’t rational agents and often make decisions that appear entirely irrational.
For example, taxi drivers tend to work long hours on days when there is little business but go home early on days when they have plenty. A perfectly rational driver would do the exact opposite, of course.
When this kind of irrational behaviour is incorporated into formal mathematical models of economies, the likelihood of boom and bust phenomena becomes all too clear. A market equilibrium is about as likely as finding a pencil standing on its point. It’s possible in theory of course but in practice, the only way to achieve it is by constant, vigilant measurement and adjustment to avoid the all too likely collapse.
By this way of thinking a gift economy ought to be just as susceptible to the boom and busts that afflict conventional economies, perhaps even more so.
Indeed, anecdotal accounts of these kinds of economies back this up, such as open source software projects that rely on volunteer contributions. Some are successful beyond dreams while others fail in spectacular fashion
So while Weijland’s analysis of a gift economy is a welcome development, his devotion to equilibrium theory is a backward step.
What’s needed, of course, is an approach to new economic systems that properly captures the irrational behaviour of humans. And that’s not entirely wishful thinking.
A new breed of scientist has begun to take the economic bull by the horns with the goal of properly understanding the behaviour of humans and incorporating this into computer models of economies.
The initial results are humbling—we will probably never be free of the threat of economic collapse. But formal work on alternative economies, like Weijland’s, suggests that there may be other ways of doing business that are equally worthy of exploration.
Ref: arxiv.org/abs/1401.4664: Mathematical Foundations for the Economy of Giving
