December 12, 2017

Free market inequality

Let’s say there are two individuals: Richy and Bill. Both are completely selfish. Richy, by the astrological virtues of his name, is rich. Bill is poor.

One day while strolling they stumble upon 100 bucks stuck under a large boulder. The boulder is large enough to resist the force of an individual pusher but will oblige if both of them push together. Richy and Bill would need to cooperate to retrieve the money.

“Hey Bill,” says Richy, “help me push this boulder and I will give you 20.”
“How about this,” says Bill. “You help me push it instead and I will give you 20.”
“No, no, I have a better idea,” says Richy. “I’ll give you 20 for helping me push this boulder.”

This went on for a while. Eventually, the sun was about to set. Both were considering the possibility of returning home without the money. Richy thought of the lovely four-course meal awaiting him. He could’ve used the 100 to buy some candy on the way, but oh well. Meanwhile, Bill was dreading another hungry night. He needed that 100 to buy five days’ worth of food. In a moment of resignation, he decided to settle for 20. That way, he will at least get some money instead of nothing.

The above tale is a reference to Nash’s bargaining problem, which concludes that the net bargaining surplus is divided in the ratio of the bargaining powers of the two individuals. Here, 100 is the net bargaining surplus, i.e. the overall amount gained if the bargain is accepted. Richy gets to keep 80% of the surplus because he has more bargaining power — simply by not needing the money as much as Bill. For similar reasons, the stereotypical factory owner keeps a larger share of the produced wealth while the workers agree to work for pennies.

Money gives greater bargaining power to the rich which in turn ensures larger chunks of all future profits. We have a positive feedback loop through which the rich get richer and the poor get poorer (comparatively, not absolutely).

Thus, rising inequality seems inevitable in a free market.

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A random person with few hobbies here and there.

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