The hot potato effect is an entropic force

According to an oft-repeated but probably embellished account, when Laplace gave a copy of Mécanique Céleste to his physics-literate friend Napoleon Bonaparte, Napoleon asked him what role God played in the construction and regulation of the heavens. "Sire," Laplace replied, "I have no need of that hypothesis."

Neil deGrasse Tyson 

The "hot potato effect" describes how injections of so-called high powered money, like cash or monetary base reserves, are like hot potatoes. Individuals are already holding as much money as they want in equilibrium at a given price level, so the additional cash is 'sold' to re-balance their portfolios. That ends up in a cascade of exchanges until everyone is back in equilibrium at a new higher price level.

Scott Sumner wrote a post about this effect awhile ago, calling it the sine qua non of monetary economics. He said something remarkable in that post:

"[people] want explanations they can understand at the individual behavior level.  But that just won’t work in this case."

Something that doesn't exist at the individual behavior level? Sounds like an entropic force! Here's Sumner from the same post explaining the hot potato effect using a parable with gold:

Because before the discovery [of additional gold] people were already in equilibrium, they held as much gold as they wanted to hold at existing prices.  The extra gold is a sort of “hot potato” that people try to get rid of.  But obviously not by throwing it away!  They get rid of it by selling it.  But notice that while that works at the individual level, it doesn’t work in aggregate.  Now someone else has the extra gold. (That’s why attempts to understand money at the level of the representative consumer fail.)  The only way for society as a whole to get rid of the extra gold is by driving down the price of gold [i.e. driving up the price level] until people want to hold the new and larger quantity.

The thing is that this explanation doesn't really explain why the price level goes up. I may have more gold than I want to hold, but I don't want to give it away or get a bad deal. It seems like Sumner is implying that the price level just happens to rise over the course of several 'mistakes' (the price of bacon is too high at this store, but I have the money, i.e. extra gold, and I'm too lazy to go to the other store so I'll buy it anyway even though its not optimal). This is remarkably close to the entropic force view.

The entropic force view would say that the additional 'gold' (high powered money) randomly moves around (and prices randomly fluctuate) until the new most likely configuration (of prices and gold held) with the new larger amount of gold is happened upon by chance. In the simplest case that new most likely configuration is a uniform distribution across the agents. The new most likely price level is also higher since people will randomly accept both high and low prices, but more high prices (bad deals) will be accepted than were accepted before the additional gold was added because those 'mistakes' were made possible (the state space was opened up) by the additional gold in the market.

In the language of thermodynamics, if you add energy to a system, that opens up new parts of phase space with higher momentum states, raising the temperature of the system.

I made a short animation showing how a large injection of high powered money into a segment of the economy eventually finds its way across the entire economy through random exchanges. You can imagine each vertical light blue (well, purplish in the compressed youtube version) bar is an agent, firm or market sector (e.g. imagine the injection happens in the banking sector). The horizontal blue line is the average and median before the injection, the horizontal red dashed line is the average after the injection.

The solid red line is the median level; 50% of the agents are holding high powered money above this level and 50% below. When the median meets the average, that means the typical agent won't make a biased 'mistake', i.e. randomly accept a price that is too high more often than one that is too low. If the median is below the average -- as it is when the high powered money is injected -- then more than half of the agents will tend to increase their holdings since they have below the average level [1].

Effectively, the injection of high powered money is "thermalized" and heads toward a new equilibrium (uniform) distribution at the new average. We see the median (solid red line) rise from the previous average (blue line) to the new average (dashed red line).

The difference here is that there is no real requirement for human behavior in the explanation -- even at the macro level. Agents aren't thrown off of their original "desired" equilibrium and don't "want" to get rid of excess holdings of high powered money. The new equilibrium is just the new most likely state and the agents, if they have more than the average, just tend to reduce their holdings by random exchanges.

Utility maximizing agents? I have no need of that hypothesis.

Footnotes:

[1] This assumes non-preferential attachment -- i.e. all agents are equal. This illustration selects which agents trade money from a uniform distribution. A different mechanism leads to different distributions. See e.g. Bouchaud and Mezard http://arxiv.org/abs/cond-mat/0002374.