Roger Farmer always has done interesting and different stuff. We need economists like that. But it's risky of course. What I'm trying to do here is articulate something that makes me uneasy about his recent line of macro theorising. Like his simple model here with Konstantin Platanov (pdf).
Consider a simple model with three goods: Apples, Bananas, and Mangoes. Mangoes are used as money. So there are two markets: the apple market (where apples are traded for money); and the banana market (where bananas are traded for money. And there are two prices: the price of apples in terms of money; and the price of bananas in terms of money. Something like my old minimalist model.
If both prices are perfectly flexible, and instantly adjust to clear the two markets, this model has a unique equilibrium.
Now let's change the model. Assume the apple market has costly search. It is difficult for individual buyers and sellers of apples to find each other. So when they do meet there will be strictly positive gains from trade to that particular pair of individuals. It's not like a textbook competitive market where each can credibly threaten to switch to another trading partner if the other raises/lowers his price by a penny from the market-clearing price. Because it's costly to find another trading partner. So there is a range of prices within which each would prefer to accept that price rather than search for another partner.
But the banana market is textbook.
Economists usually assume that in these cases of bilateral monopoly/monopsony the apple price will be determined by relative bargaining power, so if the two have equal relative bargaining power (for example) they will split the difference and agree on a price in the middle of that range. The Nash Bargaining Solution is one way to model cases like this.
But Roger Farmer does not want to follow that path. OK, let's follow Roger.