Indivisibilities, Lotteries, and Monetary Exchange

@article{Berentsen2002IndivisibilitiesLA,
  title={Indivisibilities, Lotteries, and Monetary Exchange},
  author={Aleksander Berentsen and Miguel Molico and Randall Wright},
  journal={J. Econ. Theory},
  year={2002},
  volume={107},
  pages={70-94}
}
We introduce lotteries (randomized trading) into search-theoretic models of money. In a model with indivisible goods and fiat money, we show goods trade with probability 1 and money trades with probability τ, where τ<1 iff buyers have sufficient bargaining power. With divisible goods, a nonrandom quantity q trades with probability 1 and, again, money trades with probability τ where τ<1 iff buyers have sufficient bargaining power. Moreover, q never exceeds the efficient quantity (not true… 

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TLDR
This framework potentially generates three types of inefficiencies: the no-trade inefficiency, where no trade takes place even though it would be socially efficient to trade; and the too-much-trade and too-little-tradeInefficiencies, where the quantities produced and exchanged are either larger or smaller than what the solution to a social planner's problem would mandate.
...

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