A note on convergence of Peck-Shell and Green-Lin mechanisms in the Diamond-Dybvig model

We study the effects of population size in the Peck-Shell analysis of bank runs. We find that a contract featuring equal-treatment for almost all depositors of the same type approximates the optimum. Because the approximation also satisfies Green-Lin incentive constraints, when the planner discloses positions in the queue, welfare in these alternative specifications are sandwiched. Disclosure, however, it is not needed since our approximating contract is not subject to runs.

A model of private bank-note issue

A random-matching model (ofmoney) is formulated in which there is complete public knowledge of the trading histories of a subset of the population, called the banking sector, and no public knowledge of the trading histories of the complement of that subset, called the non bank sector. Each person, whether a banker or a non banker, is assumed to have the technological capability to create indivisible and durable objects called notes. If outside money is indivisible and sufficiently scarce, then the optimal mechanism is shown to have note issue and note destruction (redemption) by members of the banking sector.