A Dynamic Model of the Payment System

Abstract

We study the design of e¢ cient intertemporal payment arrangements when the ability of agents to perform certain welfare-improving transactions is subject to random and unobservable shocks. E¢ ciency is achieved via a payment system that assigns balances to participants, adjusts them based on the histories of transactions, and periodically resets them through settlement. Our analysis addresses two key issues in the design of actual payment systems. First, e¢ cient use of information requires that agents participating in transactions that do not involve monitoring frictions subsidize those that are subject to such frictions. Second, the payment system should explore the trade-o¤ between higher liquidity costs from settlement and the need to provide intertemporal incentives. In order to counter a higher exposure to default, an increase in settlement costs implies that the volume of transactions must decrease, but also that the frequency of settlement must increase.

Optimal Pricing of Payment Services When Cash Is an Alternative

“…When the Friedman rule is in e¤ect, we can then use (16) These calculations demonstrate that a cash-card equilibrium in the model can mimic the seemingly paradoxical real-world preference for card payments over cash. For the cases considered, consumers who have a low-cost alternative to the card club (i.e., cash) still have an incentive to pay with a card, since the price of paying by card is no more than paying by cash.…”

“…In words, condition (16) states that the sum of the consumer's balance adjustment L and the monitoring cost cannot exceed the cost of acquiring the necessary cash to defect from the card arrangement, which is q at the Friedman rule. Condition (16) clearly implies that the no-surcharge rule (15) must hold at the Friedman rule. And, since q < q , then by continuity, no-surcharge must also hold for rates of money growth slightly larger than .…”

Optimal Pricing of Payment Services When Cash is an Alternative

“…Under Proposition 2, a cash-card equilibrium can in some cases continue to exist (in steady state) even if the Friedman rule is implemented, and despite the risk of default. 16 Such an equilibrium would run counter to the rationale for the card club, however, since it would deliver the same allocation as cash but at a higher cost.…”

“…In words, condition (16) states that the sum of the consumer's balance adjustment L and the monitoring cost cannot exceed the cost of acquiring the necessary cash to defect from the card arrangement, which is q at the Friedman rule. Condition ( 16) clearly implies that the no-surcharge rule ( 15) must hold at the Friedman rule.…”

“…In this case we must set the inactive agents' balance B = 0 in conditions ( 10)- (14). Under the Friedman rule, the producers'participation constraint (13) reduces to 22) which is inconsistent with the no-default condition (16). Not coincidentally, ( 22) also violates the no-surcharge rule (15); agents would have no incentive to keep making card purchases, and the card club collapses.…”