Money and Banking in Search Equilibrium*

Abstract

We develop a new theory of money and banking based on the old story in which goldsmiths start accepting deposits for safe keeping, then their liabilities begin circulating as media of exchange, then they begin making loans. We first discuss the history. We then present a model where agents can open bank accounts and write checks. The equilibrium means of payment may be cash, checks, or both. Sometimes multiple equilibria exist. Introducing banks increases the set of parameters for which money is valued-thus, money and banking are complements. We also derive a microfounded version of the usual money multiplier.The theory of banking relates primarily to the operation of commercial banking. More especially it is chiefly concerned with the activities of banks as holders of deposit accounts against which checks are drawn for the payment of goods and services. In Anglo-Saxon countries, and in other countries where economic life is highly developed, these checks constitute the major part of circulating medium. Encyclopedia Britannica (1954, vol. 3, p. 49).

Credit and identity theft

“…Since the sign of V (s) is the same as the sign of (u s), independent of the realization of ; we know that it is both constrained e¢ cient 11 and individually rational for all agents with costs less than or equal to u to join the credit club. So, provided that the penalties available are su¢ cient to deter the marginal member from failing to honor the contract-that is, provided (4) holds for all s u-the constrained e¢ cient outcome can be sustained by club membership.…”

“…The equilibrium continuation value of being a member with supply cost s is given by V (s); by the maximum principle V is decreasing in s. Condition (10) requires that club members prefer membership to impersonation (and therefore to autarky, since attempted impersonation is costless), while condition (11) guarantees that members prefer to remain members. The latter requirement is automatically satis…ed by making X su¢ ciently large.…”

Money, intermediation, and banking

“…10 Hence, if μ is sufficiently small in this sense, then conditional on all other successful type-1 producing agents surrendering their output, a successful type-1 producing agent will not have an incentive to hide his output. In other words, the ex ante efficient allocation can be implemented under an institutional arrangement that separates the businesses of the money-issue from intermediation.…”

“…Naturally, our review of the literature above should not be construed as a criticism, as most of these papers do not focus on the question of whether a banking system is essential. The one exception to this may be He, Huang and Wright (2005), although their work is better thought of as emphasizing a different aspect of the business of banking. Our own approach is to ignore any meaningful role for fiat money.…”

Payment Networks in a Search Model of Money

“…However, if there is a single coincidence of wants and the meeting partner has a unit of money (probability m 1 ), then an exchange can occur using money (probability θ) or the CDB. 10 In all other meetings, no exchange can occur. Similar reasoning applies for the case of an agent who has access to the CDB and holds one unit of money.…”