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Suppose we have the kind of Diamond-Dybvig model of a bank discussed near the end of chapter 18. I There are a large number N
Suppose we have the kind of Diamond-Dybvig model of a bank discussed near the end of chapter 18. I There are a large number N of consumers, each with one dollar in the bank. So the bank start with N dollars in deposits. I The bank can invest in an asset with interest rate r = 1. This means that for the bank has at the end of period 1, they'll have 1 + r = 2 dollars at the start of period 2. (In this example, there's no inflation, so real interest mte is equal to nominal interest rate.) I The bank offers consumers a contract where they get (:1 dollars if they withdraw their money in period 1, and (:2 dollars if they withdraw in period 2. I Half of the consumers will want to consume in period 1 (\"early consumers\. An average of tril is paid out per person in period 1 . This means that only,r 1 tdl per person is left to invest. . An average of (l tidg is paid out per person in period 2. {d2 paid to each person who still has their money' in the bank.) For the bank to break even. the following resource constraint must be satisfied: (1 +1")' {1 td|] = [:1 t}dg td1+(1t)- (1??) =1 {1 tri ){1+r) d2: {llt] The way that Diamond and Dyhvig describe the process, the contract sets 1:3,, and then everyone who doesn 't withdraw early gets a share of the banks assets in period 2. From that perspective, the resource constraint describes the value of each person's share
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