Question
Consider the basic setup of the Diamond-Dybvig (1983) model. Specifically, there are three periods, denoted t=0,1,2, a single consumption good, and an illiquid investment opportunity
Consider the basic setup of the Diamond-Dybvig (1983) model. Specifically, there are three periods, denoted t=0,1,2, a single consumption good, and an illiquid investment opportunity that pays gross return 1 if liquidated at t=1, or gross return 1.9 if liquidated at t=2.
There are 1000 people in the economy, each endowed with 1 unit of the consumption good at t=0. At t=1, exactly half (500 people) will randomly realize that they need to consume at t=1 (the early consumers), the remaining 500 people will need to consume at t=2 (the late consumers). The utility derived from consumption is 1 - (1/c1) 2 for early consumers, 1 - (1/c2) 2 for late consumers, where the subscript denotes the time of consumption.
- Calculate the expected return (from a t=0 perspective) of depositing with this bank. How does it compare to the expected return from direct investing?
Suppose the bank offers a different asset instead, one that pays the same return, Rd, to all depositors (i.e., regardless of the time of liquidation).
- What is the highest gross return Rd that the bank can offer all depositors?
- Now suppose the late consumers pretend to be impatient and withdraw early. How many people can be paid before the bank runs out of funds?
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