DIAMOND-DEVICE [1983} RELATED PRAC'HCE QUESTIONS 1. Consider the basic setup of the Diamond-Dybvig {1933] model. Specically, 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 2 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 impatient types}, the remaining 500 people will need to consume at t=2 [the patient types]. The utility derived from consumption is 1 (11m): if impatient, 1 - (12'ch if patient, where the subscript denotes the time of consumption. {i} Calculate the expected return {from a t=0 perspective] of direct investing. {ii} Calculate the expected utility {from a t=0 perspective) derived from direct investing. Suppose a bank can offer an asset that is more liquid, with gross returns Rd], = 1.1 and R\"I = 1.3 [depending on the time of liquidation}. {iii} Calculate the expected utility {from a t=0 perspective) derived from depositing with the bank. Do you conclude that people would prefer banking to direct investing at t=0? {iv} Explain how the temporary suspension of withdrawals could help mitigate the adverse consequences of a bank run, or even prevent one altogether