please give a detailed answer (with all computations) of the next problem.
AN ILLUSTRATION OF DIAMOND-DYBVIG Suppose there are 100 risk-averse individuals, each with $1 to invest in a project at t=0. The project will yield l=$0.8 if liquidated at t=1 and R=$2.25 if liquidated at t=2. At t=0, no individual knows what his "type" (denoting his consumption preference) will be at t=1. However, it is common knowledge that p=0.35 of the individuals will end up being "diers", while the remaining will end up being "livers" at t=1. If the individual turns out to be a "dier" (Type D), then his utility function for consumption will be: UD=C1. If he turns out to be a "liver" (type L), then his utility function for consumption will be UL=0.6C1+C2. Assume a scenario with a discount rate r=0. a) Assume first there is no bank in the economy. What is the best strategy for an individual consumer? Invest? Store? Diversify (i.e., invest a fraction of its endowment)? b) Suppose that consumers blindly believe that the bank would horror a promise of 0.8$ at t=1 and 2.25S at t=2. Would they deposit their money at me bank? c) Which investment strategy would allow the bank to honor that promise? (Notice that there might be many). d) What is the optimal contract that the bank could offer? c) What is the minimum proportion of individuals f needed to trigger a bank run? (i.e., the minimal f such that, if an individual observes that a fraction f of consumers is attempting to withdraw at t=1, while the remaining consumers are waiting until t=2 to withdraw their money, it would be optimal for him to withdraw his own money as well). f) How can deposit insurance eliminate the bank-run equilibria? g) In which area of a financial institution could this model likely be used as a theoretical base? AN ILLUSTRATION OF DIAMOND-DYBVIG Suppose there are 100 risk-averse individuals, each with $1 to invest in a project at t=0. The project will yield l=$0.8 if liquidated at t=1 and R=$2.25 if liquidated at t=2. At t=0, no individual knows what his "type" (denoting his consumption preference) will be at t=1. However, it is common knowledge that p=0.35 of the individuals will end up being "diers", while the remaining will end up being "livers" at t=1. If the individual turns out to be a "dier" (Type D), then his utility function for consumption will be: UD=C1. If he turns out to be a "liver" (type L), then his utility function for consumption will be UL=0.6C1+C2. Assume a scenario with a discount rate r=0. a) Assume first there is no bank in the economy. What is the best strategy for an individual consumer? Invest? Store? Diversify (i.e., invest a fraction of its endowment)? b) Suppose that consumers blindly believe that the bank would horror a promise of 0.8$ at t=1 and 2.25S at t=2. Would they deposit their money at me bank? c) Which investment strategy would allow the bank to honor that promise? (Notice that there might be many). d) What is the optimal contract that the bank could offer? c) What is the minimum proportion of individuals f needed to trigger a bank run? (i.e., the minimal f such that, if an individual observes that a fraction f of consumers is attempting to withdraw at t=1, while the remaining consumers are waiting until t=2 to withdraw their money, it would be optimal for him to withdraw his own money as well). f) How can deposit insurance eliminate the bank-run equilibria? g) In which area of a financial institution could this model likely be used as a theoretical base
