There are three time periods: t = 0, 1, 2 and 100 individuals who are (ex-ante) identical, endowed with 1 unit in period 0, and will need to consume in either period 1 (type 1) or period 2 (type 2). Assume that 1/4 of the individuals will be type 1 and 3/4 of them will be type 2. Types are revealed in period 1. There are two assets: storage (each unit put in storage in period 0 generates 1 unit available to consume in either period 1 or period 2) and illiquid investment (each unit invested in period 0 will yield r1 = 1 in period 1 and r2 = 2 in period 2). All individuals have the following utility function of consumption:

b) (2pt) Explain why it is feasible for a bank to offer the following asset (deposit) in period 0 with payoff structure: d = 1.28 in period 1 and 'r = 1.81 in period 2. c) (4pt) With the bank in part b), let f be the fraction of type2 individuals who also withdraw in period 1. How many units of investment (depending on f) does the bank need to liquidate in period 1 in order to meet the total withdraw demand? What will be the (gross) return for the type2 individuals who do not withdraw in period 1? Under what condition on f will it be optimal for each type2 individual to withdraw in period 1