Please answer thoroughly and show work.

3. There are n individuals with each having 1 unit of wealth in t = 0 (period 0). They will need to consume in either t = 1 (period 1) or t = 2 (period 2). A type 1 individual must consume in t = 1. A type 2 individual can wait to consume until t = 2. Let n1 denote the number of type 1 individuals and 712 the number of type 2 individuals (n = m | n2 and n1 is the fraction of type 1 individuals). Types are revealed in t = 1. Thus, each individual is uncertain about his or her type in t = 0. There are two assets: storage (saving 1 unit in t = 0 can have 1 unit to consume in either t = 1 or t = 2) and less liquid investment (investing 1 unit in t = 0 can have L = 0.8 if liquidated in t = 1 and R = 2 if liquidated in t = 2). All individuals have the following utility function: u(c)=1E where c is measured in the same unit as for returns on investment. a) (2pt) Assume n2 2 n1. Verify that all individuals prefer investment to storage. For parts b)-e), a bank offers an asset (deposit) in t = 0 paying r1 = 1.20 and r2 = 1.8 (return depending on date of liquidation). b) (2pt) Assume m = 50 and 712 = 100. Explain why it is feasible for the bank to offer the above deposit assuming bank run does not occur. c) (2pt) Assume m = 50 and 712 = 100. Verify that each individual achieves higher expected utility from the deposit than from the less liquid investment. (1) (3pt) Assume m = 50 and 712 = 100. Is it optimal for a type 2 individual to withdraw in t = 1 if he expects that 54% of the other individuals withdraw in t = 1? Explain why or why not. e) (3pt) Assume n1 : O and n2 : 2. In period 1, each individual can either stay with the bank (Stay) or go and withdraw (Run). Determine the payoff matrix of the bank game between the individuals in period 1. Is there a Nash equilibrium in which all individuals run