Useful numerical calculations: In the numerical example used by Diamond, 1 unit of initial wealth invested in period 0 has a return of 1 in period 1 (it's basically like storage) and a return of R=2 in period 2. The fraction of agents with early liquidity needs is f=1/4. 1. (5 points) If agents invest by themselves (autarky), how much will they consume in period 1 if they have an early liquidity need? How much will they consume in period 2 if they don't have an early liquidity need? Explain how a bank can improve upon the autarky solution. 2. (5 points) We know from the Diamond article that r 1 = 1.28 and r 2 = 1.813 are the socially optimal deposit returns when f=1/4. Assume that the bank offers the socially optimal deposit returns. Also assume that, even though the true fraction of agents with liquidity needs in period 1 is , agents think (incorrectly) that the proportion is f=.5. Will there be a run? Explain, referring to the relevant numerical calculations [(a), (b), and (c)]. 4 3. (5 points) Suppose when period 1 arrives agents correctly believe that the fraction with early liquidity needs is but