Suppose there are 100 young people born each period. Each young person receives 250 goods, but nothing when middle-aged or when old. People can access a storage technology that yields one good next period for every good put in storage in the current period. Alternatively, there is a capital good. For each unit of capital acquired in date t, 1.2 units of the consumption good will be received at date t + 2. If the person liquidates capital after one period, then only 0.75 units of the consumption good can be obtained date t + 1. Assume that ten percent of the people want to consume when middleaged and the remainder want to consume when old. Now, consider a case in which the bank does not expect a bank run to occur, but everyone withdraws when middle aged. Old consumers simply take their withdrawals and acquire the storage good themselves.
a. Suppose the first 10 percent of people in line receive the full value of their deposit. How much these people be able to consume?
b. Suppose the next 90 percent of people receive an equal split of remaining assets. How much will these people be able to consume?