Consider a model of demand deposits. Assume that 1000 three-period-lived people (N=1000) are born each period. Each is endowed with 90 units of the good, only when young (y=90). No one consumes when young. Everyone will want to consume in one (and only one) of the next two periods. The type 1 individuals consume in the 1st of these two periods (period 2 of life). The type 2 individuals consume in the 2nd of these two periods (period 3 of life). The type of the individuals is random: with 0.70 probability households will be type 1 and with 0.30 probability type 2. There are two ways (technologies) to pass consumption to future periods: (1) storage, which has a gross rate of return equal to 1, and (2) capital investment, which take two periods to mature and have two-period return 1.4. If capital is sold after one period of investment (liquidated), then the return is vk - =0.70. Suppose there are Banks that can offer demand deposits. Individuals deposit the money there and they can take it whenever they want. All the individuals will deposit their endowment of 90 units of consumption in the Bank.

Suppose the Bank makes zero profits (in expectation) and it promises to pay a gross rate of return of 1 to those withdrawing in period 2.

1) What are the returns that the Bank would promise to the depositors that withdraw the deposits in period 3? And what will be the allocation of investment (storage vs. capital) of the Bank?