Assume N=900 three-period-lived people are born each period in overlapping generations, each endowed with y=10 goods only when young. No one consumes when young. Each person wants to consume in one of the next two periods of life, depending on his type. Specifically, type 1 consumes in the second period of his life and type 2 consumes in the third period of his life. No one knows his own type when young; an individual only learns his type in the second period of his life. Let each young person have a 2/3 chance of being type 1 and a 1/3 chance of being type 2.

People have access to two assets, storage and capital. Storage pays the gross rate of return 1 over one period, while capital pays the gross rate of return X=1.2 over two periods. The liquidation price of capital is v^k if the capital is sold before maturity, and the verification cost of the capital is 0. Assume v^k-0=0.9

A) if all people deposit their endowment in a bank, what bank portfolio can guarantee the rate of return 1 to all type 1 people and the rate of return 1.2 to all type 2 people? How many units of goods are placed in storage? In capital?

B) now suppose the type 2 people pretend to be type 1 people and withdraw early, how many people can be paid before the bank run out of assets?

C) suppose a type 2 individual learns that all the other type 2 people are about to pretend to be type 1 people so they can withdraw early. Is it in his self-interest to also try to withdraw early?

D) what are the possible policy prescriptions to prevent a bank run?