Consider the model of demand deposits described in class. Suppose N = 900, y = 10, vk = 0:9, and X = 1: Let each person have a two-thirds chance of...

Consider the model of demand deposits described in class. Suppose N = 900, y = 10, vk - θ = 0:9, and X = 1:2. Let each person have a two-thirds chance of being a type 1 and a one-third chance of being a type 2. vk is price of capital when sold before capital produces the return of consumption good, and is the verication costs of capital. X is the two-period rate of return on capital.1. 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 goods are placed in storage? In capital?2. Now suppose the type 2 people pretend to be type 1 people and withdraw early. How many people can be paid before the bank runs out of assets?3. Suppose that in the period after you made your deposit at the bank, you turn out to be a type 2 person and you learn that all of the other type 2 people are about to pretend to be type 1 people so that they can withdraw early. Is it in your self-interest to also try to withdraw early?4. Are type 2 people better o¤ than they would be if no type 2 person tried to withdraw early? Reconcile your answer with your answer to the first situation.