The problem is in the below images

Question 1 [22 points] Consider an economy with three dates (T20, 1, 2) and the following investment opportunity. If an agent invests $1 in a project at T:0, the project yields $4 at T:2. The project can be liquidated at T=1 but early liquidation yields $1 at T=1. An agent has $1 and is risk avers and can be of two types. With probability 0.2 an agent is a type-1 consumer and with probability 0.8 an agent is a type-2 consumer. If an agent is a typel-consumer, he only values consumption at T:1 and his utility function is 241220i 1 where cl is the amount consumed at T=1. If an agent is a type-2 consumer, he values consumption at both T:1 and T:2 according to the utility function 1 uz 22 +0 C l 2 where c1 and c2 are the amounts consumed at T:1 and T:2, respectively. a) What is the expected utility of the agent? [3 Points] Now consider a bank that invests in these projects. There are N21,000 agents. All agents are identical ex ante in the above sense. Suppose they all deposit $1 each with the bank. The bank offers the following demand deposit contract (d1, d2) where d1 is the amount and agent can withdraw at T=l and d2 is the amount he can withdraw at T=2. b) Suppose d1:1.2. What is the amount (I; that the bank can offer an agent who withdraws at T22? What is the expected utility of an agent? [4 Points] c) Suppose d2:3.6. What is the amount (11 that the bank can offer an agent who withdraws at T:l? What is the expected utility of an agent? [4 Points] Suppose the bank offers (dbdz) : (1.4, 3.6). An agent expects that M:630 other agents will withdraw at T21. d) What is the best response of the type-2 consumer, i.e. does he has an incentive to run to the bank and withdraw at T:l ? [3 Points] e) What is the maximum number of withdrawals at T:l such that a type-2 consumer has no incentive to withdraw at T:1. [8 Points]