Question 1 Consider an economy with three dates (T-0, 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 averse 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 Hi = 2 - where c, 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 H2 = 2 –- C1 +C2 where C1 and C2 are the amounts consumed at T=1 and T-2, respectively. a) What is the expected utility of the agent? Now consider a bank that invests in these projects. There are N=1,000 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 (d,, d2) where d, is the amount and agent can withdraw at T=1 and de is the amount be can withdraw at T-2
Question 1 Consider an economy with three dates (T-0, 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 averse 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 Hi = 2 - where c, 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 H2 = 2 –- C1 +C2 where C1 and C2 are the amounts consumed at T=1 and T-2, respectively. a) What is the expected utility of the agent? Now consider a bank that invests in these projects. There are N=1,000 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 (d,, d2) where d, is the amount and agent can withdraw at T=1 and de is the amount be can withdraw at T-2
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Thank you for your answering part a to c already. Please answer part d & part e ONLY.
Expert Solution
Step 1
Utility function of type 1 : U = 2 - 1/c1
Utility function of type U = 2 - 1/ (c1+ c2 )
d1 & d2 are the return values that the bank provides in the period t = 1 & 2 respectively .
d1 = 1.4
d2 = 3.6
Now ,
For type 2 customer to withdraw at T= 1 time period :
Utility of type 2 customer liquidating from bank in T = 1 > Utility of type 2 customer liquidating in T = 2
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