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

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter17: Making Decisions With Uncertainty

Section: Chapter Questions

Problem 4MC

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