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Question 3 [12 points] Consider the following economy with three dates (t=0, 1, 2). A firm needs to raise $100 to finance a project at

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Question 3 [12 points] Consider the following economy with three dates (t=0, 1, 2). A firm needs to raise $100 to finance a project at t=0. At t=2, the project is either a failure and pays 01f nothing or generates $320 . Both states are equal likely .At t=1, the firm learns about the outcome of the project .If it is a success it expands the project and wants to raise additional capital .This is observable in the market .If the project is a failure there is no additional capital needed . There is an early consumer who has $100 at t=0 and the utility function a; =[CM+1.3cm+cl?2 if cE15100 3 _ . icsu+1'3'100+(Cai_100)+cm if cEl>100 In addition ,there is alate consumer who has $400 at t=1 and the utility function it; = Cm + 631+ 632' Suppose the firm issues equity at t=0. If the early consumer buys equity at t=0, he sells his equity holding to the late consumer at t=1. a) What equity contract does the firm o'er the early consumer so as to get $100?1Hhat is the price of the equity at t=1 if there is no additional equity issuance T'What is the price of the equity at t=1 if there is additional equity issuance 'F' [10 Points ] b) What is the expected profit of the firm ?[2 Points] Question 4 [12 points ] Now suppose there is bank in the above economy .The bank provides loans to firms and keeps information secret . Consumers do not observe whether the firm needs more funding or not. At t=2 the bank is liquidated and consumers who have deposits with the bank get back what the bank owns at t=2. r1he bank o'ers the early consumer the following demand deposit contract .Ifthe early consumer deposits $100 at t=0,he can withdraw $100 at t=1. The bank offers the late consumer the following contract .If he deposits $100 at t=1,he gets back the loan that the firm repays to the bank since the bank is liquidated at t=2. a) What loan contract does the firm offer the bank so as to get $100 from the bank '? Does the early consumer deposit $100 at t=0 and does the late consumer deposit $100 at t=1

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