Question 3 [18 points] Consider the following economy with three dates (t=0, 1, 2). A rm needs to raise $100 to nance a project at t=0. At t=2, the project can be a failure and pays off nothing or a success which generates $400. Both states are equally likely. There is an early consumer who has SW endowment at F0 and the utility function . ' 100 There is a late consumer who has $1,000 at t=1 and the utility function ab = cm + Cu +cL2. For questions (a) to (d), suppose a : 2 and w=$100. Suppose the rm issues equity at t=0. At F1, the equity market reveals whether the project is a success or failure. a) What equity contract does the rm offer the early consumer so as to get $100 to invest in the project? [3 Points] b) What is the expected prot of the rm? [1 Points] Now suppose the rm seeks bank nance. The bank provides loans to rms and keeps information secret. At t=2 the bank is liquidated and consumers who have deposits with the bank get back what the bank owns at t=2. The bank offers the early consumer the following demand deposit contract. If the early consumer deposits $100 at F0, he can withdraw $100 at t=1. c) What loan contract does the rm offer the bank so as to get $100 from the bank and the late consumer is willing to deposit? [2 Points] d) What is the expected prot of the rm? [1 Points] Now suppose the early consumer has a higher marginal valuation of consumption for the rst $100 and a = 4. His endowment is SW. e) If w=$100, is there equity issuance? Compared to (a) what is an intuition for this result? [4 Points] f) If w=$200, is there equity issuance? If so what is the prot of the rm? [7 Points]