Assume that a bank can choose two dierent projects, a safe project and a risky project. The safe project delivers a payo of 1 for sure to the bank and a payo of 1 for sure to the consumers. On the other hand, the risky project delivers a payo of 3 to the bank and 1 to the consumers with 50 percent probability. However, there is also the remaining 50 percent probability that the risky project busts and delivers a payo of -3 to banks and -3 to consumers.
(a) Discuss why one bank going into a bust might cause a severe negative payoff to consumers (no math here)
(b) What is the expected payoff of banks if it chooses a risky project? Assume that the bank chooses its investment project that delivers higher (expected) payoff. Which project will the bank choose? Which project will the consumers prefer?
(c) Assume that the bank for some reason chose the risky project and the project busted. The government is considering whether it should bailout the bank. If the government chooses to bailout the bank if the project busts, then the bank will now get a payoff of 0 (instead of -3) and consumers will get a payoff of -1 (instead o -3). Hence given that the bank project ran into a bust, the consumer would always prefer the government to bailout the bank. Suppose that the bank understands this bailout policy. What will be the bank's new expected payoff when choosing the risky project?
(d) with government bailouts taken into account, which project will the bank choose? Com pare with (b)
(e) Suppose that the government is able to commit to not bailing out the bank. What project will the bank choose?
(f) In practice, what are the difficulties that the government might face when it commits to not bailing out a bank?