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A bank has $1000 to lend and is choosing whether to lend to a safe borrower or a risky borrower. If it lends to the safe borrower, the bank will be paid back the full amount plus 6% interest for sure. If it lends to the risky borrower, there is an 80% chance that it is paid back in full plus 25% interest, and a 20% chance that the borrower defaults on the loan (doesn't pay anything back).
a) Which borrower would the bank prefer to loan to? Calculate the expected profits in each case.
b) Suppose the bank knows that if the risky borrower defaults, there will be a partial government bailout, where the government pays back $600 of the original $1000 loan. Now which borrower will the bank choose, and what is the expected profit? What is the expected cost for the government?
c) Now consider the case that the bank thinks there is a possibility of a government bailout (like in part b), but isn't sure. What probability of bailout does there have to be in order for the bank to want to make risky loans?
d) Which market failure concept is exhibited here?
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