UNIVERSAL SAVINGS & LOAN has $1000 to lend. Risk-free loans will be paid back in full next year with 4% interest. Risky loans have a 20% chance of defaulting (paying back nothing) and an 80% chance of paying back in full with 30% interest.
a. How much profit can the lending institution expect to earn? Show that the expected profits are the same whether the lending institution makes risky or risk-free loans.
b. Now suppose that the lending institution knows that the government will “bail out” UNIVERSAL if there is a default (paying back the original $1000). What type of loans will the lending institution choose to make? What is the expected cost to the government?
c. Suppose that the lending institution doesn’t know for sure that there will be a bail out, but one will occur with probability P. For what values of P will the lending institution make risky loans?