The government of Bolivia takes out a loan of fixed size (L) and agrees to pay r interest on it. The loan is extended by a group of large banks in New York. The loan is due in one year's time. If Bolivia chooses to default, it will lose a fraction c of its income (Y ) due to trade sanctions and other financial distress. The rest will be consumed. Otherwise, the country can pay principal and interest on the loan and consume whatever is left. The level of income in one year's time is unknown when the terms of the loan are decided. Both lenders and the borrower face the same uncertainty over its eventual realization.
(a) Write down expressions for the levels of consumption associated with defaulting and repaying, respectively. Use a diagram to argue that default will happen if and only if income in one year's time is below a certain threshold level. Solve for that threshold.
(b) Describe how the likelihood of default changes with the size of the loan, the share of income lost due to default, and the interest rate owed.
(c) The US banks extending this loan can borrow and lend freely at 3% per year, to each other and to other risk-free customers. Moreover, their analysts estimate Bolivia's default probability, given the size of the loan, to be 2%. What is the lowest interest rate r that the banks can charge Bolivia and still break even in expectation?
(d) In no more than 1 paragraph, explain intuitively why this setup might have two equilibria, one in which the interest rate is high and another in which Bolivia borrows cheaply.
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