Answer Happy

A) In the current period, a consumer gets an endowment y and pays lump-sum tax t. In the future period, the consumer is endowered with y' and faces the lump-sum tax of t'. The consumer can borrow at the rate r2 and lend at the rate r1, where r1<r2. The fraction of the borrowers defaulting is (1-a), so a is the fraction of good borrowers in the population. For each Lunits of deposits acquired by the bank, the bank will have to pay out L(1-r1) to depositors in the future period; the average payoff to the bank will be al(1-r2). Derive equilibrium r2 and illustrate the effect of a decrease in creditworthy borrowers on the consumer's lifetime budget constraint in a diagram. B) Now suppose a credit market has "a" good borrowers and (1-a) bad borrowers. The borrowers are all identical and always repay their loans. Banks issue deposits that pay a real interest rate r and make loans to borrowers. Bank cannot tell the difference between a good borrower and a bad one. Each borrower has collateral that worth "A" units of future consumption. i) Determine the interest rate on. loans made by banks and explain how the interest rate change if each borrower has more collateral.