申論題

1.Consider a two-period endowment model with income (y and y') and the consumer pays lump-sum tax (t and t') in the current and future period, respectively. The consumer chooses consumption (C and C') in the current and future periods, and saving (s) in the current period. The real interest rate is r. Consider that a representative consumer lives in this two-period economy and has a convex preference over the current and future consumption. [50 pts]

(d) Suppose that the ratio of good borrowers is 2 (0<λ<1) and that of bad borrowers is (I-λ) in the credit market. The good borrowers are all identical, and always repay their loans. Bad borrowers never repay their loans. Banks issue deposits that pay a real interest rate "p" to a lender, and make loans to borrowers. Banks cannot tell the difference between a good borrower and a bad one. Consider that banks are in a perfectly competitive market and make zero profits. Find the interest rate on loans (i.e., the interest rate paid by a borrower) determined by banks. Explain the details how you derive it, and whether it is higher or lower than r. Besides, show the consumer's lifetime budget constraint in a figure with C' on the vertical axis and C on the horizontal axis. [10 pts]