Question $2.$ Consider a risk$-$neutral no$-$discounting environment. Firms have projects

requiring one unit of investment and yielding $y$ with probability $p$ and $0$ otherwise. If the

project succeeds, the firm can invest another unit in a similar project in the following period.

Before providing a loan, banks have to incur, once and for all, a sunk cost $$ for collecting

info about the firm. Once this investment is made, the bank is able to grant future loans to

the same firm without any additional cost$-$benefit of maintaining a continued relationship

with the same bank.

Answer the following questions:

$(1$ point$)$ If there are two periods, is it beneficial for a firm to enter relationship

banking? Explain your answer.

$(5\mathrm{.}5$ points$)$ Suppose that there are three periods. If a firm and a competive bank

enter relationship banking for three periods, what will be the interest rates charged

for each period? Explain your answer.

$(1$ point$)$ In the case of three periods, should a firm enter three$-$period relationship

banking, two$-$period relationship banking $($starting from the first period or second

period$),$ or no relationship banking at all? Explain your answer.