Ex ante Moral Hazard

In this scenario we$$re going to simplify and assume the borrower needs $1$ unit of capital

from the lender. Once he gets the loan, he has two choices in investments:

$$A "safe" project that yields yS with certainty

$$A "risky" project that yields yR with probability p and $0$ with probability $1-$p

The lender lender lends at gross rate i$,$ so she requires i to be paid back for the $1$ unit

lent.

$[$No response required$]$

$1.$

$($a$)$ What is the borrower$$s net payout to investing in the safe project?

$($b$)$ If the borrower invests in the risky project, two things can happen.

$2$

i$.$ If the project succeeds, he has to repay the lender. What is his payout in this case?

ii$.$ If the project fails, he doesn$$t have to repay. What is his payout?

iii. What is the borrower$$s expected payout to the risky project? $($Hint: multiply the

payout in each state$$succeed or fail$$ by the probability and add them together$)$

Use formula L$($p x i $-$ r$)=$ expected profit. L$=$loan amt, p$=$probability, i$=$interest rate, r $=$cost of capital