A competitive lender makes loans to a pool of borrowers that are identical. After borrowers have received their loans they choose one of two investment projects. Project G pays the borrower a rate of return of
π
π
r
g
with probability
π
π
p
g
. With probability
1
β
π
π
1βp
g
, the project earns a zero rate of return, the borrower defaults on the loan, and the lender receives back the initial loan amount. Project B pays the borrower a rate of return of
π
π
r
b
with probability
π
π
p
b
. With probability
1
β
π
π
1βp
b
, the project earns a zero rate of return, the borrower defaults on the loan, and the lender receives back the initial loan amount. We assume that
π
π
<
π
π
r
g
π
π
p
g
>p
b
, and
π
π
(
1
+
π
π
)
>
π
π
(
1
+
π
π
)
p
g
(1+r
g
)>p
b
(1+r
b
).
The lender canβt observe in which project the borrower invests and so it charges all borrowers the same interest rate
π
πΏ
r
L
. The lender lends an amount
πΏ
L and pays interest
π
π·
r
D
on funds acquired from depositors.
Question 1.1