Question

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 𝑟 𝑔 r g with probability 𝑝 𝑔 p g . With probability 1 − 𝑝 𝑔 1−p 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 𝑟 𝑏 r b with probability 𝑝 𝑏 p b . With probability 1 − 𝑝 𝑏 1−p 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 𝑟 𝑔 < 𝑟 𝑏 r g 𝑝 𝑏 p g >p b , and 𝑝 𝑔 ( 1 + 𝑟 𝑔 ) > 𝑝 𝑏 ( 1 + 𝑟 𝑏 ) p g (1+r g )>p b (1+r b ). The lender can’t observe in which project the borrower invests and so it charges all borrowers the same interest rate 𝑟 𝐿 r L . The lender lends an amount 𝐿 L and pays interest 𝑟 𝐷 r D on funds acquired from depositors. Question 1.1

          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 
𝑟
𝑔
r 
g
  with probability 
𝑝
𝑔
p 
g
 . With probability 
1
−
𝑝
𝑔
1−p 
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 
𝑟
𝑏
r 
b
  with probability 
𝑝
𝑏
p 
b
 . With probability 
1
−
𝑝
𝑏
1−p 
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 
𝑟
𝑔
<
𝑟
𝑏
r 
g
𝑝
𝑏
p 
g
 >p 
b
 , and 
𝑝
𝑔
(
1
+
𝑟
𝑔
)
>
𝑝
𝑏
(
1
+
𝑟
𝑏
)
p 
g
 (1+r 
g
 )>p 
b
 (1+r 
b
 ).
The lender can’t observe in which project the borrower invests and so it charges all borrowers the same interest rate 
𝑟
𝐿
r 
L
 . The lender lends an amount 
𝐿
L and pays interest 
𝑟
𝐷
r 
D
  on funds acquired from depositors.
Question 1.1

Added by Natalie D.

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