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RISK, UNCERTAINTY AND INFORMATION
LECTURE 5 CREDIT RATIONING

Credit rationing exists when some borrowers cannot obtain loans, even though indistinguishable from other borrowers who do obtain loans. The rate of interest (which differs from a lender‟s expected rate of return because of the risk of default) influences the quality of a loan, by acting as: (a) a screening device; (b) an incentive device. “Both effects derive directly from the residual imperfect information which is present in loan markets after banks have evaluated loan applications.” (Stiglitz and Weiss) Thus, for lenders, such as banks, there may be an optimal rate of interest. When there is, credit rationing may exist, even in equilibrium. The lender does not respond to excess demand for loans by raising the rate of interest above its optimal level.
1. Model 1
A lender is faced by borrowers, indexed by θ. A borrower who obtains a loan invests in a specific project. All projects have the same mean return, but risk increases with θ. The (gross) return on a project, denoted by R, is uniformly distributed between k and s, where s-k increases with θ. (The increase in s-k is an example of an increase in „mean preserving spread‟ and implies an increase in R‟s variance.) The amount of a loan is B, the rate of interest r and collateral C. There is limited liability. The lender‟s and borrower‟s returns are, respectively:
ρ(r,θ)= min [B(1+r), C+R]
π(r,θ)= max [RB(1+r), C].
ρ π
B(1+r)
C B(1+r)C R
B(1+r)C R C
2
The borrower‟s expected return is:s
k
R B r C dR
s k
max[ (1 ), ] .
1
Π is decreasing in r and, since π(r,θ) is convex, increasing in θ. Suppose, for given r,
Π=0 when θ=θ̃. Borrowers for whom θ<θ̃ find loans unprofitable and exit the market.
Borrowers for whom θ>θ̃ find loans profitable and remain in the market . As r
increases , the threshold for borrowers , θ̃, also increases.
Π
r1
r2
θ̃1 θ̃2 θ
θ̃ increases from θ̃1 to θ̃2 when r increases from r1 to r2.
The lender‟s expected return is:
  1
Ω is increasing in r and, since ρ(r,θ) is concave, decreasing in θ.
Suppose there are several distinct classes of borrower . As r increases , θ̃ increases.
First, the class with the safest projects leaves the market, then the class with the next
safest, etc. When a class exits the market, EΩ falls. C lasses with riskier projects
remain in the market, i.e. increasing r causes adverse selection. Thus, typically, there
exists a value for r, r=r*, that maximizes the expected return to the lender, averaged
over borrowers. This optimal value for r can be an equilibrium rate.

0 r* r
3
2. Model 2
Consider next a borrower who can choose either a safe or a risky project. Denote
these by θ1 and θ2. The return to the safe project is R
~
, and the return, R, to the risky
project, which has a lower mean, is uniformly distributed between k and s. The
amount borrowed is B, the rate of interest r and collateral C. As r increases (1+r < R
~
),
the borrower initially chooses θ1. However, at some critical value for r, r=r*, the two
projects yield the same expected return to the borrower. At higher levels of r, he or
she chooses the risky project. r* 论文英语论文网提供整理，提供论文代写英语论文代写代写论文代写英语论文代写留学生论文代写英文论文留学生论文代写相关核心关键词搜索。