2. Suppose there are two types of potential borrowers. Half are Type A borrowers

Question

2. Suppose there are two types of potential borrowers. Half are Type A borrowers who have projects that require an investment of 1 unit. They have equal probability of returning 3 or 0 gross in one year. The other half are Type B borrowers, who have projects that also require 1 unit investment and a gross return of 8 with probability 1/8 or 0 with probability 7/8 in one year. Lenders require one unit gross in one year on one unit loaned (i.e. they will lend if they receive a net interest rate of 0). Assume that there is perfect competition so that lenders must earn their minimum (0 net) in any equilibrium.

First, find the equilibrium interest rates on the on loans to each in the case of symmetric information. (Note that they will differ.) Under asymmetric information, where the lenders cannot distinguish between types but know the distribution of potential borrowers, what equilibrium interest rate will be charged and who will borrow? Explain. Characterize the inefficiency that results from asymmetric information.

Explanation / Answer

The equilibrium interest rates on the on loans to Type A in the case of symmetric information will be such that

Present value expected returns = amount loaned

So, expected return = 0.5*3 + 0.5*0 = 1.5

So , 1.5/1+r = 1

1 + r = 1.5

r = 50%

Now , Similarly for type B

Expected returns = 8*1/8 + 0*7/8 = 1

S0, Present value of expected returns = 1/1+r

Present value of expected returns = Amount loaned

1/1+r = 1

r = 0

The combined expected returns = 0.5*[expected returns of typeA] + 0.5*[expected returns of typeB]

= 0.5*1.5 + 0.5*1

= 1.25

So the for required interest rate,

The present value combined expected returns = Amount loaned

1.25/1+r = 1

r = 25%

So equlibrium r = 25% . So only Type 1 borrower will take the loan

Due to the assymetric information, the lender cann't differentiate between the borrowers and hence cann't provide different interest rates as per their expected returns and hence inefficiency is created due to asymetric information.

If anything is not clear to you , you can comment , i can explain it in more details.

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