Suppose two types of firms wish to borrow in the bond market. Firms of type A are in good financial health and are relatively low risk. The appropriate premium over the risk-free rate for lending to these firms is 2%. Firms of type B are in poor financial health and are relatively high risk. The appropriate premium over the risk-free rate for lending to these firms is 6%. As an investor, you have no other information about these firms except that type A and type B firms exist in equal numbers. A. At what interest rate would you be willing to lend if the risk-free rate were 6%?
B. Would this market function well? What type of asymmetric information problem does this example illustrate?

A. I would be willing to lend at average rate of 10%

B-1. No, this market will not function well.

B-2. This example illustrates an adverse selection problem.

Explanation:

A. At what interest rate would you be willing to lend if the risk-free rate were 6%?

Appropriate interest rate for type A firm bond = Premium over the risk-free rate of Type A firm + Risk-free rate = 2% + 6% = 8%

Appropriate interest rate for type B firm bond = Premium over the risk-free rate of Type B firm + Risk-free rate = 6% + 6% = 12%

Average rate = (Appropriate interest rate for type A firm bond + Appropriate interest rate for type B firm bond) / 2 = (8% + 12%) / 2 = 10%

Since the probability of any of the two firms is equal and I do not have the knowledge of which type of firm they are dealing with, I would be willing to lend at average rate of 10%.

B-1. Would this market function well?

No, this market will not function well.

The reason is that the average rate of 10% is higher than the Appropriate interest rate for type A firm bond of 8%. This would make the type A firm to withdraw from the market and only type B firm will be left in the market.

B-2. What type of asymmetric information problem does this example illustrate?

This example illustrates an adverse selection problem. This is because after type A firm which is a desirable leaves the market, only type B firm which is  the less desirable firms will be willing to borrow. This makes the quality of the market to detoriorate.

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