Suppose the market for loans is made up of 75% low default risk borrowers and 25%...

Suppose the market for loans is made up of 75% low default risk borrowers and 25% percent high default risk borrowers. A financial intermediary must collect a 3% interest rate on a low-risk loan and 9% interest rate on a high risk loan in order to be profitable. Assume the financial intermediary cannot verify whether a borrower is high-risk or low-risk. However, the intermediary knows that low-risk borrowers are willing to pay a 4% interest rate and high-risk borrowers are willing to pay a 10% interest rate. What is the minimum interest rate the intermediary will charge?

The answer is 9 but how...

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Expert Solution

Given the information the intermediary knows that if it charges an interest rate of 4% from all types of borrowers, this decision will not be profitable because it must collect 3% on low-risk loan and 9% on high risk loan. Charging an interest rate less than 9% will attract both type of borrowers and this will be unprofitable. Therefore the best possible decision in this case is to charge a minimum rate of interest of 9% so that all the low risk borrowers are driven out of the market and the intermediary has full information that all the leftover borrowers are high risk.

Rahul Sunny answered 1 year ago

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