We have an economy with a proportion \alpha of "good" firms, and a proportion of 1-\alpha of "bad firms". All firms have the opportunity to invest in a project requiring an investment cost I=50, which gives a payoff X=100 if succesfull and zero if unsuccessfull. Good firms are always credit worthy and have a probability of success equal to 0,7, whereas bad firms only have a 0,4 probability of succeeding. All firms have to borrow the full investment cost from a perfectly competitive banking sector. Firms know their own type but banks are unable to distinquish between good and bad firms. All agents are risk neutral and indifferent with regard to the time allocation of consumption.
- What is the minimum proportion of good borrowers in the economy required for banks to be willing to lend?
- What is the interest rate that banks will charge at this proportion?
Now suppose that these is a business cycle upswing which doubles the proportion of good borrowers (the proportion of bad borrowers drops correspondingly), and that this change is expected to last for the duration of the investment project. Further assume that the project runs over 5 years. Everything else is unchanged.
- What is the annual interest rate charged by banks?