Financial Market Imperfections (Stiglitz and Weiss)

"Theorem 1: For a given interest rate \(\hat r\), there is a critical value \(\hat \theta\) such that a firm borrows from the bank if and only if \(\theta > \hat \theta\).
Theorem 2: As the interest rate increases, the critical value of \(\theta\), below which individuals do not apply for loans, increases.  
Theorem 3: The expected return on a loan to a bank is a decreasing function of the riskiness of the loan.
Theorem 4: If there are a discrete number of potential borrowers (or types of borrowers), each with a different \(\theta, \bar \rho (\hat r)\) will not be a monotonic function of \(\hat r\) since as each successive group drops out of the market, there is a discrete call in \(\bar \rho\) (where \(\bar \rho (\hat r)\) is the mean return to the bank from the set of applicants at the interest rate \(\hat r\))."