Consider a rm that wants to borrow $100. It has to post collateral to borrow (for example, mortgage-backed security). The value of the collateral is unknown. It is high quality with probability .5 , and its value is $120. With the remaining probability, its value is $20. If the firm defaults, it will give collateral to the bank. If the firm does not default, it pays $130. The probability of default of this firm is .3 . Suppose that the bank is risk-neutral and wants to maximize expected profit. a) Suppose that the bank knows for sure that the value of the collateral is 20. Show that the bank does not lend to the rm in this case