An entrepreneur with initial wealth 1- 1 dollars has a new project in which to invest. To com- plete the project the entrepreneur needs additional I dollars that they can borrow from a bank. If they borrow l dollars. they invest the 1 euro in the project. With probability p the project succeeds and brings R > 1 dollars and with probability 1 p it fails and brings 0.11\" the entrepreneur does not borrow the money they keep the l l dollars (outside option]. There are two types of entrepreneurs: those who have good projects with a high probability of success p = p" and those who have bad projects with a lower probability of success p = pL I. How can we interpret this assumption? {b} What is the expected payoff ofan entrepreneur oi tupe j = L. H if they borrow at rate 17 ? Show that a type L will borrow if and only ifi i L. (c) What are the bank's updated beliefs about the entrepreneur's type if a loan is taken at i > :1? At i