An entrepreneur with initial wealth l - I dollars has a new project in which to invest. To com- plete the project the entrepreneur needs additional l dollars that they can borrow from a bank. If they borrow (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. If the entrepreneur does not borrow the money they keep the l 1 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 of tupe j = L. H if they borrow at rate 1'? Show that a type L will borrow ifand only ifi i1, (c) What are the bank's updated beliefs about the entrepreneur's type if a loan is taken at i > :1? At 1'