This question examines the problem of lending money to entrepreneurs, possibly in the presence of informational frictions. Here is the basic setup. Entrepreneurs start with initial wealth I/VO = 1. They have a project to create a startup, which requires 2 in initial investment. If the startup is successful, it will be worth 4 in the end (that is, the total profit associated with the investment is 4-2=2). On the other hand, if the startup fails, it will be worth zero. Each item below specifies the probability of success, along with the utility function of the entrepreneur. Entrepreneurs may try to create the startup or not. If not, the final wealth is equal to the initial wealth. If they want to create the startup, they must get a loan from a bank, because the initial investment is more than their initial wealth. We will assume that banks are risk neutral, so they make choices that maximize their expected profit associated with the lending operation. Because the startup will be set as a Limited Liability Company (LLC), we will assume that, if the project fails, the bank will just lose the money it loaned. So the loan contracts specify two things: (i) the amount loaned, L; and (ii) the amount the entrepreneur pays back to the bank if the project is successful, R. The utility of the entrepreneur over final wealth is u(w) = 10g2(w). Hint: 10g2(0.5) = 1 10g2(1) = 0 10g2(1.5) m 0.585 log2(2) = 1 10g2(3) m 1.585 10g2(4) = 2