This is an exercise on moral hazard in credit markets. Assume that a borrower must borrow 100 for an investment. The borrower can choose between a safe project yielding a return of R, with 100% probability and a risky project yielding a return of R, with probability p_r and a return of 0 with probability (1 - p_r). Assume that the lender cannot observe or control the type of project chosen by the borrower. What are the conditions for the borrower to choose the risky over the safe project under limited liability? What is the minimum level of collateral that will lead the borrower to choose the safe project instead? Alternatively, assume that the borrower has some money of his or her own to invest in the project that costs 100. Assuming that the bank cannot collateralize the loan, what is the maximum amount of the loan such that the borrower will prefer the safe over the risky project?