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Consider a borrower who needs exist100 at, t = 0 to invest in a project that will pay off at t = 1. The borrower can choose between two mutually exclusive projects, S and R. Project S will yield a payoff of exist300 with probability 0.9 and nothing with probability 0.1. Project R. will yield a payoff of exist400 with probability 0.6 and nothing with probability 0.4. The borrower has sufficient personal assets that can be used as collateral. However, liquidating the assets at t = 0 to finance the project is prohibitively costly. As such, the borrower has to solicit the entire amount of exist100 from a bank at t = 0. Assume that collateral worth exist1 to the borrower is worth only 80 cents to the bank. There are no taxes and no bankruptcy costs. Everybody is risk neutral and the riskless rate of interest is 10%. The bank is competitive in that it earns zero expected profits. Suppose that the bank is able to directly control the borrowers choice of project. Which project will the borrower choose? Why? Suppose that the bank is unable to directly control the borrowers choice of project. Which project will the borrower choose if the bank loan contract consists of the interest rate only? How large is the agency cost due to the asset substitution problem in this case? Suppose that the bank is unable to directly control the borrowers choice of project. Which project will the borrower choose if the bank loan contract consists of not only the interest rate but also the collateral requirement? How much should the borrower pledge as collateral? How large is the agency cost due to the asset substitution problem in this case? Comparing parts (b) and (c), why is there a reduction in the agency cost due to the asset substitution problem when collateral is used