Consider an economy with risk-neutral individuals. And suppose the following timing of events: At date 0, an individual wants to borrow an amount I in order to invest in a project that yields a gross return y with certainty at date 1. The bank cannot verify the return realization on that individual’s project, but it knows that the return should be y. Now suppose that, conditioning on the borrower repaying an amount R, the bank will extend a new loan of size I at date 1. The borrower then invests the entire proceeds from the new loan I, and obtains y at date 2 with certainty. But if the borrower defaults at date 1, that is, if she fails to repay R, the bank does not extend a new loan I at date 1.

Therefore, the borrower can not invest. The lender’s gross cost of lending I is K. Let d denote the borrower’s discount factor. Define the R at which the bank would wish to extend a loan and the borrower would wish to repay.

a. If I = \($100;\) y = \($200;\) K = \($150;\) δ = 0.9, and the bank is an NGO that just wants to break even, is there scope for lending and borrowing?

Explain your answer.

b. Now suppose that y = \($360,\) and assuming everything else remains same, would you expect borrowing and lending in this case? Explain your answer.