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Exercise 2 [20 points]: A risk neutral entrepreneur borrows 25,000 from a risk neutral bank and invests it in one of two projects: a safe one and a risky one. The returns from this investment are verifiable but they are subject to some uncertainty. The table below gives the probabilities of reaching each possible returns for each project. X = 5,000 X = 40,000 X = 50,000 Risky Project 0.4 0.2 0.4 Safe Project 0.2 0.7 0.1 The bank manager and the entrepreneur have signed a contract whereby the entrepreneur must repay R(x) when he obtains returns X. The entrepreneur is then left with a profit m = X-R(X) while the bank gets " = R(X) There is no need to subtract the 25,000 which is a sunk cost for the bank. The entrepreneur is protected by limited liability meaning that when X = 5,000 he cannot repay the loan. This means that R(5,000) = 0. Repayments are made when X = 40,000 or when X = 50,000. The two parties play a sequential game and the timing is the following First, the bank manager proposes one of four contracts which are detailed in the table below. R(5,000 (40,000 R(50,000) Contract A 0 30,000 30,000 Contract B 29,000 31,000 Contract C 0 27,000 33,000 Contract D 26,000 34,000 0 0 i. Second, the entrepreneur, aware of the repayments that he must make, selects a project. (8 points) Explain what happens when each one of these contracts is proposed to the entrepreneur (6 points) Which contract should the bank manager offer to the entrepreneur? (Explain why.) (6 points) Assuming that the bank manager is told that he should make sure that the risky project is selected, what contract should he offer? ii. . iii. Exercise 2 [20 points]: A risk neutral entrepreneur borrows 25,000 from a risk neutral bank and invests it in one of two projects: a safe one and a risky one. The returns from this investment are verifiable but they are subject to some uncertainty. The table below gives the probabilities of reaching each possible returns for each project. X = 5,000 X = 40,000 X = 50,000 Risky Project 0.4 0.2 0.4 Safe Project 0.2 0.7 0.1 The bank manager and the entrepreneur have signed a contract whereby the entrepreneur must repay R(x) when he obtains returns X. The entrepreneur is then left with a profit m = X-R(X) while the bank gets " = R(X) There is no need to subtract the 25,000 which is a sunk cost for the bank. The entrepreneur is protected by limited liability meaning that when X = 5,000 he cannot repay the loan. This means that R(5,000) = 0. Repayments are made when X = 40,000 or when X = 50,000. The two parties play a sequential game and the timing is the following First, the bank manager proposes one of four contracts which are detailed in the table below. R(5,000 (40,000 R(50,000) Contract A 0 30,000 30,000 Contract B 29,000 31,000 Contract C 0 27,000 33,000 Contract D 26,000 34,000 0 0 i. Second, the entrepreneur, aware of the repayments that he must make, selects a project. (8 points) Explain what happens when each one of these contracts is proposed to the entrepreneur (6 points) Which contract should the bank manager offer to the entrepreneur? (Explain why.) (6 points) Assuming that the bank manager is told that he should make sure that the risky project is selected, what contract should he offer