Problem 1: Assume a project has a probability of success of p_H=0.8 if the borrower behaves and p_L=0 if the borrower misbehaves. The size of the investment is I = $1,000,000. If successful, the project earns $1,300,000. Selling off the equipment after it has been purchased would earn the borrower $500,000. The risk-free interest rate is zero. How much income can the borrower maximally pledge?How much of her own wealth does the borrower need to invest?Verify that the borrower actually wants to behave and that the investor fulfils its participation constraint! How small would the scrap value need to be to allow for a contract where no own wealth of the borrower is invested?

Problem 2 Assume an entrepreneur wants to undertake a deepening investment. The basics of the original contract are as follows (abbreviations as in the lecture slides):

I = 794,000, p_H = 0.99, p_L=0.79, R = 1,000,000, A = 200,000, B = 80,000.

The new investment is debt financed and yields p_H'=1 and p_L'=0.8 at a cost of J=20,000.

a) What is R_l and R_b in the original contract if the borrower spends A = 200,000? Demonstrate that the original contract fulfills the participation constraint of the original lender and the incentive compatibility constraint of the entrepreneur (borrower).b) Consider the new debt contract. Will investors expect the entrepreneur to exhibit good behaviour? What is R_l' and R_b'?

c) What would the new private benefit B' need to be to make misbehaving an equilibrium outcome after the investment has been realized?