problem: Consider a world with two points in time, t0 and t1. John Smith has just inherited 5 million dollar. He has only two projects he can invest in. Project A costs 3 million dollar at t0 and pays off 3.8 million dollar at t1. Project B costs 2 million dollar at t0 and pays off $2.5 million at t1. He can lend and borrow at a bank at an interest rate of 20%. John is only interested in consumption today at t0. He does not get any utility from consumption at t1.
[A] What is the most John can consume at t0? How does he achieve this, i.e., what projects does he do, and how much does he borrow or lend at the bank?
[B] How would your answers to [A] be changed if John could lend to the bank at a rate of 15% but could borrow at 30%?