Consider exercise 8, except that in this case, the utility function of the man is now um = (x0.8/0.8) and that project 2 yields a gross return of $1,120 with 50 percent probability and zero otherwise. To whom will the bank decide to extend the loan in this case?

Data from in exercise 8

Consider a man and a woman who request a loan of size I from a bank. If the loan is obtained by either individual, it can be invested in either of the following two projects. If invested in project 1, which involves an investment I, the yield is y1 = \($520.\) If invested in project 2, which also requires an investment I, the yield is y2 = \($1,020\) with 50 percent probability and zero otherwise. Suppose that the man is risk neutral and only seeks to maximize expected profits, while the woman is risk-averse. Her utility function is u_w = (x0.5/0.5), and both the man and the woman are assumed to both start with zero wealth. Suppose that the gross interest rate set by the bank is R = \($120,\) and that this rate is fixed. Borrowers are protected by limited liability. Will the bank decide to lend to the man or to the woman?