This exercise helps explain how wealthier borrowers have greater investment opportunities. Consider two borrowers who are equally productive. Borrower 1 is rich. She has cash equivalent to A = \($50\) in her pocket. Borrower 2 is poor, lacking any cash. Both borrowers are interested in a project that requires an investment of \($100\). If they put in “adequate” levels of effort, either would get a gross return of y =

\($300\) with certainty. Otherwise, the probability of success is just 25 percent. The cost of exerting effort is c = \($145\), and the gross cost of lending capital per one dollar of a competitive bank is k = \($150\). Show that only the rich can invest. Is this efficient?