This exercise helps explain how the use of collateral facilitates investment. Consider the case of two borrowers. Borrower 1 has some collateral w = \($20\), unlike borrower 2 who has no collateral. Borrower 1 is as productive as borrower 2, so both can invest in projects that require \($100\), and produce a gross return y = \($190\) with certainty conditional on “adequate” levels of effort. But putting in the effort will cost c = \($20\). If the borrowers do not work hard enough, the probability of success falls to 50 percent. The gross cost of capital lent is K = \($140\) for each \($100\) loan. Show that if the lender can observe the effort made by each borrower, it is socially efficient to lend money to both borrowers.

If, on the other hand, the borrowers’ behavior cannot be observed, then show that only the one with collateral can borrow. (Note that the collateral itself cannot be invested in production.)