Problem: A large number of independent loan prospects are available, each paying a net return (on $100) of $16 with probability 3/4 and $4 with probability 1/4. There are as many savers each with $100 to lend, as there are loans. Each saver derives Utility (U) from income (I) according to:
U = sqrt(I)
There is competition between intermediaries and each has costs --including "normal " profits --of .40 on every $100 invested
1. What return will intermediaries pay? Why ?
2. At this rate will they attract savers away from " going -it - alone-- i.e. from lending directly , with each saver making a single loan ? How do you know ?
3. What is the gain in utility per saver from the existence of intermediaries ?
4. If there were a single intermediary with no competition, what return would the intermediary seeking maximum profit offer? Explain.