Question

Large number of independent loan prospects are available, each paying return of $16 on $100 with probability of 1/2 and 1/2 of $2 return. Each saver in economy derives happiness from income according to: H= I^(1/2) Competition between banks so each have costs--including normal profits--of $1.00 on every $100. What return will banks pay? Why? At this rate will they attract savers away from "going it alone" from lending directly, with each saver making a single loan? How do you know? What is the gain in happiness per saver from the existence of intermediaries? If there were a single intermediary with no competition, what return would the intermediary seeking maxim profit offer? Explain

Answer 1

The two probabilities are

.5=16
.5=4

10=.1+payout= 9.90
They will pay this to cover the cost the intermediaries incur. This will happen because if payout increases then intermediaries will not do it because they will be losing money and if payout decreases then more intermediaries will come into market until eventually price will be back to 9.90. At this rate, they will not chose to go alone because with the 9.90 return you will be getting 3.15 utils of happiness while going alone you will only get 3 utils of happiness. The gain of happiness per saver is .15 with intermediaries existing. I would expect an intermediary to payout 9 or 9.01 to make it better than going alone still but paying the minimum amount to the saver to maximize their profit.