Question

Two independent loan prospects exist, call them A and B. Both will pay the agreed-upon $12 return (on $100) with probability 3/4. With probability 1/4, on the other hand, they default and pay only $4.00. a. For an individual saver investing in one or the other, what is the average return (expected return)? What is the variance? b. Suppose that an intermediary forms by merging the funds of the 2 savers and investing in both projects, splitting the total return equally between the 2 savers. What is the average return to the individual saver? What is the variance? c. Compare a. and b. Does your result confirm the Law of Large Numbers? Explain.

Answer #1

A large number of independent loan prospects are available, each
paying a net return (on $100) of $16 with probability 1/2 and $2
with probability 1/2. There are as many savers as loans, each with
$100. Each saver in the economy derives Happiness (H) from income
(I) according to :
H= (square route) I
There is competition between intermediaries and each
costs--including "normal" profits--of $1.00 on every $100 invested.
What return will intermediaries pay? Why? At this rate will they...

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...

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