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Monday, May 12, 2008
[a] 9:34 AM

Economics anyone?

There are 6 types of investment projects.
Safe investment projects yield an output q in all states of the world.
Risky investment projects yield an output of 2q in the "good" state of the world (probability 1/2) and 0 in the "bad" state of the world (probability 1/2).
Lucrative investment projects yield an output of 3q in the "good" state of the world (probability 1/2) and 2q in the "normal" state of the world (probability 1/4) and q in the "bad" state of the world (probability 1/4).
Profitable projects yield an output of 4q in the "good" state of the world (probability 1/3) and 2q in the "normal" state of the world (probability 1/3) and q in the "bad" state of the world (probability 1/3).
Powerful projects yield an output of 5q in the "good" state of the world (probability 1/6) and 2q in the "normal" state of the world (probability 1/6) and q in the "bad" state of the world (probability 2/3).
Incredible projects yield an output of 6q in all states of the world.

1000 investors are aware of safe projects with q(low)= 1, 1/2 the time, and q(high)=2, 1/2 the time (because these are safe projects, they know whether the quality is low or high).
1000 investors are aware of the risky projects, with quality distributed as before. Because these are risky projects, they do not know whether the quality will be low or high (they know the project is risky with outcomes 0 or 2q but do not know whether the intrisic is 1 or 2.)
1000 investors are aware of the lucrative projects, with quality as described above. Because these are lucrative projects, investors who get "bad" state of the world die after getting it and cannot return the loan. However, only 1/5 of the investors who get "bad" states die. The rest of the 4/5 are able to return their loan as they are deemed to be "richer" than the people who invest in safe and risky projects. Assume that 0< E<2.
1000 investors are aware of the profitable projects, with quality distributed as before. Because these are profitable projects, they do not know whether the quality will be low or high. Assume that 0< e<1.
1000 investors are aware of the powerful projects, with quality distributed as before. Because these are powerful projects, they know whether the quality will be low or high. Quality is distributed normally with mean 5 and variance 3. Assume that there is NO equity.
1000 investors are aware of the incredible projects, with quality distributed as before. Since incredible projects always yield 6q in all states of the world, the lender will charge an interest that is double of the intrinsic value of q. q, in this case, has uniform distribution [1,8].

(a) What is the demand for loans when i = 1?
(b) What is the demand for loans when i = 2?
(c) Assume that the lenders lend out the loans "on premium", they charge 75% less for lenders who are able to return the loans. What is the demand for loans at i = 1?
(d) Find the profit-maximising value of i so that lenders can make the most money.
(e) Given the distribution of the incredible projects [1,8], find the pdf and subsequently find the moment generating function. Comment on how useful it is in determining whether an investor borrows or not.

This is an economics question that dearest tag asked me (and i'm sure a lot of other ppl) this morning. can see how free he is right, still can design his own question. -.-