I need to prove a sustainability condition given below for a homework assignment:
? ? (?D -?C) / (?D -?N)
?D is the profit that can be earned if a firm cheats on a collusion agreement, ?C is the profits that can be earned if the firm keeps the agreement, ?N is the profit a firm can earn in the Nash equilibrium after its cheating has been discovered, and ? is the discount factor.
Can anyone help me prove this? I don’t know where to even begin. Thanks.
Excuse me, please replace the first question mark with the symbol “Delta”, the second question mark with the symbol “greater than or equal to” and the question marks inside the parentheses should all be the symbol “Pi.” So the equation should read:
“Delta” is “Greater than or equal to” (PiD - PiC) / (PiD - PiN) Sorry about that. Thanks.
And one other follow up: The D, C, and N within the parentheses are all subscripts, so it is not Pi times D, it is Pi subscript D, for example. Now I am done. Thanks again.
Well, I’m glad I’m not the only one who is stumped. 
:bump:
I’m putting this one back on top one last time in hopes that a “math expert” might be see it.
Two things:
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We don’t do your homework for you. It’s your grade; you do it.
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We don’t know what you are allowed to use as a postulate/axiom. Even if we wanted to help you, we can’t.
Without knowing what “delta” represents, there is nothing to prove.
ultrafilter: I’ve seen posts on this site where people have asked general questions regarding assignments and the like, because they can’t find anyone who is able to help them. My friends, just as I, were stumped. I was merely asking a question, and did not mean to insult you. My apologies; in the future, I will remember that no one is to ask questions in the General Questions forum. My mistake.
manduck: Delta represents a discount factor. It doesn’t matter, though. I’ve figured out the problem. I had a mistake in my algebra, and corrected it with the help of an eraser.
ultrafilter: I however do understand your response in the context that I may have appeared eager in passing off a problem I could not solve. That was not my intention. I was merely aggravated that no one around me at the time was able to spot my error (one of my roommates [I’m at college] is a Math major, and even he wasn’t able to help me; although he was able to help me get the problem started). I had read these boards in the past and seen some very bright people on here, and figured maybe someone here would be able to help. Once again, I really wasn’t trying to “pass off” my work. I do apologise if it seemed that way. Thank you.
Now, nothing against you personally, TheLastBeginner, but this is what always gets me in these math problem threads. In your first post, you said you didn’t even know where to begin. But now you say you had already done the problem, but you made an algebra mistake. I’ve seen this with people I’m tutoring, too: if their answer does not match that in the back of the book, they assume they have no idea how to do the problem, even if the two answers are as simliar as 2sin(x)cos(x) and sin(2x). One of the most outstanding examples of this on this board was someone who asked for a theoretical dissection of the problem, when they already understood the problem fine, but their answer was in inches and the book’s was in feet. If you would just tell us the right answer and your answer to begin with, it would save a lot of time.
Sorry for rambling.
Achernar: I didn’t know how to begin when I first posted my question. But after a while thinking about it, I got the answer (at least, I think it’s the answer). Basically, I was trying to find the condition under which Delta is greater than or equal to (PiD - PiC) divided by (PiD - PiN), and Delta is equal to 1/(1+r). Under one condition, Pi subscript (present value) = PiC + PiC(Delta) + PiC(Delta)squared + PiC(Delta)n = (PiC)/(1-Delta)
Under the next condition: Pi subscript present value = PiD + PiD(Delta) + PiN(Delta) + PiN(Delta)squared + PiN(Delta)n = PiN(Delta)/1-Delta. In this respect: Pi subscript present value C = PiC/1-Delta = PiD + (PiN/1-Delta) = Pi subscript present value(PiDN)
Thus, (PiC - PiNDelta)/1-Delta = PiD. PiC -PiNDelta = PiD - PiC, and thus Delta = (PiD - PiC)/(PiD-PiN), and the equation is proven. (The above C’s, D’s, and N’s are all subscripts. It really is easier to see in symbol form). Okay, I promise I won’t bother anyone by bringing this thread back to the top again. Thanks!
That last part, that’s the key.
It’s nothing personal. But there is a standing board policy against doing homework. If you’ve got the answer and don’t really understand how to get it, or you’re pretty far but there’s one last bit you’re having trouble with, that’s fine. I’ve posted questions like that. What we don’t like to see is questions that sound like “do this homework problem for me.” Please don’t be insulted; no offense was intended. Welcome to the boards!
Apparently we’re okay with spanish homework.
Everybody makes their own choice, as to whether or not to help, but why are you so sure that was Spanish homwork?
That has to rank as one of the classiest apologies I’ve seen in a long time. Good to have you on board TheLastBeginner, hope you stay around.