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05-04-2010, 04:51 AM | #2 |
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I have finished A, B, and D.
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05-04-2010, 04:52 AM | #3 |
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i = any whole number (1 to 12)
n = Any whole number (0 to 11) N = 12 B(i,n) = 2.2 + n - i S(i,n) = i - n |
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05-04-2010, 04:52 AM | #4 |
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****, at 6:51am you're asking for the answer?! Chiefsplanet can hardly read english or numbers...
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05-04-2010, 04:56 AM | #5 |
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A:
i = 1 Country (i = 1) will choose option IN as long as B(1,0) > S(1,0) and [B(1, n + 1) - S(1,n)] > 0 B(1,0)= 2.2 + 0 - 1 = 1.2 > S(1,0) = 1 - 0 = 1 1.2 > 1 and B(1,n+1) - S(1,n) = 2.2 + 1 - 1 - (1-0) = 1.2 1.2 > 0 Marginal gain of choosing IN with respect to n is B(1,n') which is 1. Marginal gain of choosing OUT with respect to n is S(1,n') which is -1. For all n: (0 through 11), country (i = 1) is better off choosing IN. |
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05-04-2010, 05:01 AM | #6 |
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B is really similar, it's just that you've proved n must be >= 1 since we have proven that country (i=1) will choose IN, so N now must = at least 1.
B: i=2 Country (i = 2) will choose option IN if: B(2,n+1)-S(2,n) > 0 2.2 + 2 - 2 - (2 - 1) = 0.2 0.2 > 0 Therefore, Country (i = 2) will choose IN for all n. |
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05-04-2010, 05:04 AM | #7 |
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C is what I can't figure out.
Do they want me to do the same steps from B for all i: (3-12) manually? Or is there some mathematical proof I'm missing that would prove that the minimum n will always be i -1, and then using that I can prove that all countries must choose IN (Payoff B)? |
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05-04-2010, 05:05 AM | #8 |
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D is pretty easy, I just need a payoff table for all i where n = 11, then compare that payoff table to when n = 0.
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05-04-2010, 05:05 AM | #9 |
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Any and all help will be much appreciated it. I'm going to nap for a few hours before class and hopefully figure this out then.
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05-04-2010, 05:07 AM | #10 |
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There are a lot of really smart planeteers. I'm hoping one or more of them that are really bored at work this morning will take a few minutes to ponder this for me. I've been up all day and night working on papers, homework, and studying for finals. I hate this time of year.
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05-04-2010, 05:11 AM | #11 | |
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Quote:
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05-04-2010, 05:17 AM | #12 |
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D: Tables
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05-04-2010, 05:20 AM | #13 |
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D:
From the tables, looks to me that 6 countries lose out by the formation of the union. That finishes the problem other than C. I just don't think manually working through each i is what the problem is asking for there. Seems to menial and basic. Please let me know if any of you come up with a proof. |
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05-04-2010, 05:22 AM | #14 |
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I swear they call up everything from 7th grade through College level Calc 2 and I simply cannot recall everything on demand like they want. The math isn't crazy hard by any means, it's just too much for me at this ungodly hour. Night.
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05-04-2010, 05:24 AM | #15 | |
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Quote:
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