Assumptions: ----------- A catastrophe is an event that prevents the utilitarian from making a donation. Examples: - World is destroyed - Stock market crashes permanently - Utilitarian becomes apathetic and stops caring. In any given year, the probability that a catastrophe happens by next year is 0.01. Annual rate of inflation = 3%. Annual rate of return on stock-market investments = 12%. Interest rate on loans = 6%. Year right now = 2007. Age right now = 19. Lifespans are determined as the average of 2 random draws from a uniform distribution of integers between 63 and 93. Years of retirement is determined by this formula: (lifespan - 63)/3 + 10, except that years of retirement cannot be lower than 4 or higher than 20. Amount of wealth utilitarian starts with = 0. Here is a list of values for what income and cost of living would be (in 2007 dollars) if the utilitarian had the listed status: Status = undergrad In year 1 of this status, income = 0 and cost of living = 0. In year 2 of this status, income = 0 and cost of living = 0. In year 3 of this status, income = 0 and cost of living = 0. In year 4 of this status, income = 0 and cost of living = 0. Status = gradSchool math or science In year 1 of this status, income = 10,000 and cost of living = 0. In year 2 of this status, income = 11,250 and cost of living = 0. In year 3 of this status, income = 12,500 and cost of living = 0. In year 4 of this status, income = 13,750 and cost of living = 0. In year 5 of this status, income = 15,000 and cost of living = 0. In year 6 of this status, income = 15,000 and cost of living = 0. Status = working average property/casualty actuary In year 1 of this status, income = 53,000 and cost of living = 33,000. In year 2 of this status, income = 60,000 and cost of living = 33,000. In year 3 of this status, income = 65,000 and cost of living = 33,000. In year 4 of this status, income = 70,000 and cost of living = 33,000. In year 5 of this status, income = 78,000 and cost of living = 33,000. In year 6 of this status, income = 86,000 and cost of living = 33,000. In year 7 of this status, income = 95,500 and cost of living = 33,000. In year 8 of this status, income = 105,000 and cost of living = 33,000. In year 9 of this status, income = 112,500 and cost of living = 33,000. In year 10 of this status, income = 120,000 and cost of living = 33,000. In year 11 of this status, income = 132,666 and cost of living = 33,000. In year 12 of this status, income = 145,332 and cost of living = 33,000. In year 13 of this status, income = 158,000 and cost of living = 33,000. In year 14 of this status, income = 179,000 and cost of living = 33,000. In year 15 of this status, income = 200,000 and cost of living = 33,000. In year 16 of this status, income = 211,666 and cost of living = 33,000. In year 17 of this status, income = 223,332 and cost of living = 33,000. In year 18 of this status, income = 234,998 and cost of living = 33,000. In year 19 of this status, income = 246,664 and cost of living = 33,000. In year 20 of this status, income = 258,330 and cost of living = 33,000. In year 21 of this status, income = 270,000 and cost of living = 33,000. In year 22 of this status, income = 285,000 and cost of living = 33,000. In year 23 of this status, income = 300,000 and cost of living = 33,000. In year 24 of this status, income = 315,000 and cost of living = 33,000. In year 25 of this status, income = 330,000 and cost of living = 33,000. In year 26 of this status, income = 330,000 and cost of living = 33,000. In year 27 of this status, income = 330,000 and cost of living = 33,000. In year 28 of this status, income = 330,000 and cost of living = 33,000. In year 29 of this status, income = 330,000 and cost of living = 33,000. In year 30 of this status, income = 330,000 and cost of living = 33,000. In year 31 of this status, income = 330,000 and cost of living = 33,000. In year 32 of this status, income = 330,000 and cost of living = 33,000. In year 33 of this status, income = 330,000 and cost of living = 33,000. In year 34 of this status, income = 330,000 and cost of living = 33,000. In year 35 of this status, income = 330,000 and cost of living = 33,000. Status = retired In year 1 of this status, income = 0 and cost of living = 18,000. In year 2 of this status, income = 0 and cost of living = 20,000. In year 3 of this status, income = 0 and cost of living = 22,000. In year 4 of this status, income = 0 and cost of living = 24,000. In year 5 of this status, income = 0 and cost of living = 26,000. In year 6 of this status, income = 0 and cost of living = 28,000. In year 7 of this status, income = 0 and cost of living = 28,000. In year 8 of this status, income = 0 and cost of living = 28,000. In year 9 of this status, income = 0 and cost of living = 28,000. In year 10 of this status, income = 0 and cost of living = 28,000. In year 11 of this status, income = 0 and cost of living = 28,000. In year 12 of this status, income = 0 and cost of living = 28,000. In year 13 of this status, income = 0 and cost of living = 28,000. In year 14 of this status, income = 0 and cost of living = 28,000. In year 15 of this status, income = 0 and cost of living = 28,000. Status = dead In year 1 of this status, income = 0 and cost of living = 5,000. In year 2 of this status, income = 0 and cost of living = 5,000. In year 3 of this status, income = 0 and cost of living = 5,000. In year 4 of this status, income = 0 and cost of living = 5,000. In year 5 of this status, income = 0 and cost of living = 5,000. For someone with a lifespan of 67 who retires at age 56, here's a list of their statuses at various ages: At age 19, status = undergrad. At age 20, status = undergrad. At age 21, status = undergrad. At age 22, status = undergrad. At age 23, status = working. At age 24, status = working. At age 25, status = working. At age 26, status = working. At age 27, status = working. At age 28, status = working. At age 29, status = working. At age 30, status = working. At age 31, status = working. At age 32, status = working. At age 33, status = working. At age 34, status = working. At age 35, status = working. At age 36, status = working. At age 37, status = working. At age 38, status = working. At age 39, status = working. At age 40, status = working. At age 41, status = working. At age 42, status = working. At age 43, status = working. At age 44, status = working. At age 45, status = working. At age 46, status = working. At age 47, status = working. At age 48, status = working. At age 49, status = working. At age 50, status = working. At age 51, status = working. At age 52, status = working. At age 53, status = working. At age 54, status = working. At age 55, status = working. At age 56, status = retired. At age 57, status = retired. At age 58, status = retired. At age 59, status = retired. At age 60, status = retired. At age 61, status = retired. At age 62, status = retired. At age 63, status = retired. At age 64, status = retired. At age 65, status = retired. At age 66, status = retired. At age 67, status = dead. Income tax rates are based on "Schedule X - Single" at www.irs.gov/formsbups/article/0,,id=133517,00.html I assume the income levels where the rates increase keep exact pace with inflation. Number of donations the utilitarian will make = 1. List of donations: In 2053, at age 65, donate 100% of the wealth held at that time. Statistics: ----------- Num Trials = 100 Num Catastrophes = 38 Min = 0 Max = 216,628,874 Mean = 40,248,993 Individual Values: ------------------ $0, lifespan = 64, catastrophe? true $0, lifespan = 69, catastrophe? true $0, lifespan = 69, catastrophe? true $0, lifespan = 70, catastrophe? true $0, lifespan = 71, catastrophe? true $0, lifespan = 71, catastrophe? true $0, lifespan = 71, catastrophe? true $0, lifespan = 71, catastrophe? true $0, lifespan = 71, catastrophe? true $0, lifespan = 71, catastrophe? true $0, lifespan = 72, catastrophe? true $0, lifespan = 73, catastrophe? true $0, lifespan = 73, catastrophe? true $0, lifespan = 73, catastrophe? true $0, lifespan = 75, catastrophe? true $0, lifespan = 76, catastrophe? true $0, lifespan = 77, catastrophe? true $0, lifespan = 78, catastrophe? true $0, lifespan = 79, catastrophe? true $0, lifespan = 79, catastrophe? true $0, lifespan = 79, catastrophe? true $0, lifespan = 79, catastrophe? true $0, lifespan = 80, catastrophe? true $0, lifespan = 81, catastrophe? true $0, lifespan = 81, catastrophe? true $0, lifespan = 82, catastrophe? true $0, lifespan = 82, catastrophe? true $0, lifespan = 82, catastrophe? true $0, lifespan = 82, catastrophe? true $0, lifespan = 83, catastrophe? true $0, lifespan = 84, catastrophe? true $0, lifespan = 85, catastrophe? true $0, lifespan = 85, catastrophe? true $0, lifespan = 85, catastrophe? true $0, lifespan = 87, catastrophe? true $0, lifespan = 90, catastrophe? true $0, lifespan = 90, catastrophe? true $0, lifespan = 91, catastrophe? true $20,631,125, lifespan = 64, catastrophe? false $20,631,125, lifespan = 64, catastrophe? false $20,631,125, lifespan = 64, catastrophe? false $27,528,441, lifespan = 67, catastrophe? false $27,528,441, lifespan = 67, catastrophe? false $27,528,441, lifespan = 67, catastrophe? false $30,430,127, lifespan = 68, catastrophe? false $30,430,127, lifespan = 68, catastrophe? false $33,061,071, lifespan = 69, catastrophe? false $33,061,071, lifespan = 69, catastrophe? false $36,492,003, lifespan = 70, catastrophe? false $36,492,003, lifespan = 70, catastrophe? false $36,492,003, lifespan = 70, catastrophe? false $36,492,003, lifespan = 70, catastrophe? false $40,222,725, lifespan = 71, catastrophe? false $40,222,725, lifespan = 71, catastrophe? false $43,709,332, lifespan = 72, catastrophe? false $43,709,332, lifespan = 72, catastrophe? false $43,709,332, lifespan = 72, catastrophe? false $43,709,332, lifespan = 72, catastrophe? false $43,709,332, lifespan = 72, catastrophe? false $43,709,332, lifespan = 72, catastrophe? false $48,120,509, lifespan = 73, catastrophe? false $48,120,509, lifespan = 73, catastrophe? false $48,120,509, lifespan = 73, catastrophe? false $52,917,130, lifespan = 74, catastrophe? false $52,917,130, lifespan = 74, catastrophe? false $52,917,130, lifespan = 74, catastrophe? false $57,512,957, lifespan = 75, catastrophe? false $57,512,957, lifespan = 75, catastrophe? false $57,512,957, lifespan = 75, catastrophe? false $57,512,957, lifespan = 75, catastrophe? false $57,512,957, lifespan = 75, catastrophe? false $57,512,957, lifespan = 75, catastrophe? false $57,512,957, lifespan = 75, catastrophe? false $57,512,957, lifespan = 75, catastrophe? false $63,184,443, lifespan = 76, catastrophe? false $63,184,443, lifespan = 76, catastrophe? false $63,184,443, lifespan = 76, catastrophe? false $63,184,443, lifespan = 76, catastrophe? false $63,184,443, lifespan = 76, catastrophe? false $63,184,443, lifespan = 76, catastrophe? false $69,351,498, lifespan = 77, catastrophe? false $69,351,498, lifespan = 77, catastrophe? false $69,351,498, lifespan = 77, catastrophe? false $69,351,498, lifespan = 77, catastrophe? false $69,351,498, lifespan = 77, catastrophe? false $69,351,498, lifespan = 77, catastrophe? false $75,383,337, lifespan = 78, catastrophe? false $82,675,214, lifespan = 79, catastrophe? false $90,604,245, lifespan = 80, catastrophe? false $90,604,245, lifespan = 80, catastrophe? false $98,493,121, lifespan = 81, catastrophe? false $98,493,121, lifespan = 81, catastrophe? false $107,868,345, lifespan = 82, catastrophe? false $118,062,765, lifespan = 83, catastrophe? false $118,062,765, lifespan = 83, catastrophe? false $128,350,930, lifespan = 84, catastrophe? false $128,350,930, lifespan = 84, catastrophe? false $153,511,781, lifespan = 86, catastrophe? false $199,246,946, lifespan = 89, catastrophe? false $216,628,874, lifespan = 90, catastrophe? false Histogram: ---------- 0 - 4,332,576: ************************************** 4,332,577 - 8,665,153: 8,665,154 - 12,997,730: 12,997,731 - 17,330,307: 17,330,308 - 21,662,884: *** 21,662,885 - 25,995,461: 25,995,462 - 30,328,038: *** 30,328,039 - 34,660,615: **** 34,660,616 - 38,993,192: **** 38,993,193 - 43,325,769: ** 43,325,770 - 47,658,346: ****** 47,658,347 - 51,990,923: *** 51,990,924 - 56,323,500: *** 56,323,501 - 60,656,077: ******** 60,656,078 - 64,988,654: ****** 64,988,655 - 69,321,231: 69,321,232 - 73,653,808: ****** 73,653,809 - 77,986,385: * 77,986,386 - 82,318,962: 82,318,963 - 86,651,539: * 86,651,540 - 90,984,116: ** 90,984,117 - 95,316,693: 95,316,694 - 99,649,270: ** 99,649,271 - 103,981,847: 103,981,848 - 108,314,424: * 108,314,425 - 112,647,001: 112,647,002 - 116,979,578: 116,979,579 - 121,312,155: ** 121,312,156 - 125,644,732: 125,644,733 - 129,977,309: ** 129,977,310 - 134,309,886: 134,309,887 - 138,642,463: 138,642,464 - 142,975,040: 142,975,041 - 147,307,617: 147,307,618 - 151,640,194: 151,640,195 - 155,972,771: * 155,972,772 - 160,305,348: 160,305,349 - 164,637,925: 164,637,926 - 168,970,502: 168,970,503 - 173,303,079: 173,303,080 - 177,635,656: 177,635,657 - 181,968,233: 181,968,234 - 186,300,810: 186,300,811 - 190,633,387: 190,633,388 - 194,965,964: 194,965,965 - 199,298,541: * 199,298,542 - 203,631,118: 203,631,119 - 207,963,695: 207,963,696 - 212,296,272: 212,296,273 - 216,628,849: 216,628,850 - 220,961,426: *