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 wall street quant In year 1 of this status, income = 120,000 and cost of living = 33,000. In year 2 of this status, income = 143,333 and cost of living = 33,000. In year 3 of this status, income = 166,666 and cost of living = 33,000. In year 4 of this status, income = 190,000 and cost of living = 33,000. In year 5 of this status, income = 207,777 and cost of living = 33,000. In year 6 of this status, income = 225,554 and cost of living = 33,000. In year 7 of this status, income = 243,331 and cost of living = 33,000. In year 8 of this status, income = 261,108 and cost of living = 33,000. In year 9 of this status, income = 278,885 and cost of living = 33,000. In year 10 of this status, income = 296,662 and cost of living = 33,000. In year 11 of this status, income = 314,439 and cost of living = 33,000. In year 12 of this status, income = 332,216 and cost of living = 33,000. In year 13 of this status, income = 350,000 and cost of living = 33,000. In year 14 of this status, income = 350,000 and cost of living = 33,000. In year 15 of this status, income = 350,000 and cost of living = 33,000. In year 16 of this status, income = 350,000 and cost of living = 33,000. In year 17 of this status, income = 350,000 and cost of living = 33,000. In year 18 of this status, income = 350,000 and cost of living = 33,000. In year 19 of this status, income = 350,000 and cost of living = 33,000. In year 20 of this status, income = 350,000 and cost of living = 33,000. In year 21 of this status, income = 350,000 and cost of living = 33,000. In year 22 of this status, income = 350,000 and cost of living = 33,000. In year 23 of this status, income = 350,000 and cost of living = 33,000. In year 24 of this status, income = 350,000 and cost of living = 33,000. In year 25 of this status, income = 350,000 and cost of living = 33,000. In year 26 of this status, income = 350,000 and cost of living = 33,000. In year 27 of this status, income = 350,000 and cost of living = 33,000. In year 28 of this status, income = 350,000 and cost of living = 33,000. In year 29 of this status, income = 350,000 and cost of living = 33,000. In year 30 of this status, income = 350,000 and cost of living = 33,000. In year 31 of this status, income = 350,000 and cost of living = 33,000. In year 32 of this status, income = 350,000 and cost of living = 33,000. In year 33 of this status, income = 350,000 and cost of living = 33,000. In year 34 of this status, income = 350,000 and cost of living = 33,000. In year 35 of this status, income = 350,000 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 78 who retires at age 63, 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 = gradSchool. At age 24, status = gradSchool. At age 25, status = gradSchool. At age 26, status = gradSchool. 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 = working. At age 57, status = working. At age 58, status = working. At age 59, status = working. At age 60, status = working. At age 61, status = working. At age 62, status = working. At age 63, status = retired. At age 64, status = retired. At age 65, status = retired. At age 66, status = retired. At age 67, status = retired. At age 68, status = retired. At age 69, status = retired. At age 70, status = retired. At age 71, status = retired. At age 72, status = retired. At age 73, status = retired. At age 74, status = retired. At age 75, status = retired. At age 76, status = retired. At age 77, status = retired. At age 78, 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 2064, at age 76, donate 100% of the wealth held at that time. Statistics: ----------- Num Trials = 100 Num Catastrophes = 44 Min = 0 Max = 317,968,765 Mean = 71,606,202 Individual Values: ------------------ $0, lifespan = 67, catastrophe? true $0, lifespan = 68, catastrophe? true $0, lifespan = 69, catastrophe? true $0, lifespan = 70, catastrophe? true $0, lifespan = 71, catastrophe? true $0, lifespan = 72, catastrophe? true $0, lifespan = 72, catastrophe? true $0, lifespan = 73, catastrophe? true $0, lifespan = 74, catastrophe? true $0, lifespan = 74, catastrophe? true $0, lifespan = 74, catastrophe? true $0, lifespan = 74, catastrophe? true $0, lifespan = 75, catastrophe? true $0, lifespan = 75, catastrophe? true $0, lifespan = 76, catastrophe? true $0, lifespan = 76, catastrophe? true $0, lifespan = 76, catastrophe? true $0, lifespan = 77, catastrophe? true $0, lifespan = 77, catastrophe? true $0, lifespan = 77, catastrophe? true $0, lifespan = 77, catastrophe? true $0, lifespan = 77, catastrophe? true $0, lifespan = 77, catastrophe? true $0, lifespan = 78, catastrophe? true $0, lifespan = 79, catastrophe? true $0, lifespan = 79, catastrophe? true $0, lifespan = 80, catastrophe? true $0, lifespan = 80, catastrophe? true $0, lifespan = 80, 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 = 83, catastrophe? true $0, lifespan = 84, catastrophe? true $0, lifespan = 85, catastrophe? true $0, lifespan = 88, catastrophe? true $0, lifespan = 89, catastrophe? true $0, lifespan = 89, catastrophe? true $0, lifespan = 89, catastrophe? true $0, lifespan = 90, catastrophe? true $31,869,395, lifespan = 64, catastrophe? false $50,252,437, lifespan = 69, catastrophe? false $50,252,437, lifespan = 69, catastrophe? false $50,252,437, lifespan = 69, catastrophe? false $50,252,437, lifespan = 69, catastrophe? false $50,252,437, lifespan = 69, catastrophe? false $55,218,197, lifespan = 70, catastrophe? false $60,617,859, lifespan = 71, catastrophe? false $60,617,859, lifespan = 71, catastrophe? false $60,617,859, lifespan = 71, catastrophe? false $60,617,859, lifespan = 71, catastrophe? false $60,617,859, lifespan = 71, catastrophe? false $60,617,859, lifespan = 71, catastrophe? false $65,886,566, lifespan = 72, catastrophe? false $65,886,566, lifespan = 72, catastrophe? false $65,886,566, lifespan = 72, catastrophe? false $65,886,566, lifespan = 72, catastrophe? false $72,271,082, lifespan = 73, catastrophe? false $72,271,082, lifespan = 73, catastrophe? false $72,271,082, lifespan = 73, catastrophe? false $79,213,470, lifespan = 74, catastrophe? false $79,213,470, lifespan = 74, catastrophe? false $86,107,035, lifespan = 75, catastrophe? false $86,107,035, lifespan = 75, catastrophe? false $86,107,035, lifespan = 75, catastrophe? false $103,241,547, lifespan = 77, catastrophe? false $103,241,547, lifespan = 77, catastrophe? false $103,241,547, lifespan = 77, catastrophe? false $103,241,547, lifespan = 77, catastrophe? false $103,241,547, lifespan = 77, catastrophe? false $112,234,653, lifespan = 78, catastrophe? false $112,234,653, lifespan = 78, catastrophe? false $122,788,550, lifespan = 79, catastrophe? false $122,788,550, lifespan = 79, catastrophe? false $122,788,550, lifespan = 79, catastrophe? false $134,264,633, lifespan = 80, catastrophe? false $134,264,633, lifespan = 80, catastrophe? false $134,264,633, lifespan = 80, catastrophe? false $145,968,494, lifespan = 81, catastrophe? false $145,968,494, lifespan = 81, catastrophe? false $159,537,724, lifespan = 82, catastrophe? false $159,537,724, lifespan = 82, catastrophe? false $159,537,724, lifespan = 82, catastrophe? false $159,537,724, lifespan = 82, catastrophe? false $174,292,616, lifespan = 83, catastrophe? false $174,292,616, lifespan = 83, catastrophe? false $174,292,616, lifespan = 83, catastrophe? true $189,494,068, lifespan = 84, catastrophe? false $206,940,140, lifespan = 85, catastrophe? false $245,622,387, lifespan = 87, catastrophe? false $245,622,387, lifespan = 87, catastrophe? false $245,622,387, lifespan = 87, catastrophe? false $268,052,944, lifespan = 88, catastrophe? false $292,443,453, lifespan = 89, catastrophe? false $292,443,453, lifespan = 89, catastrophe? false $292,443,453, lifespan = 89, catastrophe? false $317,968,765, lifespan = 90, catastrophe? false Histogram: ---------- 0 - 6,359,374: ******************************************* 6,359,375 - 12,718,749: 12,718,750 - 19,078,124: 19,078,125 - 25,437,499: 25,437,500 - 31,796,874: 31,796,875 - 38,156,249: * 38,156,250 - 44,515,624: 44,515,625 - 50,874,999: ***** 50,875,000 - 57,234,374: * 57,234,375 - 63,593,749: ****** 63,593,750 - 69,953,124: **** 69,953,125 - 76,312,499: *** 76,312,500 - 82,671,874: ** 82,671,875 - 89,031,249: *** 89,031,250 - 95,390,624: 95,390,625 - 101,749,999: 101,750,000 - 108,109,374: ***** 108,109,375 - 114,468,749: ** 114,468,750 - 120,828,124: 120,828,125 - 127,187,499: *** 127,187,500 - 133,546,874: 133,546,875 - 139,906,249: *** 139,906,250 - 146,265,624: ** 146,265,625 - 152,624,999: 152,625,000 - 158,984,374: 158,984,375 - 165,343,749: **** 165,343,750 - 171,703,124: 171,703,125 - 178,062,499: *** 178,062,500 - 184,421,874: 184,421,875 - 190,781,249: * 190,781,250 - 197,140,624: 197,140,625 - 203,499,999: 203,500,000 - 209,859,374: * 209,859,375 - 216,218,749: 216,218,750 - 222,578,124: 222,578,125 - 228,937,499: 228,937,500 - 235,296,874: 235,296,875 - 241,656,249: 241,656,250 - 248,015,624: *** 248,015,625 - 254,374,999: 254,375,000 - 260,734,374: 260,734,375 - 267,093,749: 267,093,750 - 273,453,124: * 273,453,125 - 279,812,499: 279,812,500 - 286,171,874: 286,171,875 - 292,531,249: *** 292,531,250 - 298,890,624: 298,890,625 - 305,249,999: 305,250,000 - 311,609,374: 311,609,375 - 317,968,749: 317,968,750 - 324,328,124: *