ࡱ> 21  @\pDavid Ellerman Ba==h,#8X@"1.Times New Roman1Arial1Arial1Arial1Arial1.Times New Roman1.Times New Roman1.Times New Roman1.Times New Roman1.Times New Roman1.Times New Roman"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)                + ) , *  (   # "      "   h@@   h@  `@   h` @   h@   h  `   h`   h`@   h`  ``   h``  ! ! !0@@  @   @ !0@    !0@     ! !  "  (   (     wrap8 ``i̜̙3f3333f3ffff333ff333f33f33BBB\`N Polya CityIndex:Iter:Itercnt:Jump: MaxIter:Rand:  <9PProbability of Jump in Xi is Proportional to Relative Size of (Xi-1)+(Xi)+(Xi+1)5Otherwise Jump/19 is Subtracted to Keep Constant Sum.IndexItercntMaxIter Corr. RatioXiX1X2X3X4X5X6X7X8X9X10X11X12X13X14X15X16X17X18X19X20Initial Values Curr. Values Cumul. SumNew Sums = Rand = JumpEUse T)ools, O)ptions, and Calculation tab to check Manual, Iteration,@and set Maximum Iterations to whatever is in MaxIter cell (F16).[Be sure Index cell (A4) is 1. If not, double-click cell and hit Enter to recalculate cell.KUse F9 to start manual recalculation. Don't touch spreadsheet during a run. Polya Citynspreadsheet (A17 to A36). You can change those initial endowments in row 6. The probability of Xi increasingpby 1 (or whatever is in the Jump cell) on each iteration is proportional to the average of the value in the cellqand the two cells on either side. The two end cells containing the value X1 and X20 are mathematically connectedltogether so that they are neighbors. Thus we have a city that is a circle or ring of locations. To run themOne can model increasing returns-type processes using a Polya's Urn model programmed on a spreadsheet. 8model as is, hit function key F9, the Calculate Now key.gThere are 20 locations each of which has an inital endowment value, Xi = 25 for i=1,...,20 in the abovencan again go positive if it has a non-zero neighbor, and then it is possible for the next broke neighbor to gonpositive, and so forth--but that is very improbable. In other words, once a city or cluster has locked in, itmwill "almost certainly" be sustained with only a few blips around the edges. Forget trickle down. Everywheremelse is a wasteland of "broke" neighborhoods. But it is quite random which block of locations will lock in aspWhen a location hits zero, it goes "broke." Due to the neighborhood effect, a location that has gone broke Mthe successful city. To change the outcome, you need to change the dynamics.!Changing the Number of Iterationsland then change the set number of iterations in Excel by clicking T(ools, O(ptions, and the Calculation tab,qThe spreadsheet is set to run in iteration mode. To change the number of iterations, put the new value in F16, p Descriptionvand then set Maximum Iteration to whatever is in the Maxiter cell F16 (default is 5000). Hit F9 to run. Do not touchYthe spreadsheet while it is running. 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