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[null,"Optimal number of candidates to interview"]
[null,null,"for Figure 14.1 in Kuhn, P. Personnel Economics"]
[{"$nulls":5},"Baseline"]
[{"$nulls":5},"Values:"]
[null,"Expected net productvity (u):",null,null,{"v":10,"d":"10.0"},{"v":10,"d":"10.0"}]
[null,"Standard deviation of productivity (σ):",null,null,2.5,2.5,null,null,"Optimal group size:",null,{"$f":"MAX(G13:G42)","v":4}]
[null,"Application processing cost (c):",null,null,0.5,0.5]
[]
[]
[null,"Number of","Expected Net","Total","Expected"]
[null,"applicants:","Prod of Best","Processing","Profit"]
[null,"(N)","applicant: ","Costs (cN)","E(Π)"]
[null,1,{"$f":"$E$5+$C$34*$E$6*LN(B13)","v":{"v":10,"d":"10.000"}},{"$f":"$E$7*B13","v":{"v":0.5,"d":"0.50"}},{"$f":"C13-D13","v":{"v":9.5,"d":"9.500"}},null,{"$f":"IF(E13=MAX($E$13:$E$41),B13,0)","v":0}]
[null,{"$f":"B13+1","v":2},{"v":11.351111598666826,"d":"11.351"},{"$f":"$E$7*B14","v":{"v":1,"d":"1.00"}},{"$f":"C14-D14","v":{"v":10.351111598666826,"d":"10.351"}},null,0]
[null,3,{"v":12.141461218176334,"d":"12.141"},{"v":1.5,"d":"1.50"},{"v":10.641461218176334,"d":"10.641"},null,0]
[null,4,{"v":12.702223197333653,"d":"12.702"},{"v":2,"d":"2.00"},{"v":10.702223197333653,"d":"10.702"},null,4]
[null,5,{"v":13.137183980272683,"d":"13.137"},{"v":2.5,"d":"2.50"},{"v":10.637183980272683,"d":"10.637"},null,0]
[null,6,{"v":13.49257281684316,"d":"13.493"},{"v":3,"d":"3.00"},{"v":10.49257281684316,"d":"10.493"},null,0]
[null,7,{"v":13.793049796766434,"d":"13.793"},{"v":3.5,"d":"3.50"},{"v":10.293049796766434,"d":"10.293"},null,0]
[null,8,{"v":14.05333479600048,"d":"14.053"},{"v":4,"d":"4.00"},{"v":10.05333479600048,"d":"10.053"},null,0]
[null,9,{"v":14.282922436352667,"d":"14.283"},{"v":4.5,"d":"4.50"},{"v":9.782922436352667,"d":"9.783"},null,0]
[null,10,{"v":14.48829557893951,"d":"14.488"},{"v":5,"d":"5.00"},{"v":9.48829557893951,"d":"9.488"},null,0]
[null,11,{"v":14.674078184735606,"d":"14.674"},{"v":5.5,"d":"5.50"},{"v":9.174078184735606,"d":"9.174"},null,0]
[null,12,{"v":14.843684415509987,"d":"14.844"},{"v":6,"d":"6.00"},{"v":8.843684415509987,"d":"8.844"},null,0]
[null,13,{"v":14.999707023347831,"d":"15.000"},{"v":6.5,"d":"6.50"},{"v":8.499707023347831,"d":"8.500"},null,0]
[null,14,{"v":15.14416139543326,"d":"15.144"},{"v":7,"d":"7.00"},{"v":8.14416139543326,"d":"8.144"},null,0]
[null,15,{"v":15.278645198449016,"d":"15.279"},{"v":7.5,"d":"7.50"},{"v":7.778645198449016,"d":"7.779"},null,0]
[null,16,{"v":15.404446394667307,"d":"15.404"},{"v":8,"d":"8.00"},{"v":7.404446394667307,"d":"7.404"},null,0]
[null,17,{"v":15.522618453932996,"d":"15.523"},{"v":8.5,"d":"8.50"},{"v":7.022618453932996,"d":"7.023"},null,0]
[null,18,{"v":15.634034035019493,"d":"15.634"},{"v":9,"d":"9.00"},{"v":6.634034035019493,"d":"6.634"},null,0]
[null,19,{"v":15.73942413370956,"d":"15.739"},{"v":9.5,"d":"9.50"},{"v":6.23942413370956,"d":"6.239"},null,0]
[null,20,{"v":15.839407177606336,"d":"15.839"},{"v":10,"d":"10.00"},{"v":5.839407177606336,"d":"5.839"},null,0]
[{"$nulls":6},0]
["k:",null,{"$f":"SQRT(6)/PI()","v":{"v":0.779696801233676,"d":"0.780"}},{"$nulls":3},{"$f":"IF(E34=MAX($E$13:$E$41),#REF!,0)","v":0}]
[{"$nulls":6},{"$f":"IF(E35=MAX($E$13:$E$41),#REF!,0)","v":0}]
["Main Lessons:  ",{"$nulls":5},{"$f":"IF(E36=MAX($E$13:$E$41),#REF!,0)","v":0}]
[null,"Expected net prod of best applicant increases at a diminishing rate with group size; processing costs increase linearly",{"$nulls":4},{"$f":"IF(E37=MAX($E$13:$E$41),#REF!,0)","v":0}]
[null,"Expected net prod of best applicant increases at a faster rate when variance is high",{"$nulls":4},{"$f":"IF(E38=MAX($E$13:$E$41),#REF!,0)","v":0}]
[null,"Optimal batch size increases with std deviation of candidate productivity, falls with application processing costs",{"$nulls":4},{"$f":"IF(E39=MAX($E$13:$E$41),#REF!,0)","v":0}]
[null,"If higher skill demands raise the mean and std deviation together, optimal batch size rises with skill",{"$nulls":4},{"$f":"IF(E40=MAX($E$13:$E$41),#REF!,0)","v":0}]
[{"$nulls":6},{"$f":"IF(E41=MAX($E$13:$E$41),B41,0)","v":0}]
[{"$nulls":6},{"$f":"IF('cdf calculation'!F2=MAX($E$13:$E$41),'cdf calculation'!C2,0)","v":0}]

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[]
[null,"To give a sense of the Gumbel cdf for this u and σ (for the footnote):"]
[null,"Euler's constant (gamma): ",null,{"v":0.5772156649,"d":"0.5772"}]
[null,null,"beta =",{"$f":"'main calculation'!E6*'main calculation'!C34","v":{"v":1.9492420030841902,"d":"1.949"}}]
[null,null,"v=",{"$f":"10 - 2.5*'main calculation'!C34*D3","v":{"v":8.874866981138751,"d":"8.875"}}]
[]
[null,null,"x","e","F(e)"]
[null,null,1,{"$f":"C8-$D$5","v":{"v":-7.8748669811387515,"d":"-7.875"}},{"$f":"EXP(-EXP(-D8/$D$4))","v":{"v":2.096660691991589E-25,"d":"0.000"}}]
[null,null,{"$f":"C8+1","v":2},{"v":-6.8748669811387515,"d":"-6.875"},{"v":1.6802448591991437E-15,"d":"0.000"}]
[null,null,3,{"v":-5.8748669811387515,"d":"-5.875"},{"v":1.4277569123554751E-9,"d":"0.000"}]
[null,null,4,{"v":-4.8748669811387515,"d":"-4.875"},{"v":5.0632042178836083E-6,"d":"0.000"}]
[null,null,5,{"v":-3.8748669811387515,"d":"-3.875"},{"v":6.7549120177640457E-4,"d":"0.001"}]
[null,null,6,{"v":-2.8748669811387515,"d":"-2.875"},{"v":0.012645654641859549,"d":"0.013"}]
[null,null,7,{"v":-1.8748669811387515,"d":"-1.875"},{"v":0.07305686062868856,"d":"0.073"}]
[null,null,8,{"v":-0.8748669811387515,"d":"-0.875"},{"v":0.20878103691075037,"d":"0.209"}]
[null,null,9,{"v":0.1251330188612485,"d":"0.125"},{"v":0.39147977736730016,"d":"0.391"}]
[null,null,10,{"v":1.1251330188612485,"d":"1.125"},{"v":0.5703760016745321,"d":"0.570"}]
[null,null,11,{"v":2.1251330188612485,"d":"2.125"},{"v":0.7145250009071565,"d":"0.715"}]
[null,null,12,{"v":3.1251330188612485,"d":"3.125"},{"v":0.8177159052847296,"d":"0.818"}]
[null,null,13,{"v":4.1251330188612485,"d":"4.125"},{"v":0.8864952385332905,"d":"0.886"}]
[null,null,14,{"v":5.1251330188612485,"d":"5.125"},{"v":0.9304106165430112,"d":"0.930"}]
[null,null,15,{"v":6.1251330188612485,"d":"6.125"},{"v":0.9577363955728943,"d":"0.958"}]
[null,null,16,{"v":7.1251330188612485,"d":"7.125"},{"v":0.9744784943414402,"d":"0.974"}]
[null,null,17,{"v":8.125133018861249,"d":"8.125"},{"v":0.9846414668870723,"d":"0.985"}]
[null,null,18,{"v":9.125133018861249,"d":"9.125"},{"v":0.9907765366292999,"d":"0.991"}]
[null,null,19,{"v":10.125133018861249,"d":"10.125"},{"v":0.9944677880740432,"d":"0.994"}]
[null,null,20,{"v":11.125133018861249,"d":"11.125"},{"v":0.9966842623107285,"d":"0.997"}]
[]
[]
[null,null,"Share of values between 8 and 12: ",null,null,{"$f":"E19-E15","v":{"v":0.6089348683739793,"d":"0.609"}}]
[null,null,"Share of values between 6 and 14: ",null,null,{"$f":"E21-E13","v":{"v":0.9177649619011516,"d":"0.918"}}]

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