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[null,"Self-Selection Problem"]
[null,null,"for Section 15.4 in Kuhn, P. Personnel Economics"]
[]
[null,"Setup:","Two periods (1 and 2), two worker types (A and B)  [one of each for simplicity]"]
[null,null,"Type-As stay in the labor market for two periods"]
[null,null,"Type-Bs leave the labor market at the end of period 1. "]
[null,null,"Utility outside the firm in each period = v for both worker types"]
[null,null,"No discounting"]
[null,null,"Firms announce and precommit to a wage profile, w1, w2 when they hire workers"]
[]
[{"$nulls":4},"baseline:"]
["Output per period (q):",null,null,6,6]
["Alternative U (v):",null,null,3,3]
["Training costs in first period (c): ",null,null,5,5]
[]
["Suppose first that the firm has to train everyone it hires-- prod is low until you learn the job and there's no way around it.  "]
[]
["Flat wage profiles (w1=w2):",{"$nulls":5},"Selection-inducing wage profiles (i.e. wage profiles that only attract A's):"]
[]
[null,null,"baseline:",{"$nulls":5},"baseline:"]
["w1:",3,3,{"$nulls":3},"w1:",2,2]
["w2:",{"$f":"B21","v":3},{"$nulls":4},"w2:",4,4]
[]
["Type-A net PVU if accepts ",null,null,{"$f":"B21-D13 + B22-D13","v":0},null,null,"Type-A net PVU if accepts ",null,null,{"$f":"H21-D13 + H22- D13","v":0},{"$f":"IF(J24<0, \"Stop!!- violation\", \"OK\")","v":"OK"},"Must be (weakly) positive to induce self-selection!"]
["Type-B net PVU if accepts ",null,null,{"$f":"B21-D13","v":0},null,null,"Type-B net PVU if accepts ",null,null,{"$f":"H21-D13","v":-1},{"$f":"IF(J25<0, \"OK\", \"stop!!-violation\")","v":"OK"},"Must be strictly negative to induce self-selection!"]
[]
["Therefore:  Any flat-wage profile of w=2 or greater ",{"$nulls":5},"Therefore:  Type-As refuse all contracts with w1<2"]
[null,"will be accepted by both worker types",{"$nulls":4},"Type-B's don’t care about the timing of wages, but need w1+w2>4"]
[]
["Profits (accounting for workers' acceptance decisions): ",{"$nulls":5},"Profits (accounting for workers' acceptance decisions): "]
["on the Type-As:  ",null,{"$f":"IF(D24>=0,D12-D14-B21 + D12-B22,0)","v":1},{"$nulls":3},"on the Type-As:  ",null,{"$f":"IF(J24>=0,D12-D14-H21 +D12-H22,0)","v":1}]
["on the Type-Bs:  ",null,{"$f":"IF(D25>=0,D12-D14-B21,0)","v":-2},{"$nulls":3},"on the Type-Bs:  ",null,{"$f":"IF(J25>=0,H21-D13,0)","v":0}]
["Total ",null,{"$f":"C31+C32","v":-1},{"$nulls":3},"Total",null,{"$f":"I31+I32","v":1}]
[]
["If v=3, there's no way for the firm ever to make money"]
["with a flat wage profile."]
[]
["Key:"]
["Values to enter"]
["Results"]

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