# Adverse Selection and Market Efficiency

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Adverse selection1Solution 1)Quality of worker = which is distributed in interval 0,1Worker produce quantity worth \$Worker can produce at home \$r12r For every 0,1Equilibrium exist when ( )EwwErwwSince 12rfor all, 0,1Thus, if W*= 0 nobody workW*=1/2 everybody workThus, the rational expectation equilibrium for the economy is:**( )Erww*1( )2ErwYes, all above equilibrium is efficient, because1( )2ErEverybody work since they earn at home is less than given wages and1( )2Ereverybody work at home and can earn higher wages.Solution 2)Workers have access to a costless test through which they can verify their ability to prospective employers so that they can be paid according to their true ability. A worker who takes the test is paid a wage equal to her productivity
Adverse selection2Given that ris increasing in , which means higher the productivity higher will be the gap between wage worker can earn at home and wages he can work from working outside.a)Given that Ø is the set of workers types that don’t take the testExpected revenue from set of workers that don’t take the test = EØand wages for these worker will be w.Since there is perfect competition, thus firm will earn zero profit0ØEwThus, the firms will pay a wagewØEb)Given that the firms offer a wage w to those employers that don’t take the test.Thus worker who will choose to work has efficiency greater than and are not a part of Set Ø (set of workers types that don’t take the test)Symbolically,( )EØErØThus, worker those has higher productivity and can earn higher wage given to worker that don’t take the test.c)From above solution we know that there is a set of worker who don’t take test i.e. 0,Øfor some 0,1Since is distributed uniformly 0,1Half of the worker are belong to set Ø set of workers types that don’t take the test and half who take test.22ØEEØThe wage offered to workers who don’t take the test

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