The Rational Expectation Equilibrium

Added on - 30 Sep 2019

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Adverse selection0ADVERSE SELECTION
Adverse selection1Solution 1)Quality of worker =which is distributed in interval0,1Worker produce quantity worth $Worker can produce at home$r12rFor every0,1Equilibrium exist when( )EwwErwwSince12rfor all,0,1Thus, ifW*= 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 prospectiveemployers so that they can be paid according to their true ability. A worker who takes the test ispaid a wage equal to her productivity
Adverse selection2Given thatris increasing in, which means higher the productivity higher will be thegap 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 theseworker 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 thanand 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’ttake the test.c)From above solution we know that there is a set of worker who don’t take testi.e.0,Øfor some0,1Sinceis distributed uniformly0,1Half of the worker are belong to set Ø set of workers types that don’t take the test and half whotake test.22ØEEØThe wage offered to workers who don’t take the test
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