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Theinversemarketdemandforacertaingoodis: P =100 Q/2 where Q istheindustry output.Therearetwosymmetric firmsproducingthegood,eachwiththefollowingcostfunction: TC i =10 q i , where q i istheoutputofthe i thfirm( i =1 , 2).

Theinversemarketdemandforacertaingoodis:

P=100 Q/2

whereQistheindustry output.Therearetwosymmetric firmsproducingthegood,eachwiththefollowingcostfunction:

TCi=10qi,whereqiistheoutputoftheithfirm(i=1,2).

  1. Supposethatthefirmsarecompetinginquantities.Ifsomeoneproduces morethantheirshareofthecarteloutput,theotherfirmpunishesthembyrevertingtotheCournot output.Whatisthecritical valueofthediscountfactor?
  2. Nowassumethatthedetectionlag(thetimerequiredtodiscoverandrespondtocheating) istwoperiods.Whatisthecritical valueofthediscountfactor?
  3. Nowassumethatthefirmswiththeabovecostfunctions competeinprices(withoutcapacityconstraint).Ifsomeoneproduces morethantheirshareofthecartel output,theotherfirmpunishes thembyrevertingtotheBertrandequilibrium.Whatisthecriticalvalueofthediscountfactor?
  4. Inwhichoftheabovecasesiscartelformation mostlikely?

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