Supposeaunionisthesolesupplier of labor toallthefirmsin anoligopoly,such as the United Auto Workersisto General Motors,Ford, Chrysler,and soon. Letthe timing of moves be analogous to the model inSection 2.1.C: (1)the union makesasingle wage demand,w,that applies toallthefirms; (2)thefirmsobserve (andaccept)wandthen simultaneously choose employ- mentlevels, Li for firmi;(3)payoffsare(w-wa)Lforthe union, whereWaisthe wage that union members can earn in alternative employment andL=Ll+...+Lnistotal employment in the union- izedfirms,and profit7r(w,Li)for firmi,where the determinants of firmi'sprofit are describednext.

All firmshave the following productionfunction:output equalslabor;qi=Li.The market-clearing priceisP(Q)=a-Qwhen the aggregate quantity on the marketisQ=ql+...+qn.Tokeep things simple, suppose that firms have nocostsother than wages. Whatisthe subgame-perfect outcome of this game? How (and why) does the number of firmsaffectthe union's utility in the subgame-perfect outcome?