▁prof its , ▁taking ▁the ▁other ' s ▁choice ▁as ▁given . ▁The ▁( first ▁order ) ▁conditions ▁for ▁profit ▁maxim ization ▁are ▁ ▁for ▁the ▁domestic ▁firm ▁and ▁ ▁for ▁the ▁foreign ▁firm , ▁where ▁sub script ed ▁variables ▁denote ▁partial ▁derivatives . ▁Sol ving ▁these ▁for ▁y ▁implicitly ▁defines ▁a ▁best ▁response ▁function ▁for ▁each ▁firm ; ▁ ▁and ▁. ▁These ▁are ▁illustrated ▁in ▁the ▁figure ▁below , ▁with ▁the ▁domestic ▁firm ' s ▁output ▁on ▁the ▁x ▁axis ▁and ▁foreign ▁firm ' s ▁output ▁on ▁the ▁y ▁axis . ▁ ▁With ▁no ▁government ▁subs id y ▁( s = 0 ) ▁the ▁resulting ▁equilibrium ▁will ▁be ▁the ▁standard ▁Cour not ▁outcome , ▁as ▁shown ▁in ▁the ▁graph ▁by ▁the ▁intersection ▁of ▁the ▁best ▁response ▁functions . ▁A ▁subs id y ▁however ▁has ▁the ▁effect ▁of ▁sh ifting ▁the ▁domestic ▁firm ' s ▁best ▁response ▁function ▁to ▁the ▁right . ▁Because ▁its ▁output ▁is ▁subs id ized , ▁the ▁domestic ▁firm ▁increases ▁production . ▁This ▁in ▁turn ▁means ▁that ▁the ▁foreign ▁firm ' s ▁best ▁response ▁is ▁to ▁cut ▁output , ▁although ▁not ▁proportion ally ▁( h ence , ▁the ▁market ▁price ▁falls ). ▁In ▁the ▁new ▁equilibrium ▁domestic ▁firm ▁produces ▁more ▁and ▁foreign ▁firm ▁produces ▁less . ▁ ▁In ▁the ▁model , ▁domestic ▁social ▁w elf are ▁can ▁be ▁defined ▁as ▁the ▁home ▁firm ' s ▁profit ▁net ▁of ▁the ▁subs id y ▁( the ▁model ▁can ▁be ▁extended ▁so ▁that ▁social ▁w elf are ▁includes ▁the ▁firm ' s