$4.$ Suppose there are J identical rms$,$ that entry by additional rms is

eectively blocked, and that each rm has identical costs, C $($qj$)=$ cqj :

Let inverse market demand be the linear form, p $=$ a $$ b

PJ

j$=1$ qj $,$ where

a $>0$; b $>0$:

$($a$)(10\%)$ Show that the Cournot$-$Nash equilibrium outputs are the same

for all rms$.$

$($b$)(10\%)$ Show that perfect competition is a limit case of imperfect

competition.