Firms.

$($a$)(10)$ There are two $$rms$,$ both of whom face demand curve QD$($P $)=10$ P: Firm $1$s cost

function is C$1($q$)=$ q$2,$ and $$rm $2$s is C$2($q$)=2$q$2.$ Find the NE price, assuming they

compete in quantities and choose these simultaneously.

$($b$)(8)$ Same setting as in $($a$),$ but now assume the market becomes perfectly competitive. At

a point where there are N$1$rms with cost function C$1($q$)($from $($a$))$ and N$2$rms with

cost function C$2($q$),$ what will the short run equilibrium price be$?$

$($c$)(10)$ Same setting as $($b$),$ but now suppose a disgruntled former employee from one of the

more e$$ cient $$rms$,$ with cost function C$1$; shares their technology with some of the less

e$$ cient $$rms $($those with cost function C$2)$: As a result, N$1$ rises and N$2$ falls, with no

change in the total # $$rms$.$ What do you expect the equilibrium impact to be$?($On things

like prices and $$rm$/$consumer welfare; you can get full credit without completely analyzing

all of this, but make a reasonable e$$ort to address at least some of it :$).)$