$(28)$ Firms.

$(a)(10)$ There are two firms, both $of$ whom face demand curve $Q^D(P)=10-P.$ Firm $1\text{'}scost$

function $is{C}^1(q)=q^2,$ and firm $2\text{'}sis{C}^2(q)=2q^2.$ Find the $NE$ price, assuming they

compete $in$ quantities and choose these simultaneously.

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

a point where there are $N_1$ firms with cost function $C^1(q)(from(a))$ and $N_2$ firms 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 efficient firms, with cost function $C^1{C}^2{N}_1$ rises and $N_2$ falls, with $no$

change $in$ the total # firms. What $do$ you expect the equilibrium impact $tobe?(On$ things

like prices and fir$\frac{m}{c}$onsumer welfare; you can get full credit without completely analyzing

all $of$ this, but make a reasonable effort $to$ address $at$ least some $ofit.)$