Consider ?the ?following ?market ?for ?a ?single ?good ?X ?with? two? firms ?that ?compete ?via? price?(Bertrand).?You? are ?given ?that ?P?=?30-3Q.
a)?Suppose ?initially ?that ?both ?firms ?have ?unlimited? capacities ?and? marginal? cost? of? 3.?What ?is? the? resulting? equilibrium? price? and ?total?quantity? in? the ?market???Prove ?your? answer.
b)?Now? suppose? that? the ?first ?firm? has? a ?capacity ?of ?2 ?and? the? second? firm? has ?a ?capacity ?of ?4.? What? is? the? resulting ?equilibrium ?price?and? quantity? for? each? firm ?and? for ?the? market? as ?a? whole??Prove ?your ?result?.