Question

The OUTPUT is already answered BUT STILL NEED PROFITS FOR EACH FIRM. please don’t forget to answer profits for part 1!!!

Two firms compete as a duopoly. The demand they face is P 100-3Q. The cost function for each firm is C(Q) = 4Q. Determine output, and profits for each firm in a Cournot oligopoly 2 If firms collude, determine output and profit for each firm. 3. If firm 1 cheats on the collusion in item 2, determine output and profit for each firm 4. Graph the reaction functions and identify the points from parts 1, 2 and 3. 5 Determine output, and profits for each firm in a Stackelberg oligopoly Given the inverse demand function is P-100-3Q The cost function of each firm is C(Q)-4Q a) Firm-1 leads firm-2. Firm-1 is leader and firm-2 is follower Firstly find the reaction function of firm-2, substitute this reaction function into firm-1'sprofit function and calculate for the optimalprice, quantity and profits of each firm. P 100-3 where-+ Thus, P-100-3g-3q TR -P() -(100-3-3q,)4 -(100-3a,-34:)9-4 Derivate w.r.tq2 and equate it to zero: dt. r-100-3q, -64,-4 dq2 0-96-34,-6g 96-3q, +6g2 96-39 96-3q Thus, the reaction function of firm-2 (follower) is Now, substitute this reaction function intofirm-1's profit function. TR-TC 100-34-3(26-34)- -(100-3g, -48+1.5q,)g, -4g -(52-1.5g,)a-4 Derivate wr.tq, and equate it to zero: dt 52-3q -4 da 0-48-3q 48-3q 16-q, Thus, the output produced by firm-1 (leader) is 16 units. Substitute this into reaction function of firm-2. 96-39 96-3(16) 92 96-48 6 -"4 Thus, the output produced by firm-2 (follower) is 8 units 16-gl Thus, the output produced by firm-1 (leader) is 16 units. Substitute this into reaction function of firm-2 96-3g 96-3(16) 96-48 92 Thus, the output produced by firm-2 (follower) is & units In the case where firm-2 is leader and firm-1 is follower, the result will remain the same. Only the name of the firm change. In general terms, the leader will produce 16 units and the follower producers 8 units Comment >

Answer 1

TC model BR 96-39า 6 2,10091039 22 Scanned with

69/+ 34, - 26 92 10.67 6 10.67 Camscanner

Under Cournot model, firms compete on quantities.