please do #3 A-C

written work for thumbs up need help understanding

l

below are the answers just need help understand how to get that

1. Assume two companies, A and B, are duopolists who produce the same product. Demand for the products is given by the following linear demand, Where Qa and Qb are the quantities sold by the respective firms and is the selling P=200-Qa-Qb price. Total cost functions for the two companies are. TCa=1500 +55Qa+Qa2 TC)=1200+200b+20b^2 Assume the firms act independently as in the cournot model A Determine the long run equilibrium output and selling price for each firem B. Determine Firm A, Firm B and industry profits at the equilibrium solution from A. a 2. Assume the same firm form a cartel to act as monopolist and maximize total industry profits A. Determine the optimum output and selling price for each firm. B. Determine Firm A Firm Band industry profits at the equilibrium solution from C Show that the marginal cost of the two firms are equal at the optimal solution in part A 3. Compare the optimal solutions obtained in #1 and #2. a. How much higher (lower) is the optimal selling price when the two firms form a cartel to maximize industry profits compared to when they act independently? b. How much higher (lower) is the total industry output? c. How much higher (lower) are the total industry profits? In Class Problem Answers Value Act Independently Form Cartel 30 25.5 Qa* Qb* 25 21.5 Qtotal-Qa*+Qb* 55 47 Price 145 153 Profit A 300 348.75 Profit B 675 735 Total Profit 975 1083.75