C pq c tc c 600 q c q d q c 25000 100q c 25000 500q c

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C = PQ C TC C = (600 Q C Q D )Q C (25,000 + 100Q C ) = 25,000 + 500Q C Q C 2 Q C Q D D = (600 Q C Q D ) QD (20,000 + 125Q D ) = 20,000 + 475Q D Q D 2 Q C Q D  C /Q C = 500 2Q C Q D and  D /Q D = 475 2Q D Q C Conditions for an optimum require that both partials be set equal to zero and the resulting equations be solved simultaneously for optimal values of Q C and Q D : Q D * = 150 units and QC* = 175 units. P = 600 – 150 – 175 = $275, so P* = $275.
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Myisha Coleman Week 6 CYU b) Determine the total profits for each firm at the equilibrium output found in Part (a). C * = 25,000 + 500(175) (175) 2 175(150) = $5,625. D * = 20,000 + 475(150) (150) 2 175(150) = $2,500 2. Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function: P = 200 – QA – QB where QA and QB are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TCA = 1,500 + 55QA + Q2A TCB = 1,200 + 20QB + 2Q2B Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change). b) Determine Firm A, Firm B and total industry profits at the optimal solution found in Part (a). a.  A = PQ A TC A = (200 Q A Q B )∙Q A (1500 + 55 Q A + Q A 2 ) A = 1500 + 145Q A 2Q A 2 Q A Q B  A /Q A = 145 4Q A Q B = 0
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Myisha Coleman Week 6 CYU B = PQ B TC B = (200 Q A Q B )∙Q B (1200 + 20 Q B + 2Q B 2 ) B = 1200 + 180Q B 3Q B 2 Q A Q B  B /Q B = 180 6Q B Q A = 0 Solving these two equations simultaneously results in: Q B * = 25 and Q A * = 30, accordingly, P = 200 -30 -25 = $145, or P* = $145 for both firms. b. 
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C PQ C TC C 600 Q C Q D Q C 25000 100Q C 25000 500Q C Q C 2...

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