WEEK 6 CYU

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

This preview shows pages 4–7. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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. 

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page4 / 8

C PQ C TC C 600 Q C Q D Q C 25000 100Q C 25000 500Q C Q C 2...

This preview shows document pages 4 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online