Wk 7 - Chapter 13 and Chapter 14 Problems

# ∂ π/∂q 1 = 96 4q 1 = 0 q 1 = 24 tons p 1 =

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Unformatted text preview: ∂ π /∂Q 1 = 96 - 4Q 1 = 0 Q 1 * = 24 tons P 1 * = 100-48 = \$52/unit ∂π / ∂ Q 2 = 76 - 2Q 2 = 0 Q 2 * = 38 tons P 2 * = 80-38 = \$42/unit. c. At these levels of output, calculate the marginal revenue in each market. TR = 100Q 1- 2Q 1 2 + 80Q 2- Q 2 2 MR 1 = ∂ (TR)/ ∂ Q 1 = 100 - 4Q 1 = 100 - 4(24) = \$4/unit MR 2 = ∂ (TR)/ ∂ Q 2 = 80 - 2Q 2 = 80 - 2(38) = \$4/unit d. What are American’s total profits if it is effectively able to charge different prices in the two markets. π * = - 20 + 96(24) + 76(38) - 2(24) 2- (38) 2 = \$2,576. Myisha Coleman May 26, 2013 5. Phillips Industries manufactures a certain product that can be sold directly to retail outlets or to the Superior Company for further processing and eventual sale as a completely different product. The demand function for each of these markets is Retail Outlets: P 1 = 60 – 2Q 1 Superior Company: P 2 = 40 – Q 2 Where P1 and P2 are the prices charged and Q 1 and Q 2 are the quantities sold in the respective markets. Phillips’ total cost function for the manufacture of this product is TC = 10 + 8(Q 1 + Q 2 ) a) Determine Phillips’ total profit function. TR 1 = P 1 ∙Q 1 = (60-2Q 1 ) ∙Q 1 = 60Q 1-2Q 1 2 TR 2 = P 2 ∙Q 2 = (40-Q 2 ) ∙Q 2 = 40Q 2 –Q 2 2 TC = 10 + 8Q 1 + 8 Q 2 π = TR - TC = - 10 + 52Q 1- 2Q 1 2 + 32Q 2- Q 2 2 b) What are the profit-maximizing price and outlet levels for the product in the two markets? Q 1 = 52 - 4Q 1 = 0 Q 1 * = 13 units P 1 * = 60 - 2(13) = \$34/unit. Q 2 = 32 - 2Q 2 = 0 Q 2 * = 16 units P 2 * = 40 - 16 = \$24/unit. c) At these levels of output, calculate the marginal revenue in each market. TR 1 = 60Q 1- 2Q 1 2 MR 1 = 60 - 4Q 1 = 60 - 4(13) = \$8/unit. TR 2 = 40Q 2- Q 2 2 MR 2 = 40 - 2Q 2 = 40 - 2(16) = \$8/unit. Myisha Coleman May 26, 2013 8. The Pear Computer Company just developed a totally revolutionary new personal computer. It estimates that it will take competitors at least two years to produce equivalent products. estimates that it will take competitors at least two years to produce equivalent products....
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∂ π/∂Q 1 = 96 4Q 1 = 0 Q 1 = 24 tons P 1 = 100-48 =...

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