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Wk 7 - Chapter 13 and Chapter 14 Problems

Chapter 14 exercise 3b c d 5a b c and 8a b c 3

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Chapter 14 Exercise 3(b, c, d), 5(a, b, c), and 8(a, b, c) 3. American Export-Import Shipping Company operates a general cargo carrier service between New York and several Western European ports. It hauls two major categories of freight: manufactured items and semi-manufactured raw material. The demand functions for these two classes of goods are P 1 = 100 – 2Q 1 P 2 = 80 – Q 2 where Qi = tons of freight moved. The total cost function for American is TC = 20 + 4(Q 1 +Q 2 ) b. What are the profits-maximizing levels of price and output for the two freight categories? 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.
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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.
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