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300hw3answer - Eco 300 HW 3 Answer Key 11.6 First prove the...

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Eco 300 HW 3 Answer Key 11.6 First prove the hint: In the graph Q max is the quantity demanded when P = 0. Since MR = 0 at 1 / 2 Q max (there e = –1), it is clear that MR bisects the distance from the P axis to the demand curve. So, if Q * represents quantity demanded when P = MC, MR = MC at 1 / 2 Q *. Notice also that the profit-maximizing price is given by 0.5 ( P max + MC ) where P max is the price for which quantity demanded is zero. Note: The results of this hint are used to solve several problems in later chapters. a. If Q 1 = 55 – P , then since MC = 5, Q 1 = 55 – 5 = 50 1 Q * = 25 2 At that output level, P 1 = 30 π = ( P 1 – 5)( Q 1 ) = 25 × 25 = 625. If Q 2 = 70 – 2 P 2 , Q 2 * = 70 – 2(5) = 60 = 70 – 2(5) = 60 * 2 30 2 Q = Therefore, P 2 = 20

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π = (20 – 5) × 30 = 450. Total profits = π 1 + π 2 = 1,075. b. The problem when transport costs = \$5 cannot be solved explicitly without calculus. In general, one would answer that the prices can in that case only differ by \$5 and that profits would fall relative to the pure separation case. Using calculus it can be shown that the exact solution to the problem requires that P 1 = 26 2 3 P 2 = 21 2 3 Q 1 = 28 1 3 Q 2 = 26
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300hw3answer - Eco 300 HW 3 Answer Key 11.6 First prove the...

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