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Unformatted text preview: complements in consumption are discussed in Chapter 3 and Appendix 3 of the text, while perfect complements in production are discussed in Chapter 9 and Appendix 9 of the text.] M32 MATH MODULE 3: SOLUTIONS TO EXERCISES 8. Using substitution, we have for Duopolist 1: Q 1 = R 1 ( Q 2 ) = 35 – 0.5 Q 2 = 35 – 0.5(40 – 0.5 Q 1 ) = 15/ 0.75 = 20 units, and hence for Duopolist 2, Q 2 = 30 units and total indus try output Q = 20 + 30 = 50 units. M33 MATH MODULE 3: SOLUTIONS TO EXERCISES y y = 2 x y = 1 x 120 • • • • 72 24 90 Sal Slim 40 36 72 120 180 45 90 x 3 FIGURE FOR ANSWER M.37 Q 2 Q 1 = R 1 ( Q 2 ) = 35 – 0.5 Q 2 Q 2 = R 2 ( Q 1 ) = 40 – 0.5 Q 1 Q 2 * = 30 Q 1 * = 20 40 80 35 70 E Q 1 [ MiniSermon : One of the interesting features of this question is that you can get the “correct” answer without ever having studied the Cournot model of duopoly, which is covered in Chapter 13 of the text, and without even understanding what on earth the question is about! There is a moral here: facility with mathematical manipulation is not a substitute for understanding the underlying concepts, and simply memorizing for mulas will not help you on tests if the instructor changes the “rules of the game” or the model even slightly, whereas understanding the underlying theory and the mathemat ics will help. If you do get a “standardized” numbercrunching question on an exam, however, then you can do just fine by memorizing the relevant formulas and “cranking the computational handle,” and you never have to understand the theory at all! We are not recommending this strategy, but it would be erroneous to deny that it can some times be effective. In our experience, moreover, it can be the case that memorizing a for mula and then puzzling over “what it really means” or “what happens if we change some of the assumptions” can actually aid in learning and understanding the econom ic concepts that the formula represents.] M34 MATH MODULE 3: SOLUTIONS TO EXERCISES...
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 Fall '12
 Danvo
 Harshad number, Elementary algebra, Sal, Math Module

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