M3 3 math module 3 solutions to exercises y y 2 x y 1

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M3-3 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.3-7 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 [ Mini-Sermon : 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-

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ics will help. If you do get a “standardized” number-crunching 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.] M3-4 MATH MODULE 3: SOLUTIONS TO EXERCISES
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