Basic Mathematics for Economists - Rosser - Chapter 4 potx

... Mike Rosser 0 –x –y y = x 3 y = x 3 y = x 2 y = x 2 x y Figure 4. 14 Table 4. 3 x 012 345 6789 y = x 0.5 0 1 1 .41 4 1.732 2 2.236 2 .44 9 2. 646 2.828 3 0 y 3 1 2 y = x 0.5 14 9 x Figure 4. 15 Table 4. 4 x ... MR 1 0.15Q 2 = 9 −MR 2 Q 1 = 40 − 3 1 3 MR 1 (1)Q 2 = 60 − 6 2 3 MR 2 (2) © 1993, 2003 Mike Rosser 0 K Q 1 Q 2 Q 3 L Figure 4. 21 Table 4. 7 KLK 0.5 L 0.5 Q 64 4 8 2 32...

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... 0.8( 649 .129 24) = 519.30 34 (9) Substituting (8) into (6) R 0.25 = 30(0.8) 0.7 ( 649 .129 24) 0.5 1 14 R = 30 4 (0.8) 2.8 ( 649 .129 24) 2 1 14 4 = 1,081.882 It is assumed that the second-order conditions for ... (1) L 0.25 = 42 186 (80 .47 1179) 0.7 = 4. 871 745 5 L = (L 0.25 ) 4 = (4. 871 745 5) 4 = 563.29822 Therefore, first-order conditions suggest that the optimum values...

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... Introduction Learning objective After completing this chapter students should be able to: • Understand why mathematics is useful to economists. 1.1 Why study mathematics? Economics is a social science. ... quantification of economic predictions requires the use of mathematics. Although non-mathematical economic analysis may sometimes be useful for making qual- itative predictions (...

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... Mike Rosser Test Yourself, Exercise 5.5 1. Solve for x, y and z when 2x + 4y + 2z = 144 (1) 4x + y + 0.5z = 120 (2) x + 3y + 4z = 144 (3) 2. Solve for x, y and z when 12x + 15y + 5z = 158 (1) 4x ... 3y + 4z = 50 (2) 5x + 20y + 2z = 148 (3) 3. Solve for A, B and C when 32A + 14B + 82C = 6 64 (1) 11.5A + 8B + 52C = 349 (2) 18A + 26.2B − 62C = 560 .4 (3) 4. Find the values of x,y and...

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... 24. 5 -6 82 35.5 -2 97 10 3 -3 7 14 -5 98 25 -6 75 36 -2 68 11 3.5 -7 3 14. 5 -6 12 25.5 -6 67 36.5 -2 38 12 4 -1 08 15 -6 25 26 -6 58 37 -2 07 13 4. 5 -1 42 15.5 -6 37 26.5 -6 48 37.5 -1 75 14 5 -1 75 16 -6 48 ... 29.5 -5 67 40 .5 38 20 8 -3 52 19 -6 93 30 -5 50 41 77 21 8.5 -3 78 19.5 -6 97 30.5...

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... 12000 10% 9563. 64 11 11% 7090. 04 12 IRR = 14. 14% 12% 47 25. 54 13 13% 246 4.06 14 14% 299. 94 15 15% -1 772. 14 16 16% -3 757. 14 17 17% -5 659.71 18 18% -7 48 4.20 19 19% -9 2 34. 68 20 20% -1 09 14. 99 Example ... 0.591898 0. 543 9 34 0.500 249 0 .46 042 8 10 0.6755 64 0.613913 0.558395 0.508 349 0 .46 3193 0 .42 241 1 0.6755 64 0.613913 0.558395 0.508 349...

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... profit? Solution Given TR = pq = (1 84 − 4q)q = 184q − 4q 2 then MR = dTR dq = 1 84 − 8q MC = dTC dq = 3q 2 − 42 q + 160 To maximize profits MC = MR. Therefore, 3q 2 − 42 q + 160 = 1 84 −8q 3q 2 − 34q − 24 = 0 (q − 12)(3q ... the function y = 12 + 0.5x 4 when x = 5? 3. Derive a formula for the slope of the function y = 4 + 4x −1 − 4x. 4. What is the slope of the function y = 4x 0.5...

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... 1 94. 4 − 0.2q 2 Solution TR = pq = (1 94. 4 − 0.2q 2 )q = 1 94. 4q − 0.2q 3 For a stationary point on this cubic function the slope must be zero and so dTR dq = 1 94. 4 − 0.6q 2 = 0 1 94. 4 = 0.6q 2 3 24 ... 000 q 2 q 2 = 16,000,000 4 = 4, 000,000 q = √ (4, 000,000) = 2,000 © 1993, 2003 Mike Rosser TR 0 £ M YZ q Figure 9.1 The slope is zero when 60 − 0.4q = 0 60 = 0.4q 150 = q There...

Ngày tải lên: 06/07/2014, 07:20