Basic Mathematics for Economists - Rosser - Chapter 1 pptx

... 1 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 ... time period is 1, 200 kg when price is zero and then decreases by 10 kg for every 1p rise in the price of a kilo of apples’. It is much easier, however, to express this mathematically as: q =...

Ngày tải lên: 06/07/2014, 07:20

... q 2 18 = q When q is 18 then the second-order derivative is d 2 TR dq 2 = 1. 2q = 1. 2 (18 ) =− 21. 6 < 0 © 19 93, 2003 Mike Rosser Returning to (6) to find the optimal level of q (360 − 5q) (1 − c) ... be dTC dq = 18 − 10 q + 3q 2 = 0 (1) However, if we try using the quadratic equation formula to find a value of q for which (1) holds we see that q = −b ± √ b 2 − 4ac 2a = −( 10 )...

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... = 10 0 9 t Qt Pt in Pt 10 0 16 0 12 .00 Stability => STABLE 11 1 70 16 .50 4.50 12 2 11 5 14 .25 -2 .25 13 3 92.5 15 .38 1. 13 14 4 10 3.75 14 . 81 -0 .56 15 5 98 .12 5 15 .09 0.28 16 6 10 0.9375 14 .95 ... 25. 31 2 .19 12 2 18 3.75 22.03 -3 .28 13 3 14 4.375 26.95 4.92 14 4 203.4375 19 .57 -7 .38 15 5 11 4.84375 30.64 11 .07 16 6 247.73438 1...

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... follows: MR 1 = 12 − 0.3Q 1 MR 2 = 9 −0 .15 Q 2 0.3Q 1 = 12 − MR 1 0 .15 Q 2 = 9 −MR 2 Q 1 = 40 − 3 1 3 MR 1 (1) Q 2 = 60 − 6 2 3 MR 2 (2) © 19 93, 2003 Mike Rosser 0 K Q 1 Q 2 Q 3 L Figure 4. 21 Table ... 3 0 y 3 1 2 y = x 0.5 14 9 x Figure 4 .15 Table 4.4 x 0 0 .1 1 2 3 4 5 y = x 1 ∞ 10 1 0.5 0.33 0.25 0.2 y = x −2 ∞ 10 0 1 0.25 0 .11 0.0625 0.04 © 19 93,...

Ngày tải lên: 06/07/2014, 07:20

... functions for q 1 and q 2 we get q = (5MC − 10 ) + (25MC − 15 0) q = 30MC − 16 0 q + 16 0 = 30MC q + 16 0 30 = MC (2) © 19 93, 2003 Mike Rosser (K) (L) B C (R) 0 y 12 A D 10 12 x 30 15 10 15 21  2000 Figure ... intersect. Therefore these two resources are used up completely and so 12 x + 21y = 252 (1) 10 x + 10 y = 15 0 (2) From (2)x= 15 − y (3) Substituting (3) into...

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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 ... -6 48 27 -6 37 38 -1 42 15 5.5 -2 07 16 .5 -6 58 27.5 -6 25 38.5 -1 08 16 6 -2 38 17 -...

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... 14 864.67 9 5 25000 9% 12 152.86 10 6 12 000 10 % 9563.64 11 11 % 7090.04 12 IRR = 14 .14 % 12 % 4725.54 13 13 % 2464.06 14 14 % 299.94 15 15 % -1 772 .14 16 16 % -3 757 .14 17 17 % -5 659. 71 18 18 % -7 484.20 19 ... 0.658008 0 .18 7467 0 .12 3355 0.75 0. 914 238 0.8358 31 0.76 414 8 0.638699 0 .16 6 412 0 .10 6287 0.80 0.908 811 0.825937 0.7506 21 0. 619...

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... 17 .98 17 9.8 10 80. 01 0. 01 272 01. 7998 1. 7998 17 9.98 11 80.0 01 0.0 01 27200 .18 0 .17 9998 17 9.998 12 80.00 01 0.00 01 27200. 018 0. 017 99998 17 9.9998 13 80.000 01 0.000 01 27200.0 018 0.0 018 00000 17 9.9999802 Test ... 500q - 2q^2 3 INITIAL q VALUE = 80 4 INITIAL TR VALUE = 27200 5 Marginal Revenue 6 q Delta q TR Delta TR (DeltaTR)/(Delta q) 7 90 10 288...

Ngày tải lên: 06/07/2014, 07:20