MATHEMATICS FOR ECONOMISTS

... record for this book has been requested ISBN 0-2 0 3-4 226 3-5 Master e-book ISBN ISBN 0-2 0 3-4 243 9-5 (Adobe eReader Format) ISBN 0–415–26783–8 (hbk) ISBN 0–415–26784–6 (pbk) © 1993, 2003 Mike Rosser ... Business School at Coventry University © 1993, 2003 Mike Rosser Basic Mathematics for Economists Second Edition Mike Rosser © 1993, 2003 Mike Rosser First edi...

Ngày tải lên: 06/07/2014, 07:20

... each other, each chapter assumes that students are familiar with material covered in previous chapters It is therefore very important that you © 19 93, 2003 Mike Rosser keep up-to-date with your ... particularly useful, especially for the sort of financial problems covered in Chapter and for performing the mathematical operations on matrices explained in Chapter 15 However, even...

Ngày tải lên: 06/07/2014, 07:20

... in Figure 4. 16 © 1993, 2003 Mike Rosser y y = x3 y = x2 y = x2 –x x y = x3 –y Figure 4. 14 Table 4. 3 x y = x 0.5 0 1 1 .41 4 1.732 2.236 2 .44 9 2. 646 y y = x0.5 1 x Figure 4. 15 Table 4. 4 x y = x ... 5120 21 340 40 80 22 360 2880 23 380 1520 24 400 25 42 0 -1 680 © 1993, 2003 Mike Rosser D E TR = 80Q – 0.2Q^2 10,000 TR 8,000 6,000 4, 000 2,000 –2,000 Q 20 60 100 140 180...

Ngày tải lên: 06/07/2014, 07:20

... price ∗ ps = pd (55 + 4q)(1 + t) = 3 75 − 2.5q 55 + 55 t + 4q + 4qt = 3 75 − 2.5q 6.5q + 4qt = 320 − 55 t q(6 .5 + 4t) = 320 − 55 t q= 320 − 55 t 6 .5 + 4t This reduced form equation for equilibrium q ... schedule Thus p = 3 75 − 2.5q = 3 75 − 2 .5 320 − 55 t 6 .5 + 4t 2,437 .5 + 1 ,50 0t − 800 + 137.5t 1,637 .5 + 1,637.5t = 6 .5 + 4t 6 .5 + 4t 1,637 .5( 1 + t) = 6 .5 + 4...

Ngày tải lên: 06/07/2014, 07:20

... 14 -5 98 -7 3 14.5 -6 12 -1 08 15 -6 25 -1 42 15.5 -6 37 -1 75 16 -6 48 -2 07 16. 5 -6 58 -2 38 17 -6 67 -2 68 17.5 -6 75 -2 97 18 -6 82 -3 25 18.5 -6 88 -3 52 19 -6 93 -3 78 19.5 -6 97 -4 03 20 -7 00 -4 27 20.5 -7 02 -4 50 ... 35.5 25 -6 75 36 25.5 -6 67 36. 5 26 -6 58 37 26. 5 -6 48 37.5 27 -6 37 38 27....

Ngày tải lên: 06/07/2014, 07:20

... 15% 16% 17% 18% 19% 20% E NPV 270 96.19 23813.36 20686.58 177 06. 57 14864. 67 12152.86 9563.64 70 90.04 472 5.54 2464.06 299.94 -1 77 2.14 -3 75 7.14 -5 659 .71 -7 484.20 -9 234.68 -1 0914.99 Example 7. 30 A ... 0 .79 6981 0 .78 7566 0 .77 8266 0 .76 9081 0 .76 0008 0 .75 1048 0 .74 21 97 0 .73 3454 0 .72 4819 0 .71 6290 0 .70 7865 0.699543 0.691324 0.683204 0. 675 18...

Ngày tải lên: 06/07/2014, 07:20

... 288 00 273 78 27217. 98 27201.79 98 27200. 18 27200.0 18 27200.00 18 Delta TR 1600 1 78 17. 98 1.79 98 0.1799 98 0.017999 98 0.00 180 0000 E Marginal Revenue (DeltaTR)/(Delta q) 160 1 78 179 .8 179. 98 179.9 98 ... shown Table 8. 2 10 11 12 13 A Ex 8. 17 B C D DIFFERENTIATION OF TR FUNCTION GIVEN FUNCTION TR = 500q - 2q^2 INITIAL q VALUE = 80 INITIAL TR VALUE = 27200 q...

Ngày tải lên: 06/07/2014, 07:20

... so dTR = 194 .4 − 0.6q = dq 194 .4 = 0.6q 324 = q 18 = q When q is 18 then the second-order derivative is d2 TR = −1.2q = −1.2(18) = −21.6 < dq © 199 3, 2003 Mike Rosser Therefore, second-order condition ... Example 9. 5 Find the profit-maximizing output for a firm with the total cost function TC = + 97 q − 8.5q + 1/3q and the total revenue function TR = 58q − 0.5q £ MC Y D X Figure 9. 4...

Ngày tải lên: 06/07/2014, 07:20

... ∂K∂R Second-order derivatives for multi-variable functions are needed to check second-order conditions for optimization, as explained in the next section Test Yourself, Exercise 10. 3 For the production ... rationale for all the second-order conditions is not quite so straightforward We shall therefore just state these second-order conditions here and give a brief intuitive explanati...

Ngày tải lên: 06/07/2014, 07:20

... the first-order conditions ∂G =0 ∂K ∂G =0 ∂L will also satisfy second-order conditions for a minimum © 1993, 2003 Mike Rosser If you refer back to Figure 11. 3(a) you can see the rationale for this ... 0.6 L0.4 = 4 (119 .16268)0.6 ( 211. 84478)0.4 = 600 Thus cost minimization is achieved when K = 119 .16 and L = 212.84 (to dp) and so total production costs will be TC = 40 (119 .16) + 1...

Ngày tải lên: 06/07/2014, 07:20

... (−975)(−0 .125 ) d2 TR → +∞ = dq Therefore this second value for q obviously does not satisfy second-order conditions for a maximum Example 12. 9 At what level of K is the function Q = 12K 0.4 (160 ... rule Assume, for example, that you wish to find an expression for the slope of the non-linear demand function p = (150 − 0.2q)0.5 (1) The basic rules for differentiation explained i...

Ngày tải lên: 06/07/2014, 07:20

... 15.00 400 -2 0 160 Change in Pt F G Qs=c+dPt c= d= -5 0 10 Equilibrium Price = Equilibrium Quantity = Stability => STABLE 4.50 -2 .25 1 .13 -0 .56 0.28 -0 .14 0.07 -0 .04 0.02 -0 .01 H 15 100 Table 13. 2 CELL ... labels and Table 13. 1 column headings shown in Table 13. 1 D4 400 D5 -2 0 F4 -5 0 F5 10 D6 160 A10 to Enter numbers A20 from to 10 B10 =D6 C10 =(B10-D...

Ngày tải lên: 06/07/2014, 07:20