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

... 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