Basic Mathematics for Economists phần 4 pdf

... 2307.35 39 35 28201.25 245 8.05 40 36 308 14. 80 2613.55 41 37 33588.65 2773.85 42 38 36527.60 2938.95 43 39 39636 .45 3108.85 44 40 42 920.00 3283.55 45 41 46 383.05 346 3.05 Your spreadsheet ... -550 41 77 21 8.5 -378 19.5 -697 30.5 -532 41 .5 117 22 9 -40 3 20 -700 31 -513 42 158 23 9.5 -42 7 20.5 -702 31.5 -49 3 42 .5 200 24 10 -45 0 21 -703 32 -47 2 43 243 25 10.5...

Ngày tải lên: 14/08/2014, 22:20

... 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 ... Rosser Solution Multiplying(1)by229x+6y+90z=680 Adding(2)25x−6y−32z=82 (2) Gives54x+58z=762 (4) Havingusedequations(1)and(2)toeliminateywenowneedtobringinequation(3)to deriveasecondequationconta...

Ngày tải lên: 14/08/2014, 22:20

... 41 − 6 + 14 = 35 + 14 = 49 (iv) 22 × 8 ÷ 4 = 176 ÷ 4 = 44 (v) 46 0 ÷5 4 = 92 4 = 368 (vi) 200 ÷ 25 × 8 × 3 ÷ 4 = 8 × 8 × 3 ÷ 4 = 64 ×3 ÷ 4 = 192 4 = 48 When a calculation involves both addition/subtraction ... 18 Example 2.17 44 7 ÷ 8 49 = 44 7 × 49 8 = 11 1 × 7 2 = 77 2 = 38 1 2 Test Yourself, Exercise 2 .4 1. 1 6 + 1 7 + 1 8 = 2. 3 7 + 2 9 − 1 4 = 3. 2 5 ×...

Ngày tải lên: 14/08/2014, 22:20

... 3.7 1. Solve for x when 16x = 2x + 56. 2. Solve for x when 14 = 6 +4x 5x 3. Solve for x when 45 = 24 + 3x. 4. Solve for x if 5x 2 + 20 = 1,000. 5. If q = 560 − 3p solve for p when q = 3 14. 6. You ... pay = (40 hours @ £8) +(10 hours @ £12) = £320 +£120 = 44 0 tax payable = ( 44 0 −£80)0.25 = (£360)0.25 = £90 Therefore net pay = 44 0 −£90 = £350 UsingtheexpressionderivedinExam...

Ngày tải lên: 14/08/2014, 22:20

... 7% 17706.57 8 4 25000 8% 148 64. 67 9 5 25000 9% 12152.86 10 6 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% -1772. 14 16 16% -3757. 14 17 17% -5659.71 18 ... 3.00% 85.152 Putting this in log form this gives log 4 = n log 1. 04 n = log 4 log 1. 04 = 0.60206 0.017033 = 35. 346 Therefore a growth rate of 4% can be sus...

Ngày tải lên: 14/08/2014, 22:20

... 1 84 − 4q and the TC function TC = q 3 − 21q 2 + 160q + 40 What output will maximize 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 ... = dTC dq = q (1) As TR = pq = (46 0 − 2q)q = 46 0q − 2q 2 then MR = dTR dq = 46 0 −4q (2) To maximize profit MR = MC. Therefore, equating (1) and (2), 46 0 −4q = q 46 0 = 5q 92 = q The...

Ngày tải lên: 14/08/2014, 22:20

... differentiation: MP K = ∂Q ∂K = 4. 8K −0.6 L 0 .4 (3) MP L = ∂Q ∂L = 4. 8K 0 .4 L −0.6 (4) Substituting (3) and (4) and the given prices for P K and P L into (2) 4. 8K −0.6 L 0 .4 40 = 4. 8K 0 .4 L −0.6 5 Dividing both sides by 4. 8 ... (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 sugge...

Ngày tải lên: 14/08/2014, 22:20

... 13 3 144 .375 26.95 4. 92 14 4 203 .43 75 19.57 -7.38 15 5 1 14. 843 75 30. 64 11.07 16 6 247 .7 343 8 14. 03 -16.61 17 7 48 .39 843 8 38.95 24. 92 18 8 347 .40 2 34 1.57 -37.38 19 9 -101.10352 57. 64 56.06 ... = (48 −4L) 0.75 giving du dL = 0.5L −0.5 dv dL = 0.75 (48 − 4L) −0.25 ( 4) =−3 (48 −4L) −0.25 Therefore dU dL = L 0.5 [−3 (48 −4L) −0.25 ]+ (48 −4L) 0.75 (0.5L −0.5 ) =...

Ngày tải lên: 14/08/2014, 22:20

... +0.6Y ∗ ) + 1 34 Y ∗ (1 − 0.6) = 40 + 1 34 0.4Y ∗ = 1 74 Y ∗ = 43 5 © 1993, 2003 Mike Rosser Table 14. 3 ty t = 2e −1.5t + 8 010 1 8 .44 626 2 8.0995 74 3 8.022218 4 8.0 049 58 5 8.001106 Table 14. 4 ty= e t y ... period. Substituting the known values into this function gives 7 84 = 940 e 10r 0.8 340 426 = e 10r ln 0.8 340 426 = 10r −0.18 147 08 = 10r −0.018 147 1 = r Therefore the r...

Ngày tải lên: 14/08/2014, 22:20

... £17,623.16 4. £ 744 .71 5. 40 ,44 1 .40 6. £5,030.03 7.2 1. 43 , 747 .41 ;12.68% 2. £501,159. 74; 7 .44 % 3. (a) APR 11.35% 4. £2,083.61; 19.25% 5. £625; 5.09% 6. 19.28% 7. 0.0 146 7% 8. 49 4,531.25; 4. 5% 7.3 1. ... calculated as: c 11 = 4 × 10 + 2 × 6 + 12 × 4 = 40 + 12 + 48 = 100 c 12 = 4 × 0.5 + 2 × 3 + 12 × 4 = 2 + 6 + 48 = 56 c 13 = 4 × 1 + 2 × 8 + 12 × 2 = 4 +16 + 24...

Ngày tải lên: 14/08/2014, 22:20