Basic Mathematics for Economists phần 4 pdf
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...
Basic Mathematics for Economists phần 3 pdf
... 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...
Basic Mathematics for Economists phần 1 ppt
... 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
×...
Basic Mathematics for Economists phần 2 ppsx
... 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...
Basic Mathematics for Economists phần 5 ppt
... 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...
Basic Mathematics for Economists phần 6 potx
... 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...
Basic Mathematics for Economists phần 7 potx
... 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...
Basic Mathematics for Economists phần 8 docx
...
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
)
=...
Basic Mathematics for Economists phần 9 ppsx
... +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...
Basic Mathematics for Economists phần 10 doc
... £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...
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