Basic Mathematics for Economists phần 6 potx
Basic Mathematics for Economists phần 6 potx
... 82q − 6q
2
+ 0.2q
3
. Therefore,
AV C =
TVC
q
= 82 −6q + 0.2q
2
and
MC =
dTC
dq
= 82 −12q + 0.6q
2
Setting MC = AV C
82 −12q + 0.6q
2
= 82 −6q + 0.2q
2
0.4q
2
= 6q
q =
6
0.4
= 15
at the minimum ... =
dTR
dq
= 60 −0.4q
© 1993, 2003 Mike Rosser
Therefore,
dp
dq
=−30 +0.5q
When q = 8,
dp
dq
=−30 +0.5(8) =−30 +4 =− 26
Also, when q = 8,
p = 900 − 30(8) + 0.25(8)
2
= 900 −240 + 16 = 67 6
Thus...
Basic Mathematics for Economists phần 7 potx
... 22.5(275, 567 .6) K
−2.5
= 0 (3)
40 =
22.5(275, 567 .6)
K
2.5
K
2.5
=
22.5(275, 567 .6)
40
= 155,0 06. 78
K = 119. 162 68
Substituting this value into (1) gives
L =
275, 567 .6
(119. 162 8)
1.5
= 211.84478
This time we ... y = 2x
3
dy
dx
= 6x
2
= 6( 10)
2
= 60 0
Therefore, predicted change in y is
y =
dy
dx
x = 60 0 × 1 = 60 0
The actual values are y = 2(10)
3
= 2,000 when x = 10
y =...
Basic Mathematics for Economists phần 1 ppt
... of 6, it means that this index of 10 is multiplied 6 times. Therefore
log 1,242 .67
6
= 6 log 1,242 .67 = 18. 566 135
Using the [10
x
] function to evaluate this number gives
3 .68 24 × 10
18
= 3 ,68 2, ... operations should be performed by working from left to right.
Example 2.4
(i) 48 − 18 + 6 = 30 + 6 = 36
(ii) 6 + 16 − 7 = 22 − 7 = 15
(iii) 68 + 5 − 32 − 6 + 14 = 73 − 32...
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 = 314.
6. You get ... 3.1
Student no. 1234 567 89101112
Height (cm) 178 175 170 166 168 185 169 189 175 181 177 180
Weight (kg) 72 68 58 52 55 82 55 86 70 71 65 68
© 1993, 2003 Mike Rosser
8.You...
Basic Mathematics for Economists phần 3 pdf
... check that the price of £12. 16 for the first 60 units corresponds to point A on the
demand schedule in Figure 5 .6 since
p = 16 − 0. 064 q = 16 − 0. 064 (60 ) = 16 − 3.84 = £12. 16
If the firm wishes to sell ... 120)
q = 6MC − 260
q + 260
6
= MC (1)
Since
p = 580 − 0.3q
MR = 580 − 0.6q (2)
To maximize profits MC = MR and so equating (1) and (2)
q + 260
6
= 580 −0.6q
q + 260 = 3,48...
Basic Mathematics for Economists phần 4 pdf
... 14.5 -61 2 25.5 -66 7 36. 5 -238
12 4 -108 15 -62 5 26 -65 8 37 -207
13 4.5 -142 15.5 -63 7 26. 5 -64 8 37.5 -175
14 5 -175 16 -64 8 27 -63 7 38 -142
15 5.5 -207 16. 5 -65 8 27.5 -62 5 38.5 -108
16 6 -238 ... 3 56. 05
20 16 261 6.80 415.55
21 17 30 96. 65 479.85
22 18 364 5 .60 548.95
23 19 4 268 .45 62 2.85
24 20 4970.00 701.55
25 21 5755.05 785.05
26 22 66 28.40 873.35...
Basic Mathematics for Economists phần 5 ppt
... 177 06. 57
8 4 25000 8% 14 864 .67
9 5 25000 9% 12152. 86
10 6 12000 10% 9 563 .64
11 11% 7090.04
12 IRR = 14.14% 12% 4725.54
13 13% 2 464 . 06
14 14% 299.94
15 15% -1772.14
16 16% -3757.14
17 17% - 565 9.71
18 ... 1.17% 384.32
5 15.25% 1.19% 385.15
6 15.50% 1.21% 385.98
7 15.75% 1.23% 3 86. 81
8 16. 00% 1.24% 387 .64
9 16. 25% 1. 26% 388.47
10 16. 50% 1.28% 389.30
11 16. 75%...
Basic Mathematics for Economists phần 8 docx
... and
dv
dq
=−0 .62 5
Therefore, employing the product rule
d
2
TR
dq
2
= u
dv
dq
+ v
du
dq
= (65 0 − 0.25q)
0.5
(−0 .62 5) + (65 0 − 0 .62 5q)(−0.125) (65 0 − 0.25q)
−0.5
=
(65 0 −0.25q)(−0 .62 5) + (65 0 − 0 .62 5q)(−0.125)
(65 0 ... 26. 95 4.92
14 4 203.4375 19.57 -7.38
15 5 114.84375 30 .64 11.07
16 6 247.73438 14.03 - 16. 61
17 7 48.398438 38.95 24.92
18 8 347.40234 1.57 -37.38
1...
Basic Mathematics for Economists phần 9 ppsx
... 5 267 .80 377.80
16 6 266 .68 3 76. 68
17 7 266 .01 3 76. 01
18 8 265 .60 375 .60
19 9 265 . 36 375. 36
20 10 265 .22 375.22
21 11 265 .13 375.13
22 12 265 .08 375.08
23 13 265 .05 375.05
24 14 265 .03 ... 134
6 b = 0 .6 New
I
value = 110
7 Old Equil Y = 435
8 Time New Equil Y = 375
9 t C Y
10 0 301.00 411.00
11 1 2 86. 60 3 96. 60
12 2 277. 96 387. 96
13 3 272.78 3...
Basic Mathematics for Economists phần 10 doc
... 2.4494897
6. 96 7. 10
8. 5.27803 16 9. 0.03423 10. 87.977857
2.10 1. 270,818.98 2. 220.9478 3. 2.8 563 ×10
9
4. 1.5728 ×10
8
5. 1. 268 3 6. 16, 552,877 7. 93 .69 63 76 8. 4.38228
9. 5.1331 868
Chapter ... (b) B, NPV
B
= £2 ,69 8.94,
NPV
A
= £2,291.34 3. IRR = 16. 93%
7 .6 1. (a) 2.5, 781.25, 50,857.3 (b) 3, 121.5, 14, 762 (c) 1.4, 10.7 56, 139 .6
(d) 0.8, 19 .66 , 267 .8 (e) 0.75, 0.5...