Basic Mathematics for Economists phần 2 ppsx
Basic Mathematics for Economists phần 2 ppsx
... any further.
Example 3 .29
2x
2
x
= 2x
Example 3.30
4x
3
− 2x
2
+ 10x
x
=
x(4x
2
− 2x + 10)
x
= 4x
2
− 2x + 10
Example 3.31
16x + 120
x
= 16 +
120
x
© 1993, 20 03 Mike Rosser
2. Sketchtheapproximateshapesofthefollowingfunctionswhenxandyareallowed
totakebothpositiveandnegativevalues.
(a)y=4+0.1x
2
(b)y=0.01x
3
(c)y=10−x
−1
3.Willthenon-lineardemandschedulep=570−0.4q
2
getflatt...
Basic Mathematics for Economists phần 9 ppsx
... 26 5 .22 375 .22
21 11 26 5.13 375.13
22 12 265.08 375.08
23 13 26 5.05 375.05
24 14 26 5.03 375.03
25 15 26 5. 02 375. 02
26 16 26 5.01 375.01
27 17 26 5.01 375.01
28 18 26 5.00 375.00
The basic method ... 1 28 6.60 396.60
12 2 27 7.96 387.96
13 3 27 2.78 3 82. 78
14 4 26 9.67 379.67
15 5 26 7.80 377.80
16 6 26 6.68 376.68
17 7 26 6.01 376.01
18 8 26 5....
Basic Mathematics for Economists phần 1 ppt
... physical analogies for powers other than 2 and 3,
in mathematics one can encounter powers of any value.
Example 2. 30
12
4
= 12 × 12 × 12 × 12 = 20 ,736
12
5
= 12 × 12 × 12 × 12 × 12 = 24 8,8 32 etc.
To multiply ... correct
answer.
Test Yourself, Exercise 2. 2
1. 9 62 − 88 + 3 12 − 26 7 =
2. 24 0 − 20 × 3 ÷4 =
3. 300 × 82 ÷ 6 25 =
4. 360 ÷ 4 × 7 − 3 =
5. 6 × 12...
Basic Mathematics for Economists phần 3 pdf
... 0.2Q ^2
2
3 Q TR
4 0 0
5 20 1 520
6 40 28 80
7 60 4080
8 80 5 120
9 100 6000
10 120 6 720
11 140 728 0
12 160 7680
13 180 7 920
14 20 0 8000
15 22 0 7 920
16 24 0 7680
17 26 0 728 0
18 28 0 ... 6 720
19 300 6000
20 320 5 120
21 340 4080
22 360 28 80
23 380 1 520
24 400 0
25 420 -1680
© 1993, 20 03 Mike Rosser
A
Demand
B
0 q
£
9.99
2. 20
94 120 166 25 0...
Basic Mathematics for Economists phần 4 pdf
... 701.55
25 21 5755.05 785.05
26 22 6 628 .40 873.35
27 23 7594.85 966.45
28 24 8659 .20 1064.35
29 25 9 826 .25 1167.05
30 26 11100.80 127 4.55
31 27 124 87.65 1386.85
32 28 13991.60 1503.95
33 29 ... 38
20 8 -3 52 19 -693 30 -550 41 77
21 8.5 -378 19.5 -697 30.5 -5 32 41.5 117
22 9 -403 20 -700 31 -513 42 158
23 9.5 - 427 20 .5 -7 02 31.5 -493 42. 5 20 0
24 10 -...
Basic Mathematics for Economists phần 5 ppt
... 80. 927
9 2. 15% 81.155
10 2. 20% 81.384
11 2. 25% 81.613
12 2.30% 81.844
13 2. 35% 82. 075
14 2. 40% 82. 307
15 2. 45% 82. 540
16 2. 50% 82. 773
17 2. 55% 83.008
18 2. 60% 83 .24 3
19 2. 65% 83.479
20 ... series
9 ,20 0 +9 ,20 0(1. 12) +9 ,20 0(1. 12)
2
+···+9 ,20 0(1. 12)
11
In this example a = 9 ,20 0, k = 1. 12 and n = 12. Therefore, the sum is
GP
n
=
9 ,20 0(1...
Basic Mathematics for Economists phần 6 potx
... the output is 92 will be
TR − TC = (460q − 2q
2
) − (20 + 0.5q
2
)
= 460q − 2q
2
− 20 − 0.5q
2
= 460q − 2. 5q
2
− 20
= 460( 92) − 2. 5(8,464) 20
= 42, 320 − 21 ,160 20 = 21 ,140
© 1993, 20 03 Mike Rosser
3. ... costs
TVC = 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 −...
Basic Mathematics for Economists phần 7 potx
... 0.1q
2
Substituting q
1
+ q
2
= q gives
TR = 320 (q
1
+ q
2
) − 0.1(q
1
+ q
2
)
2
= 320 q
1
+ 320 q
2
− 0.1(q
2
1
+ 2q
1
q
2
+ q
2
2
)
= 320 q
1
+ 320 q
2
− 0.1q
2
1
− 0.2q
1
q
2
− 0.1q
2
2
Thus profit will ... 1.2q
1
+ 1.5q
2
+ 0.2q
1
q
2
)
= 600q
1
− 0.3q
2
1
+ 500q
2
− 0.2q
2
2
− 16 − 1.2q
1
− 1.5q
2
− 0.2q
1
q
2
=−16 + 598.8q
1
− 0.3q
2
1
+ 498.5q...
Basic Mathematics for Economists phần 8 docx
... K
1 ,20 0 20 (L)
0.5
L
0 .25
(3.2L)
0.4
= 0
1 ,20 0 20 (3 .2)
0.4
L
1.15
= 0
60 = 1.5 924 287L
1.15
37.67 829 6 = L
1.15
23 .47 = L
Substituting this value for L into (5) and (6) gives
K = 23 .47 R = 3 .2( 23.47) ... 0 .25 q)
0.5
(−0. 625 ) +(650 − 0. 625 q)(−0. 125 )(650 − 0 .25 q)
−0.5
=
(650 −0 .25 q)(−0. 625 ) + (650 − 0. 625 q)(−0. 125 )
(650 −0 .25 q)
0.5
(2)
Substituting the va...
Basic Mathematics for Economists phần 10 doc
... 24 x 2. x
2
+ 4x + 93.2x
2
+ 6x + xy + 3y
4. 42x
2
− 16y
2
− 34xy + 6y 5. 33x + 2y − 20 y
2
+ 62xy − 21
6. 120 +2x + 54y + 40z −x
2
+ 6y
2
+ xy + 4xz + 8yz
7. 20 0q − 2q
2
8. 13x + 11y 9. 8x
2
+ 60x ... 1993, 20 03 Mike Rosser
2. 9 1. 25 2. 2 3. 0 .2 4. 7 5. 2. 4494897
6. 96 7. 10
8. 5 .27 80316 9. 0.03 423 10. 87.977857
2. 10 1. 27 0,818.98 2. 22 0.9478 3....