Basic Mathematics for Economists - Rosser - Chapter 3 pps
Basic Mathematics for Economists - Rosser - Chapter 3 pps
... expression.
Example 3. 16
Simplify (3x + 4y)(5x − 2y).
© 19 93, 20 03 Mike Rosser
Example 3. 11
x(4 + x) = 4x + x
2
Example 3. 12
5(7x
2
− x) 3( 3x
2
+ 6x) = 35 x
2
− 5x − 9x
2
− 18x
= 26x
2
− 23x
Example 3. 13
6y(8 ... Rosser
8.Yousell900sharesviayourbrokerwhochargesaflatrateofcommissionof£20
onalltransactionsoflessthan£1,000.Yourbankaccountiscreditedwith 34 0
fromthesharesale.What...
Basic Mathematics for Economists - Rosser - Chapter 5 ppsx
... 28.5.
Example 5.11
Solve for x, y and z in the following set of simultaneous equations:
14.5x + 3y + 45z = 34 0 (1)
25x − 6y − 32 z = 82 (2)
9x + 2y − 3z = 16 (3)
© 19 93, 20 03 Mike Rosser
The price to ... 80 = 32 0 − 80 = 240
q
3
= MC
3
− 40 = 160 − 40 = 120
q
4
= 2MC
4
− 120 = 32 0 − 120 = 200
These total to 700, which checks out with the answer for q above.
© 19 93, 20 03...
Basic Mathematics for Economists - Rosser - Chapter 6 pps
... 11 -4 93 22 -7 02 33 -4 27
5 0.5 158 11.5 -5 13 22.5 -7 00 33 .5 -4 03
6 1 117 12 -5 32 23 -6 97 34 -3 78
7 1.5 77 12.5 -5 50 23. 5 -6 93 34.5 -3 52
8 2 38 13 -5 67 24 -6 88 35 -3 25
9 2.5 0 13. 5 -5 83 24.5 ... 24.5 -6 82 35 .5 -2 97
10 3 -3 7 14 -5 98 25 -6 75 36 -2 68
11 3. 5 -7 3 14.5 -6 12 25.5...
Basic Mathematics for Economists - Rosser - Chapter 7 pps
... 0.917 431 0.961 538 0.95 238 1 0.9 433 96 0. 934 579 0.925926 0.917 431
2 0.924556 0.907029 0.889996 0.8 734 39 0.85 733 9 0.84168 0.924556 0.907029 0.889996 0.8 734 39 0.85 733 9 0.84168
3 0.888996 0.8 638 38 0. 839 619 ... 0.4750 93 0.4288 83 0 .38 7 533 0.649581 0.584679 0.526788 0.4750 93 0.4288 83 0 .38 7 533
12 0.624597 0.556 837 0.496969 0.444012 0 .39 7114 0 .35 5 535 0.624597...
Basic Mathematics for Economists - Rosser - Chapter 11 pps
... 18
C
2
= 32 4
© 19 93, 20 03 Mike Rosser
Differentiating to get first-order conditions for a minimum
∂G
∂K
= 80 − λ18K
−0.6
L
0 .3
R
0 .3
= 0 λ =
80K
0.6
18L
0 .3
R
0 .3
(1)
∂G
∂L
= 35 − λ 13. 5K
0.4
L
−0.7
R
0 .3
= ... λ 13. 5K
0.4
L
−0.7
R
0 .3
= 0 λ =
35 L
0.7
13. 5K
0.4
R
0 .3
(2)
∂G
∂R
= 50 − λ 13. 5K
0.4
L
0 .3
R
−0.7
= 0 λ =
50R
0.7
13. 5K
0.4
L
0 .3
(3)
∂G
∂λ
= 75,0...
Basic Mathematics for Economists - Rosser - Chapter 12 ppsx
... 540q −0.2q
3
TC =
MC dq +TFC =
(180 + 0.3q
2
)dq + 65 = 180q + 0.1q
3
+ 65
π = TR − TC
= 540q − 0.2q
3
− (180q + 0.1q
3
+ 65)
= 540q − 0.2q
3
− 180q − 0.1q
3
− 65
= 36 0q − 0.3q
3
− 65
Thus ... 0
Therefore, the second-order condition for a maximum is satisfied when t = 66.67. Maximum
tax revenue is raised when the per-unit tax is £66.67.
© 19 93, 20 03 Mike Rosser
y
=
2...
Basic Mathematics for Economists - Rosser - Chapter 14 pps
... then
y
0
= 34 = Ae
0
Therefore
34 = A
The definite solution is thus
y
t
= 34 e
1.5t
When t = 7 then using this definite solution we can predict
y
7
= 34 e
1.5(7)
= 34 e
10.5
= 34 (36 ,31 5.5) = 1, 234 , 727
© ... y
t
for any value of t. For example, when
t = 3, then
y
3
= 12e
5 (3)
= 12e
15
= 12 (3, 269,017.4) = 39 ,228,208
Example 14.14
Solve the differential equation dy/dt = 1....
Basic Mathematics for Economists - Rosser - Chapter 1 pptx
... divided by 3 is 3. 333 333 3
recurring, it is difficult for basic calculators to store this number accurately in decimal form.
Although modern computers have a vast memory they still perform many ... on from each other, each chapter assumes that students are
familiar with material covered in previous chapters. It is therefore very important that you
© 19 93, 20 03 Mike Rosser
Algeb...
Basic Mathematics for Economists - Rosser - Chapter 2 potx
... number of times that one is dividing by the given number.
Example 2 .34
3
6
× 3
−4
=
3
6
3
4
=
3 × 3 × 3 × 3 × 3 3
3 × 3 × 3 × 3
= 3
2
Thus multiplying by a number with a negative power (when both ... powers of the same number one adds all the
powers together.
Example 2 .31
3
3
× 3
5
= (3 × 3 × 3) × (3 × 3 × 3 3 × 3) = 3
8
= 6,561
To divide numbers...
Basic Mathematics for Economists - Rosser - Chapter 4 potx
... 10, or 10%.
© 19 93, 20 03 Mike Rosser
0 –x
–y
y
=
x
3
y
=
x
3
y
=
x
2
y
=
x
2
x
y
Figure 4.14
Table 4 .3
x 01 234 56789
y = x
0.5
0 1 1.414 1. 732 2 2. 236 2.449 2.646 2.828 3
0
y
3
1
2
y
=
x
0.5
14 ... follows:
MR
1
= 12 − 0.3Q
1
MR
2
= 9 −0.15Q
2
0.3Q
1
= 12 − MR
1
0.15Q
2
= 9 −MR
2
Q
1
= 40 − 3
1
3
MR
1
(1)Q
2
= 60 − 6
2
3
MR
2
(2)
© 19 93, 20 03 Mike Rosser
0
K
Q
1
Q...
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