Basic Mathematics for Economists - Rosser - Chapter 8 doc
Basic Mathematics for Economists - Rosser - Chapter 8 doc
... 10 288 00 1600 160
8 81 1 273 78 1 78 1 78
9 80 .1 0.1 27217. 98 17. 98 179 .8
10 80 .01 0.01 27201.79 98 1.79 98 179. 98
11 80 .001 0.001 27200. 18 0.1799 98 179.9 98
12 80 .0001 0.0001 27200.0 18 0.017999 98 179.99 98
13 ... 4x
2−1
= 8x
When x = 8, then slope = 8( 8) = 64.
© 1993, 2003 Mike Rosser
0
0
D
MR
TR
80 0
80
q
4020
£
q
p
Figure 8. 3
We know that by defi...
Basic Mathematics for Economists - Rosser - Chapter 15 doc
... 2
23
710
= 8[ 5(−16) − 2(−40) + 4( 18) ]+2[10(−40) −5(−12) + 4(−1)]
− 3[10( 18) − 5(5) + 2(−1)]
= 8[ 80 + 80 + 72]+2[−400 + 60 − 4]−3[ 180 − 25 − 2]
= 8( 72) + 2(−344) − 3(153)
= 576 − 688 − 459
=−571
© ... =
23
81
and B =
752
481
Solution
Using the method explained above, the product matrix will be
AB =
23
81
752
481
=
2 ×7 + 3 × 42× 5 +3 82 × 2...
Basic Mathematics for Economists - Rosser - Chapter 1 pptx
... order you perform the
calculations and the type of calculator you use.
There are set rules for the order in which basic arithmetic operations should be performed,
whichareexplainedinChapter2.Nowadays,theseareprogrammedintomostcalculators
but ... quantification
of economic predictions requires the use of mathematics.
Although non-mathematical economic analysis may sometimes be useful for...
Basic Mathematics for Economists - Rosser - Chapter 2 potx
... 2.54
If 460(1. 08)
n
= 925, what is n?
Solution
460(1. 08)
n
= 925
(1. 08)
n
= 2.01 086 96
Putting in log form
n log 1. 08 = log 2.01 086 96
n =
log 2.01 086 96
log 1. 08
=
0.303 383 9
0.03342 38
= 9.07 689 45
WeshallreturntothistypeofprobleminChapter7whenweconsiderforhowlonga
sum ... Mike Rosser
Solution
68 − 18 = 50 using brackets
or
92 − 24 − 20 + 2 = 50 removing brackets
Test Y...
Basic Mathematics for Economists - Rosser - Chapter 3 pps
... 123456 789 101112
Height (cm) 1 78 175 170 166 1 68 185 169 189 175 181 177 180
Weight (kg) 72 68 58 52 55 82 55 86 70 71 65 68
© 1993, 2003 Mike Rosser
Example 3. 18
Simplify (6 − 5x)(10 − 2x + 3y).
Solution
Multiplying ... expression for net weekly wage in terms of H and then
simplify it.
Solution
gross wage = 40 × 8 + (H − 40)12
= 320 + 12H − 480
= 12H − 160
net wage = 0.75...
Basic Mathematics for Economists - Rosser - Chapter 4 potx
... 18
when x = 6 then y = 54 −36 = 18
This is because the function y = 9x − x
2
is not monotonic. This can be established by
calculating y for a few selected values of x:
x 1234567
y 81 4 182 020 181 4
These ... so
TR = PQ
If we substitute the demand function P = 80 − 0.2Q for P in this TR function then
TR = (80 − 0.2Q)Q = 80 Q − 0.2Q
2
© 1993, 2003 Mike Rosser
This means that the val...
Basic Mathematics for Economists - Rosser - Chapter 5 ppsx
... equilibrium value of Y for any given level
of I. For example
whenI=200thenY =80 +2(200) =80 +400= 480 (checkwithExample5.7)
when I = 300 then Y = 80 + 2(300) = 80 + 600 = 680
From the reduced form equation ... = 1 48 (3)
3. Solve for A, B and C when
32A + 14B + 82 C = 664 (1)
11.5A + 8B + 52C = 349 (2)
18A + 26.2B − 62C = 560.4 (3)
4. Find the values of x,y and z when
4.5x + 7y + 3...
Basic Mathematics for Economists - Rosser - Chapter 6 pps
... 27 -6 37 38 -1 42
15 5.5 -2 07 16.5 -6 58 27.5 -6 25 38. 5 -1 08
16 6 -2 38 17 -6 67 28 -6 12 39 -7 3
17 6.5 -2 68 17.5 -6 75 28. 5 -5 98 39.5 -3 7
18 7 -2 97 18 -6 82 29 -5 83 40 0
19 7.5 -3 25 18. 5 -6 88 29.5 ... 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...
Basic Mathematics for Economists - Rosser - Chapter 7 pps
... 0 .81 62 98 0.79 383 2 0.772 183 0 .88 8996 0 .86 383 8 0 .83 9619 0 .81 62 98 0.79 383 2 0.772 183
4 0 .85 480 4 0 .82 2702 0.792094 0.76 289 5 0.73503 0.7 084 25 0 .85 480 4 0 .82 2702 0.792094 0.76 289 5 0.73503 0.7 084 25
5 0 .82 1927 ... 0.9615 38 0.952 381 0.943396 0.934579 0.925926 0.917431
2 0.924556 0.907029 0 .88 9996 0 .87 3439 0 .85 7339 0 .84 1 68 0.924556 0.907029 0 .88 999...
Basic Mathematics for Economists - Rosser - Chapter 9 pptx
... is
Q
q
=
200,000
q
As each order made costs 80 and each unit stored for a year costs 8 then
TC = order +stock-holding costs
=
200,000 (80 )
q
+
8q
2
= 16,000,000q
−1
+ 4q
For a stationary point
dTC
dq
=−16,000,000q
−2
+ ... Therefore, second-order condition for a maximum is satisfied and TR is a maximum when
q is 18. (Note that in this example the second-order derivative −1.2q<0 for...