Basic Mathematics for Economists - Rosser - Chapter 10 potx
Basic Mathematics for Economists - Rosser - Chapter 10 potx
... rationale for all the second-order conditions is not quite so
straightforward. We shall therefore just state these second-order conditions here and give a
brief intuitive explanation for the two-variable ... case before looking at some applications. The
second-order conditions for the optimization of multi-variable functions with more than two
variablesareexplainedinChapter15usingmatrix...
Basic Mathematics for Economists - Rosser - Chapter 2 potx
... ‘log’.
Thus the logarithm of 100 is 2 since 100 = 10
2
. This is written as log 100 = 2. Similarly
log 10 = 1
and
log 1,000 = 3
The square root of 10 is 3.1622777 = 10
0.5
and so we know that log ... 925
(1.08)
n
= 2. 0108 696
Putting in log form
n log 1.08 = log 2. 0108 696
n =
log 2. 0108 696
log 1.08
=
0.3033839
0.0334238
= 9.0768945
WeshallreturntothistypeofprobleminChapter7whe...
Basic Mathematics for Economists - Rosser - Chapter 4 potx
... in a format
such as ‘1 in 10 , meaning that the road rose vertically by 1 foot for every 10 feet travelled
in a horizontal direction. Now the European format is used and so instead of ‘1 in 10 ... Mike Rosser
TestYourself,Exercise4 .10
Fortheproductionfunctionsbelow,assumefractionsofaunitofKandLcanbe
used,and
(a)deriveafunctionfortheisoquantrepresentingthespecifiedoutputlevelinthe
for...
Basic Mathematics for Economists - Rosser - Chapter 1 pptx
... that 10 divided by 3 is 3.3333333
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 ... 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,
whichareexplainedinChap...
Basic Mathematics for Economists - Rosser - Chapter 3 pps
... the expression using basic arithmetic.
For example, if the area is 100 square metres, then we just substitute 100 for A and so
length of fencing = 4
√
A = 4
√
(100 ) = 4 × 10 = 40 metres
One of ... park to accom-
modate x cars must have a length (in metres) of 4x +10 and a width of 2x +10. If
24 square metres will be specifically allocated for visitors’ cars, write an expres-
sio...
Basic Mathematics for Economists - Rosser - Chapter 5 ppsx
... operations to solve for x and y.
10x + 3y = 250 (1)
5x + y = 100 (2)
Solution
Multiplying (2) by 3 15x + 3y = 300
Subtracting (1) 10x + 3y = 250
Gives 5x = 50
x = 10
© 1993, 2003 Mike Rosser
Note that ... input requirements are
10 units of K plus 30 units of L for each unit of A
25 units of K plus 15 units of L for each unit of B
If the per-unit profit is £80 for A and £30 for...
Basic Mathematics for Economists - Rosser - Chapter 6 pps
... 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 -6 67 36.5 -2 38
12 4 -1 08 15 -6 25 26 -6 58 37 -2 07
13 4.5 -1 42 15.5 -6 37 26.5 -6 48 37.5 -1 75
14 5 -1 75 16 -6 48 ... -6 48 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 6...
Basic Mathematics for Economists - Rosser - Chapter 7 pps
... 12152.86
10 6 12000 10% 9563.64
11 11% 7090.04
12 IRR = 14.14% 12% 4725.54
13 13% 2464.06
14 14% 299.94
15 15% -1 772.14
16 16% -3 757.14
17 17% -5 659.71
18 18% -7 484.20
19 19% -9 234.68
20 20% -1 0914.99
Example ... Interest rate= 15%
2
3 YEAR RETURN PV
4 0 -2 5000 -2 5000
5 1 5000 4347.83
6 2 6000 4536.86
7 3 100 00 6575.16
8 4 100 00 5717.53
9 5 100 0...
Basic Mathematics for Economists - Rosser - Chapter 8 doc
... expression for the slope of the function y = 52x
3
.
5. Make up your own single-term function and then differentiate it.
8.2 Rules for differentiation
The rule for differentiation can be formally ... for the demand function q = 400 − 0.1p.
Solution
Given q = 400 − 0.1p
10q = 4,000 −p
p = 4,000 − 10q
Using this inverse demand function we can now derive
TR = pq = (4,000 − 10q)q = 4,000q...
Basic Mathematics for Economists - Rosser - Chapter 9 pptx
... between 0% and 100 %. Therefore c will
take a value between 0 and 1 and so the second-order condition for a maximum will be met.
© 1993, 2003 Mike Rosser
The second-order condition for a minimum ... inflexion
(asinFigure9.2(b))whenitsslopeiszerowehavetoconsiderwhatareknownasthesecond-
order conditions. (The first-order condition for any of the three forms of stationary point is
that th...
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