Basic Mathematics for Economists - Rosser - Chapter 12 ppsx
Basic Mathematics for Economists - Rosser - Chapter 12 ppsx
... giving
d
2
TR
dq
2
=
0 + (−975)(−0 .125 )
0
→+∞
Therefore this second value for q obviously does not satisfy second-order conditions for
a maximum.
Example 12. 9
AtwhatlevelofKisthefunctionQ=12K
0.4
(160−8K)
0.4
atamaximum?(Thisis
Example11.1(reworked)whichwasnotcompletedinthelastchapter.)
© ... rule. Assume, for example, that you wish to find an
expression for the slope of the non-li...
Basic Mathematics for Economists - Rosser - Chapter 5 ppsx
... 28.5
These values for y and z can now be substituted into any of the original equations. Thus using
(1) we get
x + 12( 2) + 3(28.5) = 120
x + 24 + 85.5 = 120
x = 120 −109.5
x = 10.5
Therefore, the solutions ... 240
q
3
= MC
3
− 40 = 160 − 40 = 120
q
4
= 2MC
4
− 120 = 320 − 120 = 200
These total to 700, which checks out with the answer for q above.
© 1993, 2003 Mike Rosser
Ther...
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
... 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 = 248,832 etc.
To multiply numbers which are expressed as powers ... denominator. For example, to convert 1/6 to a fraction with 12
as its denominator, one simply multiplies top and bottom by 2. Thus
1
6
=
2 × 1
2 × 6
=
2
12
Exampl...
Basic Mathematics for Economists - Rosser - Chapter 3 pps
... Rosser
8.Yousell900sharesviayourbrokerwhochargesaflatrateofcommissionof£20
onalltransactionsoflessthan£1,000.Yourbankaccountiscreditedwith£340
fromthesharesale.Whatpricewereyoursharessoldat?
9.Yournetmonthlysalaryis£1,950.YouknowthatNationalInsuranceandpension
contributionstake15%ofyourgrosssalaryandthatincometaxisleviedatarate
of25%ongrossannualearningsabovea£5,400exemptionlimit.Whatisyour...
Basic Mathematics for Economists - Rosser - Chapter 4 potx
... Rosser
TestYourself,Exercise4.10
Fortheproductionfunctionsbelow,assumefractionsofaunitofKandLcanbe
used,and
(a)deriveafunctionfortheisoquantrepresentingthespecifiedoutputlevelinthe
formK=f(L)
(b)findthelevelofKrequiredtoachievethegivenoutputlevelifL=100,and
(c)saywhattypeofreturnstoscalearepresent.
1.Q=9K
0.5
L
0.5
,Q=36
2.Q=0.3K
0.4
L
0.6
,Q=24
3.Q=25K
0.6
L
0.6
,Q=800
4.Q=42K
0.6
L
0.75
,Q=...
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...
Basic Mathematics for Economists - Rosser - Chapter 7 pps
... 25000 9% 121 52.86
10 6 120 00 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 ... is
k =
1
1 + i
© 1993, 2003 Mike Rosser
Example 7.4 (reworked)
£5,000 invested for 2 years at 12% means that
A = £5,000 n = 2 i = 12% = 0 .12
F = A(1 + i)
n
= 5,...
Basic Mathematics for Economists - Rosser - Chapter 8 doc
... Therefore,
3q
2
− 42q + 160 = 184 −8q
3q
2
− 34q − 24 = 0
(q − 12) (3q + 2) = 0
q − 12 = 0or3q + 2 = 0
q = 12 or q =−
2
3
One cannot produce a negative quantity and so the firm must produce 12 units ... Mike Rosser
Thus, substituting this result into (1) above, the formula for point elasticity of demand
becomes
e = (−1)
p
q
1
dp/dq
Example 8.25
What is point elasticity when price is...
Basic Mathematics for Economists - Rosser - Chapter 9 pptx
... 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 is met ... inflexion
(asinFigure9.2(b))whenitsslopeiszerowehavetoconsiderwhatareknownasthesecond-
order conditions. (The first-order condition for any of the three forms of stationary point is
that the s...