Basic Mathematics for Economists phần 10 doc
Basic Mathematics for Economists phần 10 doc
... − 10. 1q
1
− 10q
2
− 10q
3
= 0 (1)
π
2
= 837 − 10q
1
− 10. 06q
2
− 10q
3
= 0(2)
π
2
= 835 − 10q
1
− 10q
2
− 10. 04q
3
= 0 (3)
These conditions can be rearranged to get
839 = 10. 1q
1
+ 10q
2
+ 10q
3
837 ... =
π
11
π
12
π
13
π
21
π
22
π
23
π
31
π
32
π
33
=
10. 1 10 10
10 10. 06 10
10 10 10. 04
© 1993, 2003 Mike Rosser
which will be
C =
(0 − 10) −(8 − 25)(8 − 0)...
Basic Mathematics for Economists phần 8 docx
... as
p = (120 − 20)
0.5
= 100
0.5
= 10
Thus, substituting these results into formula (1), point elasticity will be
e = (−1)
10
10
(−1)(120 −2q)
0.5
= (120 − 20)
0.5
= 100
0.5
= 10
Sometimes it may ... 15.38 1.13
14 4 103 .75 14.81 -0.56
15 5 98.125 15.09 0.28
16 6 100 .9375 14.95 -0.14
17 7 99.53125 15.02 0.07
18 8 100 .23438 14.99 -0.04
19 9 99.882813 15.01 0.02
20 10 100...
Basic Mathematics for Economists - Rosser - Answers docx
... 2. 106 9 3. 10
© 1993, 2003 Mike Rosser
2.9 1. ±25 2. 2 3. 0.2 4. 7 5. 2.4494897
6. 96 7. 10
8. 5.2780316 9. 0.03423 10. 87.977857
2 .10 1. 270,818.98 2. 220.9478 3. 2.8563 × 10
9
4. 1.5728 × 10
8
5. ... for Q ≥ 500
2. MR = 76 − 0.222Q for Q ≥ 22.5
3. MR = 80 − 0.555Q for Q ≥ 562.5
4. MC = 30 +0.0714Q for Q ≥ 56
5. MC = 56 +0.1333Q for Q ≥ 30
6. MC = 3 +0.0714Q for Q ≥...
Basic Mathematics for Economists phần 1 ppt
... ‘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 ... way of expressing fractions.
0.1 = 1 /10
0.01 = 1 /100
0.001 = 1/1,000 etc.
Thus 0.234 is equivalent to 234/1,000.
© 1993, 2003 Mike Rosser
Basic Mathematics for
Economists
S...
Basic Mathematics for Economists phần 2 ppsx
... 4.12)
becomes
−
P
X
P
Y
=−
20
10
=−2
(iii) The price ratio remains unchanged if income then falls to 100 . There is a parallel shift
inwards of the budget constraint to EF. The new intercepts are
M
P
Y
=
100
10
= 10 on ... Adjusted for inflation, the real price increase for food is thus
100
1.225
1.115
− 1
= 100 (1.099 −1) = 9.9%
Test Yourself, Exercise 3.8
1.RefertoTable3.1a...
Basic Mathematics for Economists phần 3 pdf
... Rosser
Giventhatthetheoryofpricediscriminationassumesthatafirmwilladjusttheamountsold
ineachmarketuntilMR
1
=MR
2
=MR,then
Q=Q
1
+Q
2
=
40−3
1
3
MR
+
60−6
2
3
MR
bysubstituting(1)and(2)
=100 −10MR
10MR =100 −Q
MR =10 0.1Q
ThissummedMRfunctionwillapplyaboveanaggregateoutputof10.
Fromtheaboveexampleitcanbeseenthatthebasicprocedureforsummingfunctions
horizontallyisasfollows:
1.transformt...
Basic Mathematics for Economists phần 4 pdf
... X will be 50 g for each container of A plus 20 g for each container of B. Total
usage must be at least 100 g. This quality constraint for X can thus be written as
50A + 20B ≥ 100
Note that the ... involved then the formula can be adapted along the same
lines.
Example 7.8
What will £20,000 invested for 10 years be worth if the expected rate of interest is 12% for
the first 3 year...
Basic Mathematics for Economists phần 5 ppt
... of 100 million gallons per day will equal demand when
100 = 25(1 +r)
100
4 = (1 + r)
100
100
√
4 = 1 + r
1.0139595 = 1 + r
0.0139595 = r
Therefore current water supplies will be sufficient for ... unit)
Over the remaining 10 weeks the total sales will therefore be
396(0.9) + 396(0.9)
2
+···+396(0.9)
10
In this geometric series a = 396(0.9), k = 0.9 and n = 10. Its sum will theref...
Basic Mathematics for Economists phần 6 potx
... −10q + 3q
2
= 0 (1)
However, if we try using the quadratic equation formula to find a value of q for which (1)
holds we see that
q =
−b ±
√
b
2
− 4ac
2a
=
−( 10) ±
√
10
2
− 4 × 18 ×3
2 ×3
=
10 ... 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 − 1...
Basic Mathematics for Economists phần 7 potx
... as
MU
A
P
A
=
MU
B
P
B
Therefore, substituting the above MU functions and the given prices of £4 and 10, this
condition becomes
10A
−0.75
B
0.5
4
=
20A
0.25
B
−0.5
10
100B = 80A
B = 0.8A (1)
Substituting (1) for B ... actual values are y = 2 (10) = 20 when x = 10
y = 2(11) = 22 when x = 11
Thus actual change is 22 −20 = 2 (accuracy of prediction 100 %)
(ii) y = 2x
2
dy
dx
= 4x = 4 (10)...
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