Article Type : Research Article
Authors : Xu R
Keywords : Maximum profit; Quantity; Modelling; coefficient; Auto mobile; Stock share market; Economics
The tendency of Q and Pr with b1 in constant b is
searched in this study. The Q and Pr will increase when b and b1 with constant
b1 and b in auto mobile and stock share. The maximum Q and Pr in auto is 3.8
and 250,000 Yuan respectively. Meantime the maximum them is 2,000 and 17,000
Yuan in stock share market respectively. Because it is concave function it has
dPr2 (b&b1)/d (b&b1)2>0 for stock share.
The maximum profit and
quantity with coefficient in stock share market and auto mobile market is very
important on economics. So the modelling about them is built to analyse and
conclude is necessary currently. In this paper the detail modelling
establishment and analysing is completed at a certain scope. The modelling is
established according to them whilst the reasonable data is done for complete
and correct direction in order to decrease the erro and increase the
preciseness [1,2]. It is to simulate the actual situation for solving the
financial practice problem and corrective instruction and operation role and
operation. For the better making decision this program is proceeded too. For
the sake of the general manager decision the coefficients are regulated to meet
the theoretical method to instruct the correct decision such as financial
investment and management in financial division [3,4].
In short the parameters
like Pr and Q with b &b1 are better to serve for the practice operation.
The detail discussion are shown as below (Table 1).
Modelling Formula Establishment
According to the line
formula and parabolic one the coefficient b and b1 will be solved respectively.
Defining the other parameter data to calculate the them with different b and
b1. Then in terms of this parameter the maximum profit and quantity will be
solved. It is supposed that P is 210 Yuan in auto mobile and 30 Yuan in stock
share, TC is 90,000 Yuan and 30 Yuan in this modelling. Here Pr is profit Yuan;
Q is quantity; a, b and a1, b1, c1 is the coefficients respectively for the
line equation and parabolic one. P is the demand; TC is total cost Yuan.
Original data arrangement is needed in advance for coefficients. It can be seen
in Table 1.
For the sake of solving
share in the stock market the modelling of maximum profit and it’s quantity in
this study has been built as following two kinds of linear and parabolic
formula according to the economics principle.
To suppose the product demand function as
Here P is the demand, Q is quantity, TC is cost, a, b & a1, b1, and c1 is the constant.
(a) Auto/b=1151
(a) Auto/b1=82
(a) Stock share/ b1=10.3
(a) Stock share/ b=11.3
Figure 1: The graph of Q, Pr & b1, b with various function on economics.
(a) Auto
(a) Stock share
Figure 2:
The graph of Q, Pr & a with various function on economics.
The constant coefficient
b and b1 as 115 for auto, 11.3 for share and b1 and b as 82 for auto, 10.3 for
share in below Figure (a~d) respectively. The detail discussion is shown as
below (Figure 1).
In Figure 1(a~d) with function and various b & b1 the Pr and Q will change with b and b1. As seen in Figure 1(a) the Pr increases from 0 to 250,000Yuan with Q being from 0 to 3.8 when b=1151 when it becomes auto mobile so the average profit is 65,789 Yuan. In Figure 1(b) the Pr increases from 0 to 238,000 Yuan with the same conditions. The Q increases from 0 and 0.3 to 3.8 and 3.9 respectively in Figure 1 (a &b) so that the average profit is about 65,000Yuan. The maximum b and b1 both is 65,000. It means that the better profit is attained somewhat when b is larger than b1 (Figure 2).
Table 1: The coefficient used in this paer for auto mobile and stock share.
Parameter item |
a |
b |
a1 |
b1 |
c1 |
Auto mobile |
-8627 |
1151 |
-2972 |
82 |
0.033 |
Stock share |
-0.003 |
11.3 |
-0.003 |
10.3 |
0 |
In Figure 1(c~d) in stock
share market when b and b1 changes from 10.3 and 11.3 the Pr and Q changes with
parabolic and linear one. Pr changes in terms of parabolic and Q is linear one.
The maximum Pr is 14,000Yuan and Q is 2,500 with b being 19 under condition
b1=10.3 in Figure 1(c) so that the average profit is 5.6Yuan. In Figure 1 (d)
the Q is 2,000 and Pr is 17,000 with b= 21 under condition b=11.3, so the
average profit is 8.5 Yuan. It means that the better profit is attained when b
is larger than b1 too. Since in stock share the Pr and b&b1 has the
nonlinear curve with minimum value for concave function it has dPr2 (b&b1)/d
(b&b1)2>0. The left side has the dPr(b&b1)/d(b&b1)<0 since it
is decreasing function whilst the right side has the
dPr(b&b1)/d(b&b1)>0 since it is increasing function. In Figure
2(a,b) Q increases from 0~37 and Pr increases from 0~148,000Yuan with -600~0 of
a for auto mobile, meantime Q?Pr increases from 0 to more than 500 with 0~-0.1
of a for stock share. It means that when the car quantity is 37 the profit will
attain 148,000Yuan for manufacturer whilst the share profit is more than 500
Yuan at the more than 500 quantity which is approximation when a is -0.1. This
is another result in terms of the coefficient variation. It still needs to
further study to clarify the factor to affect it.
The Q and Pr will
increase when b and b1 increases with constant b1 and b in auto mobile and
stock share. The maximum Q and Pr in auto is 3.8 and 250,000Yuan respectively.
Meantime the maximum them is 2,000 and 17,000 Yuan in stock share market
respectively. Because it is concave function it has dPr2 (b&b1)/d(b&b1)2>0
in stock share market.
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