The
Investment and shares have been established according to modelling with
economic equations that has a certain role in stock market. So Cobb-Douglas
function is used to complete the modelling. The detail establishment and
modelling is as related literature.
The
Cobb-Douglas function is
(1)
Here Production
quantity Q; ? is technique coefficient; ? is producing labour; ? is capital
elasticity. K is capital; L is labour; AFC is average fixed cost; AVC is
average variable cost; AR is the average revenue; TR is total revenue. The
calculated constant is ?=106086; ?=1.25; ?=-0.2 respectively. The parameter Pl
is labor price and Pk is capital price. They are from 200 to 300 and from 300
to 800 Yuan respectively. Turnover is in terms of 5Yuan per share and Q is
piece of shares. Table 1 shows the parameter of constant value with labor and
capital & quantity. It is chosen that 10groups value to acquire average
ones. The detail narration is expressed as below (Table 1) (Figure 1).

(a) K=375;
Pl & Pk=300&800

(a) L=29;
Pl & Pk=300 &800

(a) K=375;
Pl & Pk=200&800

(a) L=19.76;
Pl & Pk=200&800
Figure
1: The relationship between cost and number
of shares according to different conditions.

(a) K

(a) L
Figure 2:
The relationship between maximum &marginal production and number of capital
and labor.

(a) Pk=800~2800
Yuan

(a) Pk=750~1500
Yuan
Figure 3:
The minimum cost with labor quantity and 100,000 pieces under different Pk.
It
is found when the best labour is from 19 to 29 the number of shares are 250
thousand with the intersection of 1 RMB in Figure 1(a) with K=375 which is
turnover point from Figure 1(a~d) according to the Pl and Pk from 200 to 800.
When the best capital is 375RMB the turnover point is 63 thousand of the number
of shares with the 5 RMB in Figure 1(a). So the balance value is 5RMB which
could be satisfactory with both situations because the average revenue 1RMB
can’t be intersected with average cost line in the case of the one higher than
labor of 19 for example 29. The intersection with 1RMB is 250 and 300 thousand
in the above two cases. It excesses big the 100,000 so the 1RMB is insufficient
which needs to be promoted. The bigger one which accounts for the turn with
more than 5RMB is available.
Table
1: The conditions of original parameters and
coefficient.
|
Parameters
No.
|
l
|
K
|
Q
|
?
|
?
|
?
|
|
1
|
0.1
|
0.1
|
10?000
|
-
|
-
|
-
|
|
2
|
0.2
|
0.2
|
20?000
|
-
|
-
|
-
|
|
3
|
0.3
|
0.3
|
30?000
|
1.69
|
-0.41
|
141391
|
|
4
|
0.4
|
0.4
|
40?000
|
1.41
|
-0.29
|
111396
|
|
5
|
0.5
|
0.5
|
50?000
|
1.29
|
-0.22
|
104575
|
|
6
|
0.6
|
0.6
|
60?000
|
1.22
|
-0.18
|
102107
|
|
7
|
0.7
|
0.7
|
70?000
|
1.18
|
-0.15
|
101010
|
|
8
|
0.8
|
0.8
|
80?000
|
1.15
|
-0.13
|
100461
|
|
9
|
0.9
|
0.9
|
90?000
|
1.13
|
-0.12
|
100166
|
|
10
|
1
|
1
|
100?000
|
1.12
|
-0.11
|
100000
|
|
11
|
1.1
|
1.1
|
110,000
|
1.11
|
-0.10
|
99904
|
|
12
|
1.2
|
1.2
|
120,000
|
1.10
|
-0.09
|
99849
|
|
Average
|
-
|
-
|
-
|
1.24
|
-0.18
|
106086
|