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 20,000 to 30,000 and from
30,000 to 80,000 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. TP is the total product and
AP is the average product. MPK is capital marginal product and MPL is labor
marginal product in this study (Table 1) (Figure 1).

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

(b) K=3.75;
Pl&Pk=30,000 &80,000

(c) L=0.3;
Pl&Pk=30,000 &80,000

(d) K=4.99
; Pl & Pk=20,000&60,000

(e) L=0.35;
Pl & Pk=20,000&60,000

(f) K=10;
Pl & Pk=10,000&30,000

(g) L=0.7;
Pl & Pk=10,000&30,000
Figure 1:
The relationship between cost and number of shares according to different
conditions.

(a) L;
TC=100,000

(b) L;
TC=250,000
Figure 2:
The relationship between maximum and marginal production and number of capital
and labor.

(c) Pk=30000~80000
Yuan

(d) 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 0.3 and 0.35 to 0.7 the number of shares
are from 30 thousand and 50 thousand to 60 thousand respectively with the intersection
of 1 RMB in Figure 1(c, e & g) with K parameter which is turnover point
from Figure 1 (a ~ d) according to the Pl and Pk from 20,000 to 80,000. It
explains that labour with 0.3 is the minimum cost which is 30 thousand. When
the best capital is 3.75RMB the turnover point is 50 thousand of the number of
shares with the 5 RMB in Figure 1. 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
3.75 for example 4.99 and 10. The intersection with 1RMB is more than 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. It is expected that the revenue has been
increased so that the share decreases to normal level. Meantime the labor is
somewhat higher according to the Cobb-Douglas function than capital. In Figure
1(b & d) the normal share value exhibits the normal one will be formed in
this study. The same value is from 50 to 350 thousand with 5 RMB and 1RMB
respectively at Pl =30,000 and Pk=80,000. Therefore, because the intersection
with 1RMB is higher than 100 thousand shares and promoting revenue is necessary
for the sake of sale. To say more if labor increases share will increase. The
share will increase from 50 to 60 thousand when the capital is from 3.75 and
4.99 to 210 respectively.
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
|