Article Type : Research Article
Authors : Xu R
Keywords : Maximum profit; Its quantity; Modelling; Economics; Modelling; TR(total revenue); TC(total cost); MR(marginal revenue); AR(average revenue) ; PR(profit) ; MC(marginal cost); High price
The trend to high price share is searched in this
paper. It is found that the TR increases when Q increases. TR changes from
3,000 Yuan to 40,000 Yuan when Q becomes from 100 to 1100. Meantime’s AR
decreases from 28 Yuan to 36 Yuan. The PR and TC will increase when the Q
increases. The PR changes from 2,000 Yuan to 32,000 Yuan and TC becomes from
1,000 Yuan to 7,000 Yuan when Q becomes from 100 to 1100. It is known that the
relationship of PR=TR-TC in the curves.
The economics modeling of
maximum and its quantity at high price has been established in order to
investigate their intrinsic relationship. Meantime it is important to estimate
the maximum of them in an enterprise manufacture and finance. In this study the
stock share is searched to try to find the intrinsic relationship. For the sake
of modelling the maximum profit and quantity in stock market the data is
arranged to solve the constant of linear and parabolic equation. Only we know
the price and quantity can the share be certain to do investment correctly. The
base data is important to determine the constant to model. It will be discussed
in detail because of its scientific method. It will give us convenience and
rapidness & correct result to help us to determine the investment. In short
the maximum profit and quantity on stock market is been built in this study. Only
if they are calculated can the further other relationship be drawn to discuss
further their relationship. The reasonable and scentific value can be solved
and other information can be gained for checking the right and more
information. The high price share has been investigated here to see the
difference to low price [1-5].
When the condition has
been given as 1000 share with cost 8.6 Yuan and price 30 Yuan the constant and
equation will be completed which is exhibited below. The quantity is 2,020 in
maximum profit and the maximum profit is 40,820 Yuan according to the modelling
equation. 100~1100 and 100~3600 is defined as below Figure 1-6 to discuss in
detail. The former is actual condition and the latter is the predicted. They
are fit well to modelling equation. The coefficient a and b & a, b, c has
been solved according to the modelling equation discussed as below. In this
study TR is total revenue; TC is total cost; MR is marginal revenue; AR is average revenue; PR is profit; MC is
marginal cost; Q is quantity (Figure 1-3).
The TR increases when Q increases. TR changes from 3,000 Yuan to 40,000 Yuan when Q becomes from 100 to 1100. Meantime AR decreases from 28 Yuan to 36 Yuan when Q becomes the same. At last MR maintains 32~42 Yuan. MC is the same value to MR. from Figure 1 it is known that PR and TC will increase when the Q increases. The PR changes from 2,000 Yuan to 32,000 Yuan when Q is from 100 to 1000 and TC becomes from 1,000 to 7,500 Yuan when Q becomes from 100 to 1100. Figure 3 shows that the TC decreases from 0 Yuan to 5,000 Yuan according to Q from 0 to 1750. Figure 4 shows when the Q scope is 100~3600 the TR will increase from 500 Yuan to 170,000 Yuan and AR will decrease. Figure 4 shows TC is parabolic which maximum is 170,000 Yuan with Q=3600 meantime the PR increase from 0 to 180,000 Yuan with Q from 0 to 3600. There is MR=MC in terms of Q the same (Figure 4-6).
Figure 1: The graph of Pr and TC & Q=100~1100.
Figure 2: The graph of TR, AR?MR and MC & Q=100~1100
Figure 3: The graph of PR and TC, Q=100~3600.
Figure 4: The graph of TR, MR, AR and MC & Q=100~3600.
Figure 5: The graph of TR, TC, PR, MR &AR and Q=100~1000.
Figure 6: The graph of TR, TC, PR, MR &AR and Q=100~3600.
The modelling of maximum
profit and it’s quantity in this study has been built as following. To suppose
the product demand function as
It has
To suppose the total cost
function as
It has
And
So
Here P is the demand, Q is quantity, TC is cost, a?b &a?b?c is the coefficient. The Figure 5 and 6 shows that the relationship between TR, TC, PR, MR & AR and Q with the part of 0~1000 and 0~3600. It is known that when Q=1750 the TC will be 5,000 Yuan which is the highest result here. The extension curve TC, TR & PR?will have summit at Q=3,500 with 170,000 Yuan &180,000 Yuan respectively It is known that the relationship of PR=TR-TC in the curves.
The quantity is 2020 in
maximum profit and the maximum profit is 40,820 Yuan. The PR changes from 2,000
Yuan to 8,000 Yuan when Q is from 100 to 1000. It is predicted that TC is
parabolic which maximum is 5,000 Yuan with Q=1750 meantime the PR increase from
0 to 180,000 Yuan with Q =0~3600.